Daily Papers

Feed-forward 3D Gaussian Splatting (3DGS) models have recently emerged as a promising solution for novel view synthesis, enabling one-pass inference without the need for per-scene 3DGS optimization. However, their scalability is fundamentally constrained by the limited capacity of their encoders, leading to degraded performance or excessive memory consumption as the number of input views increases. In this work, we analyze feed-forward 3DGS frameworks through the lens of the Information Bottleneck principle and introduce ZPressor, a lightweight architecture-agnostic module that enables efficient compression of multi-view inputs into a compact latent state Z that retains essential scene information while discarding redundancy. Concretely, ZPressor enables existing feed-forward 3DGS models to scale to over 100 input views at 480P resolution on an 80GB GPU, by partitioning the views into anchor and support sets and using cross attention to compress the information from the support views into anchor views, forming the compressed latent state Z. We show that integrating ZPressor into several state-of-the-art feed-forward 3DGS models consistently improves performance under moderate input views and enhances robustness under dense view settings on two large-scale benchmarks DL3DV-10K and RealEstate10K. The video results, code and trained models are available on our project page: https://lhmd.top/zpressor.

Recently, the Segment Anything Model (SAM) gains lots of attention rapidly due to its impressive segmentation performance on images. Regarding its strong ability on image segmentation and high interactivity with different prompts, we found that it performs poorly on consistent segmentation in videos. Therefore, in this report, we propose Track Anything Model (TAM), which achieves high-performance interactive tracking and segmentation in videos. To be detailed, given a video sequence, only with very little human participation, i.e., several clicks, people can track anything they are interested in, and get satisfactory results in one-pass inference. Without additional training, such an interactive design performs impressively on video object tracking and segmentation. All resources are available on https://github.com/gaomingqi/Track-Anything. We hope this work can facilitate related research.

Despite the recent advancements in Large Language Models (LLMs), which have significantly enhanced the generative capabilities for various NLP tasks, LLMs still face limitations in directly handling retrieval tasks. However, many practical applications demand the seamless integration of both retrieval and generation. This paper introduces a novel and efficient One-pass Generation and retrieval framework (OneGen), designed to improve LLMs' performance on tasks that require both generation and retrieval. The proposed framework bridges the traditionally separate training approaches for generation and retrieval by incorporating retrieval tokens generated autoregressively. This enables a single LLM to handle both tasks simultaneously in a unified forward pass. We conduct experiments on two distinct types of composite tasks, RAG and Entity Linking, to validate the pluggability, effectiveness, and efficiency of OneGen in training and inference. Furthermore, our results show that integrating generation and retrieval within the same context preserves the generative capabilities of LLMs while improving retrieval performance. To the best of our knowledge, OneGen is the first to enable LLMs to conduct vector retrieval during the generation.

The subject of green AI has been gaining attention within the deep learning community given the recent trend of ever larger and more complex neural network models. Existing solutions for reducing the computational load of training at inference time usually involve pruning the network parameters. Pruning schemes often create extra overhead either by iterative training and fine-tuning for static pruning or repeated computation of a dynamic pruning graph. We propose a new parameter pruning strategy for learning a lighter-weight sub-network that minimizes the energy cost while maintaining comparable performance to the fully parameterised network on given downstream tasks. Our proposed pruning scheme is green-oriented, as it only requires a one-off training to discover the optimal static sub-networks by dynamic pruning methods. The pruning scheme consists of a binary gating module and a novel loss function to uncover sub-networks with user-defined sparsity. Our method enables pruning and training simultaneously, which saves energy in both the training and inference phases and avoids extra computational overhead from gating modules at inference time. Our results on CIFAR-10 and CIFAR-100 suggest that our scheme can remove 50% of connections in deep networks with less than 1% reduction in classification accuracy. Compared to other related pruning methods, our method demonstrates a lower drop in accuracy for equivalent reductions in computational cost.

Recently, the open-vocabulary semantic segmentation problem has attracted increasing attention and the best performing methods are based on two-stream networks: one stream for proposal mask generation and the other for segment classification using a pretrained visual-language model. However, existing two-stream methods require passing a great number of (up to a hundred) image crops into the visual-language model, which is highly inefficient. To address the problem, we propose a network that only needs a single pass through the visual-language model for each input image. Specifically, we first propose a novel network adaptation approach, termed patch severance, to restrict the harmful interference between the patch embeddings in the pre-trained visual encoder. We then propose classification anchor learning to encourage the network to spatially focus on more discriminative features for classification. Extensive experiments demonstrate that the proposed method achieves outstanding performance, surpassing state-of-the-art methods while being 4 to 7 times faster at inference. Code: https://github.com/CongHan0808/DeOP.git

Text-to-Image (T2I) diffusion models have made remarkable advancements in generative modeling; however, they face a trade-off between inference speed and image quality, posing challenges for efficient deployment. Existing distilled T2I models can generate high-fidelity images with fewer sampling steps, but often struggle with diversity and quality, especially in one-step models. From our analysis, we observe redundant computations in the UNet encoders. Our findings suggest that, for T2I diffusion models, decoders are more adept at capturing richer and more explicit semantic information, while encoders can be effectively shared across decoders from diverse time steps. Based on these observations, we introduce the first Time-independent Unified Encoder TiUE for the student model UNet architecture, which is a loop-free image generation approach for distilling T2I diffusion models. Using a one-pass scheme, TiUE shares encoder features across multiple decoder time steps, enabling parallel sampling and significantly reducing inference time complexity. In addition, we incorporate a KL divergence term to regularize noise prediction, which enhances the perceptual realism and diversity of the generated images. Experimental results demonstrate that TiUE outperforms state-of-the-art methods, including LCM, SD-Turbo, and SwiftBrushv2, producing more diverse and realistic results while maintaining the computational efficiency.

End-to-end relation extraction aims to identify named entities and extract relations between them. Most recent work models these two subtasks jointly, either by casting them in one structured prediction framework, or performing multi-task learning through shared representations. In this work, we present a simple pipelined approach for entity and relation extraction, and establish the new state-of-the-art on standard benchmarks (ACE04, ACE05 and SciERC), obtaining a 1.7%-2.8% absolute improvement in relation F1 over previous joint models with the same pre-trained encoders. Our approach essentially builds on two independent encoders and merely uses the entity model to construct the input for the relation model. Through a series of careful examinations, we validate the importance of learning distinct contextual representations for entities and relations, fusing entity information early in the relation model, and incorporating global context. Finally, we also present an efficient approximation to our approach which requires only one pass of both entity and relation encoders at inference time, achieving an 8-16times speedup with a slight reduction in accuracy.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@k: the agent may submit up to k responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@k inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with k and the sampling budget N. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the N samples before selecting the top-k rewards. We prove that when the sampling budget is N=tildeOmega(C^*), the regret of BoM is O(epsilon_{opt}+epsilon_{mathrm{RM}^2C^*/k}), where C^* is the coverage coefficient, epsilon_{RM} is the estimation error of the reward model, and epsilon_{opt} is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing N. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Many applications today provide users with multiple auto-complete drafts as they type, including GitHub's code completion, Gmail's smart compose, and Apple's messaging auto-suggestions. Under the hood, language models support this by running an autoregressive inference pass to provide a draft. Consequently, providing k drafts to the user requires running an expensive language model k times. To alleviate the computation cost of running k inference passes, we propose Superposed Decoding, a new decoding algorithm that generates k drafts at the computation cost of one autoregressive inference pass. We achieve this by feeding a superposition of the most recent token embeddings from the k drafts as input to the next decoding step of the language model. At every inference step we combine the k drafts with the top-k tokens to get k^2 new drafts and cache the k most likely options, using an n-gram interpolation with minimal compute overhead to filter out incoherent generations. Our experiments show that k drafts from Superposed Decoding are at least as coherent and factual as Nucleus Sampling and Greedy Decoding respectively, while being at least 2.44times faster for kge3. In a compute-normalized setting, user evaluations demonstrably favor text generated by Superposed Decoding over Nucleus Sampling. Code and more examples open-sourced at https://github.com/RAIVNLab/SuperposedDecoding.

Multi-view 3D reconstruction remains a core challenge in computer vision, particularly in applications requiring accurate and scalable representations across diverse perspectives. Current leading methods such as DUSt3R employ a fundamentally pairwise approach, processing images in pairs and necessitating costly global alignment procedures to reconstruct from multiple views. In this work, we propose Fast 3D Reconstruction (Fast3R), a novel multi-view generalization to DUSt3R that achieves efficient and scalable 3D reconstruction by processing many views in parallel. Fast3R's Transformer-based architecture forwards N images in a single forward pass, bypassing the need for iterative alignment. Through extensive experiments on camera pose estimation and 3D reconstruction, Fast3R demonstrates state-of-the-art performance, with significant improvements in inference speed and reduced error accumulation. These results establish Fast3R as a robust alternative for multi-view applications, offering enhanced scalability without compromising reconstruction accuracy.

The growing demand for efficient Large Language Model (LLM) inference requires a holistic optimization on algorithms, systems, and hardware. However, very few works have fundamentally changed the generation pattern: each token needs one forward pass and one KV cache. This can be sub-optimal because we found that LLMs are extremely capable of self-identifying the exact dose of information that a single KV cache can store, and many tokens can be generated confidently without global context. Based on this insight, we introduce HAMburger, a Hierarchically Auto-regressive Model that redefines resource allocation in LLMs by moving beyond uniform computation and storage per token during inference. Stacking a compositional embedder and a micro-step decoder in between a base LLM, HAMburger smashes multiple tokens into a single KV and generates several tokens per step. Additionally, HAMburger functions as a speculative decoding framework where it can blindly trust self-drafted tokens. As a result, HAMburger shifts the growth of KV cache and forward FLOPs from linear to sub-linear with respect to output length, and adjusts its inference speed based on query perplexity and output structure. Extensive evaluations show that HAMburger reduces the KV cache computation by up to 2times and achieves up to 2times TPS, while maintaining quality in both short- and long-context tasks. Our method explores an extremely challenging inference regime that requires both computation- and memory-efficiency with a hardware-agnostic design.

Spiking Neural Networks (SNNs) are energy efficient alternatives to commonly used deep neural networks (DNNs). Through event-driven information processing, SNNs can reduce the expensive compute requirements of DNNs considerably, while achieving comparable performance. However, high inference latency is a significant hindrance to the edge deployment of deep SNNs. Computation over multiple timesteps not only increases latency as well as overall energy budget due to higher number of operations, but also incurs memory access overhead of fetching membrane potentials, both of which lessen the energy benefits of SNNs. To overcome this bottleneck and leverage the full potential of SNNs, we propose an Iterative Initialization and Retraining method for SNNs (IIR-SNN) to perform single shot inference in the temporal axis. The method starts with an SNN trained with T timesteps (T>1). Then at each stage of latency reduction, the network trained at previous stage with higher timestep is utilized as initialization for subsequent training with lower timestep. This acts as a compression method, as the network is gradually shrunk in the temporal domain. In this paper, we use direct input encoding and choose T=5, since as per literature, it is the minimum required latency to achieve satisfactory performance on ImageNet. The proposed scheme allows us to obtain SNNs with up to unit latency, requiring a single forward pass during inference. We achieve top-1 accuracy of 93.05%, 70.15% and 67.71% on CIFAR-10, CIFAR-100 and ImageNet, respectively using VGG16, with just 1 timestep. In addition, IIR-SNNs perform inference with 5-2500X reduced latency compared to other state-of-the-art SNNs, maintaining comparable or even better accuracy. Furthermore, in comparison with standard DNNs, the proposed IIR-SNNs provide25-33X higher energy efficiency, while being comparable to them in classification performance.

We present a novel inference scheme, self-speculative decoding, for accelerating Large Language Models (LLMs) without the need for an auxiliary model. This approach is characterized by a two-stage process: drafting and verification. The drafting stage generates draft tokens at a slightly lower quality but more quickly, which is achieved by selectively skipping certain intermediate layers during drafting Subsequently, the verification stage employs the original LLM to validate those draft output tokens in one forward pass. This process ensures the final output remains identical to that produced by the unaltered LLM, thereby maintaining output quality. The proposed method requires no additional neural network training and no extra memory footprint, making it a plug-and-play and cost-effective solution for inference acceleration. Benchmarks with LLaMA-2 and its fine-tuned models demonstrated a speedup up to 1.73times.

Pretrained latent diffusion models have shown strong potential for lossy image compression, owing to their powerful generative priors. Most existing diffusion-based methods reconstruct images by iteratively denoising from random noise, guided by compressed latent representations. While these approaches have achieved high reconstruction quality, their multi-step sampling process incurs substantial computational overhead. Moreover, they typically require training separate models for different compression bit-rates, leading to significant training and storage costs. To address these challenges, we propose a one-step diffusion codec across multiple bit-rates. termed OSCAR. Specifically, our method views compressed latents as noisy variants of the original latents, where the level of distortion depends on the bit-rate. This perspective allows them to be modeled as intermediate states along a diffusion trajectory. By establishing a mapping from the compression bit-rate to a pseudo diffusion timestep, we condition a single generative model to support reconstructions at multiple bit-rates. Meanwhile, we argue that the compressed latents retain rich structural information, thereby making one-step denoising feasible. Thus, OSCAR replaces iterative sampling with a single denoising pass, significantly improving inference efficiency. Extensive experiments demonstrate that OSCAR achieves superior performance in both quantitative and visual quality metrics. The code and models will be released at https://github.com/jp-guo/OSCAR.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

The simultaneous rise of machine learning as a service and concerns over user privacy have increasingly motivated the need for private inference (PI). While recent work demonstrates PI is possible using cryptographic primitives, the computational overheads render it impractical. The community is largely unprepared to address these overheads, as the source of slowdown in PI stems from the ReLU operator whereas optimizations for plaintext inference focus on optimizing FLOPs. In this paper we re-think the ReLU computation and propose optimizations for PI tailored to properties of neural networks. Specifically, we reformulate ReLU as an approximate sign test and introduce a novel truncation method for the sign test that significantly reduces the cost per ReLU. These optimizations result in a specific type of stochastic ReLU. The key observation is that the stochastic fault behavior is well suited for the fault-tolerant properties of neural network inference. Thus, we provide significant savings without impacting accuracy. We collectively call the optimizations Circa and demonstrate improvements of up to 4.7x storage and 3x runtime over baseline implementations; we further show that Circa can be used on top of recent PI optimizations to obtain 1.8x additional speedup.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become increasingly larger. Speculative decoding employs a "draft and then verify" mechanism to allow multiple tokens to be generated in one step, realizing lossless acceleration. Existing methods mainly adopt fixed heuristic draft structures, which fail to adapt to different situations to maximize the acceptance length during verification. To alleviate this dilemma, we proposed OPT-Tree, an algorithm to construct adaptive and scalable draft trees. It searches the optimal tree structure that maximizes the mathematical expectation of the acceptance length in each decoding step. Experimental results reveal that OPT-Tree outperforms the existing draft structures and achieves a speed-up ratio of up to 3.2 compared with autoregressive decoding. If the draft model is powerful enough and the node budget is sufficient, it can generate more than ten tokens in a single step. Our code is available at https://github.com/Jikai0Wang/OPT-Tree.

We conduct experiments on the impact of increasing inference-time compute in reasoning models (specifically OpenAI o1-preview and o1-mini) on their robustness to adversarial attacks. We find that across a variety of attacks, increased inference-time compute leads to improved robustness. In many cases (with important exceptions), the fraction of model samples where the attack succeeds tends to zero as the amount of test-time compute grows. We perform no adversarial training for the tasks we study, and we increase inference-time compute by simply allowing the models to spend more compute on reasoning, independently of the form of attack. Our results suggest that inference-time compute has the potential to improve adversarial robustness for Large Language Models. We also explore new attacks directed at reasoning models, as well as settings where inference-time compute does not improve reliability, and speculate on the reasons for these as well as ways to address them.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

In recent years, particle-based variational inference (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popularity as scalable methods for Bayesian inference. Unfortunately, the properties of such methods invariably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate. In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free. We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demonstrating comparable performance to other ParVI algorithms with no need to tune a learning rate.

Distribution inference, sometimes called property inference, infers statistical properties about a training set from access to a model trained on that data. Distribution inference attacks can pose serious risks when models are trained on private data, but are difficult to distinguish from the intrinsic purpose of statistical machine learning -- namely, to produce models that capture statistical properties about a distribution. Motivated by Yeom et al.'s membership inference framework, we propose a formal definition of distribution inference attacks that is general enough to describe a broad class of attacks distinguishing between possible training distributions. We show how our definition captures previous ratio-based property inference attacks as well as new kinds of attack including revealing the average node degree or clustering coefficient of a training graph. To understand distribution inference risks, we introduce a metric that quantifies observed leakage by relating it to the leakage that would occur if samples from the training distribution were provided directly to the adversary. We report on a series of experiments across a range of different distributions using both novel black-box attacks and improved versions of the state-of-the-art white-box attacks. Our results show that inexpensive attacks are often as effective as expensive meta-classifier attacks, and that there are surprising asymmetries in the effectiveness of attacks. Code is available at https://github.com/iamgroot42/FormEstDistRisks

Large language models (LLMs) have shown exceptional performance and vast potential across diverse tasks. However, the deployment of LLMs with high performance in low-resource environments has garnered significant attention in the industry. When GPU hardware resources are limited, we can explore alternative options on CPUs. To mitigate the financial burden and alleviate constraints imposed by hardware resources, optimizing inference performance is necessary. In this paper, we introduce an easily deployable inference performance optimization solution aimed at accelerating LLMs on CPUs. In this solution, we implement an effective way to reduce the KV cache size while ensuring precision. We propose a distributed inference optimization approach and implement it based on oneAPI Collective Communications Library. Furthermore, we propose optimization approaches for LLMs on CPU, and conduct tailored optimizations for the most commonly used models. The code is open-sourced at https://github.com/intel/xFasterTransformer.

A distribution inference attack aims to infer statistical properties of data used to train machine learning models. These attacks are sometimes surprisingly potent, but the factors that impact distribution inference risk are not well understood and demonstrated attacks often rely on strong and unrealistic assumptions such as full knowledge of training environments even in supposedly black-box threat scenarios. To improve understanding of distribution inference risks, we develop a new black-box attack that even outperforms the best known white-box attack in most settings. Using this new attack, we evaluate distribution inference risk while relaxing a variety of assumptions about the adversary's knowledge under black-box access, like known model architectures and label-only access. Finally, we evaluate the effectiveness of previously proposed defenses and introduce new defenses. We find that although noise-based defenses appear to be ineffective, a simple re-sampling defense can be highly effective. Code is available at https://github.com/iamgroot42/dissecting_distribution_inference

Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit the amount of compute to only one attempt per problem. Here, we explore inference compute as another axis for scaling by increasing the number of generated samples. Across multiple tasks and models, we observe that coverage - the fraction of problems solved by any attempt - scales with the number of samples over four orders of magnitude. In domains like coding and formal proofs, where all answers can be automatically verified, these increases in coverage directly translate into improved performance. When we apply repeated sampling to SWE-bench Lite, the fraction of issues solved with DeepSeek-V2-Coder-Instruct increases from 15.9% with one sample to 56% with 250 samples, outperforming the single-attempt state-of-the-art of 43% which uses more capable frontier models. Moreover, using current API pricing, amplifying the cheaper DeepSeek model with five samples is more cost-effective and solves more issues than paying a premium for one sample from GPT-4o or Claude 3.5 Sonnet. Interestingly, the relationship between coverage and the number of samples is often log-linear and can be modelled with an exponentiated power law, suggesting the existence of inference-time scaling laws. Finally, we find that identifying correct samples out of many generations remains an important direction for future research in domains without automatic verifiers. When solving math word problems from GSM8K and MATH, coverage with Llama-3 models grows to over 95% with 10,000 samples. However, common methods to pick correct solutions from a sample collection, such as majority voting or reward models, plateau beyond several hundred samples and fail to fully scale with the sample budget.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

Leveraging recent advancements in large language models, modern neural code completion models have demonstrated the capability to generate highly accurate code suggestions. However, their massive size poses challenges in terms of computational costs and environmental impact, hindering their widespread adoption in practical scenarios. Dynamic inference emerges as a promising solution, as it allocates minimal computation during inference while maintaining the model's performance. In this research, we explore dynamic inference within the context of code completion. Initially, we conducted an empirical investigation on GPT-2, focusing on the inference capabilities of intermediate layers for code completion. We found that 54.4% of tokens can be accurately generated using just the first layer, signifying significant computational savings potential. Moreover, despite using all layers, the model still fails to predict 14.5% of tokens correctly, and the subsequent completions continued from them are rarely considered helpful, with only a 4.2% Acceptance Rate. These findings motivate our exploration of dynamic inference in code completion and inspire us to enhance it with a decision-making mechanism that stops the generation of incorrect code. We thus propose a novel dynamic inference method specifically tailored for code completion models. This method aims not only to produce correct predictions with largely reduced computation but also to prevent incorrect predictions proactively. Our extensive evaluation shows that it can averagely skip 1.7 layers out of 16 layers in the models, leading to an 11.2% speedup with only a marginal 1.1% reduction in ROUGE-L.

As industrial applications are increasingly automated by machine learning models, enforcing personal data ownership and intellectual property rights requires tracing training data back to their rightful owners. Membership inference algorithms approach this problem by using statistical techniques to discern whether a target sample was included in a model's training set. However, existing methods only utilize the unaltered target sample or simple augmentations of the target to compute statistics. Such a sparse sampling of the model's behavior carries little information, leading to poor inference capabilities. In this work, we use adversarial tools to directly optimize for queries that are discriminative and diverse. Our improvements achieve significantly more accurate membership inference than existing methods, especially in offline scenarios and in the low false-positive regime which is critical in legal settings. Code is available at https://github.com/YuxinWenRick/canary-in-a-coalmine.

We present a generic framework for creating differentially private versions of any hypothesis test in a black-box way. We analyze the resulting tests analytically and experimentally. Most crucially, we show good practical performance for small data sets, showing that at epsilon = 1 we only need 5-6 times as much data as in the fully public setting. We compare our work to the one existing framework of this type, as well as to several individually-designed private hypothesis tests. Our framework is higher power than other generic solutions and at least competitive with (and often better than) individually-designed tests.

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget varepsilon spent on training a model. Existing approaches derive confidence intervals for varepsilon from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for epsilon using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for varepsilon (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for varepsilon around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step t and corresponding state x_t, there might exist another time step t_s which exhibits superior coupling with x_t. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49\% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at https://github.com/Mingxiao-Li/TS-DPM.

Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data points one at a time. Here we study the problem of distribution-free predictive inference for a batch of multiple test points, aiming to construct prediction sets for functions -- such as the mean or median -- of any number of unobserved test datapoints. This setting includes constructing simultaneous prediction sets with a high probability of coverage, and selecting datapoints satisfying a specified condition while controlling the number of false claims. For the general task of predictive inference on a function of a batch of test points, we introduce a methodology called batch predictive inference (batch PI), and provide a distribution-free coverage guarantee under exchangeability of the calibration and test data. Batch PI requires the quantiles of a rank ordering function defined on certain subsets of ranks. While computing these quantiles is NP-hard in general, we show that it can be done efficiently in many cases of interest, most notably for batch score functions with a compositional structure -- which includes examples of interest such as the mean -- via a dynamic programming algorithm that we develop. Batch PI has advantages over naive approaches (such as partitioning the calibration data or directly extending conformal prediction) in many settings, as it can deliver informative prediction sets even using small calibration sample sizes. We illustrate that our procedures provide informative inference across the use cases mentioned above, through experiments on both simulated data and a drug-target interaction dataset.

Recent advancements in large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, single-shot inference often yields unreliable results for complex reasoning tasks, leading researchers to explore multiple reasoning paths through methods such as perplexity and self-consistency. In this paper, we present the first theoretical error decomposition analysis of these techniques, breaking down their error into estimation error and model error. Our analysis reveals a fundamental trade-off: perplexity methods suffer from substantial model error due to the absence of a proper consistency function, while self-consistency exhibits high estimation error due to a slow error convergence rate. To overcome these limitations, we propose Reasoning-Pruning Perplexity Consistency (RPC). This approach combines Perplexity Consistency, which seamlessly integrates LLM perplexity with self-consistency, and Reasoning Pruning, which eliminates low-probability reasoning paths to effectively prevent the degeneration of estimation error reduction. Theoretical analysis demonstrates that RPC not only accelerates the convergence rate of estimation error to an exponential level but also holds strong potential for further reducing model error. Extensive empirical evaluations on seven benchmark datasets confirm that RPC can significantly improve reasoning performance, sample efficiency, and confidence reliability.

Recently, Zaremba et al. demonstrated that increasing inference-time computation improves robustness in large proprietary reasoning LLMs. In this paper, we first show that smaller-scale, open-source models (e.g., DeepSeek R1, Qwen3, Phi-reasoning) can also benefit from inference-time scaling using a simple budget forcing strategy. More importantly, we reveal and critically examine an implicit assumption in prior work: intermediate reasoning steps are hidden from adversaries. By relaxing this assumption, we identify an important security risk, intuitively motivated and empirically verified as an inverse scaling law: if intermediate reasoning steps become explicitly accessible, increased inference-time computation consistently reduces model robustness. Finally, we discuss practical scenarios where models with hidden reasoning chains are still vulnerable to attacks, such as models with tool-integrated reasoning and advanced reasoning extraction attacks. Our findings collectively demonstrate that the robustness benefits of inference-time scaling depend heavily on the adversarial setting and deployment context. We urge practitioners to carefully weigh these subtle trade-offs before applying inference-time scaling in security-sensitive, real-world applications.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we show that PCs are in fact not robust to OOD data, i.e., they don't know what they don't know. We then show how this challenge can be overcome by model uncertainty quantification. To this end, we propose tractable dropout inference (TDI), an inference procedure to estimate uncertainty by deriving an analytical solution to Monte Carlo dropout (MCD) through variance propagation. Unlike MCD in neural networks, which comes at the cost of multiple network evaluations, TDI provides tractable sampling-free uncertainty estimates in a single forward pass. TDI improves the robustness of PCs to distribution shift and OOD data, demonstrated through a series of experiments evaluating the classification confidence and uncertainty estimates on real-world data.

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

Large Language Models (LLMs) have recently advanced the field of Automated Theorem Proving (ATP), attaining substantial performance gains through widely adopted test-time scaling strategies, notably reflective Chain-of-Thought (CoT) reasoning and increased sampling passes. However, they both introduce significant computational overhead for inference. Moreover, existing cost analyses typically regulate only the number of sampling passes, while neglecting the substantial disparities in sampling costs introduced by different scaling strategies. In this paper, we systematically compare the efficiency of different test-time scaling strategies for ATP models and demonstrate the inefficiency of the current state-of-the-art (SOTA) open-source approaches. We then investigate approaches to significantly reduce token usage and sample passes while maintaining the original performance. Specifically, we propose two complementary methods that can be integrated into a unified EconRL pipeline for amplified benefits: (1) a dynamic Chain-of-Thought (CoT) switching mechanism designed to mitigate unnecessary token consumption, and (2) Diverse parallel-scaled reinforcement learning (RL) with trainable prefixes to enhance pass rates under constrained sampling passes. Experiments on miniF2F and ProofNet demonstrate that our EconProver achieves comparable performance to baseline methods with only 12% of the computational cost. This work provides actionable insights for deploying lightweight ATP models without sacrificing performance.

Large Language Models (LLMs) have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking, wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide LLM test-time scaling without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time. To support flexible inference-time control, we introduce gamma-control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by over 50% on average while improving accuracy by 0.62-3.37%.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

Inference-time scaling has emerged as a powerful alternative to parameter scaling for improving language model performance on complex reasoning tasks. While existing methods have shown strong performance gains under fixed compute budgets, there has been little focus on optimally utilizing that budget during inference. In this work, we introduce A*-decoding, a search-based inference-time strategy that builds on the A* search algorithm to optimally utilize a fixed compute budget by prioritizing high-quality reasoning paths during generation. We frame language model decoding as a structured search in a state space of partial solutions, applying the A* transition model to identify promising continuations guided by an external process supervision signal. In our experiments, A*-decoding reaches the performance levels of strong inference scaling baselines like best-of-N and particle filtering while using up to 3x fewer tokens and 30% fewer PRM passes under equivalent compute budgets. On the MATH500 and AIME 2024 benchmarks, A*-decoding enables Llama-3.2-1B-Instruct to match the performance of the 70x larger Llama-3.1-70B-Instruct, and allows Qwen3-1.7B to reach o1-like reasoning accuracy. These results highlight the power of structured search in decoding, offering an alternative to brute-force sampling or scale-driven gains. Our work demonstrates how thoughtful inference-time strategies can enhance reasoning in SLMs, pointing toward future advances in more efficient and scalable language model deployment.

Techniques that enhance inference through increased computation at test-time have recently gained attention. In this survey, we investigate the current state of LLM Inference-Time Self-Improvement from three different perspectives: Independent Self-improvement, focusing on enhancements via decoding or sampling methods; Context-Aware Self-Improvement, leveraging additional context or datastore; and Model-Aided Self-Improvement, achieving improvement through model collaboration. We provide a comprehensive review of recent relevant studies, contribute an in-depth taxonomy, and discuss challenges and limitations, offering insights for future research.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, potentially benefiting other sequential algorithms. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (R\'enyi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any epsilon-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance.

Test-time scaling seeks to improve the reasoning performance of large language models (LLMs) by adding computational resources. A prevalent approach within the field is sampling-based test-time scaling methods, which enhance reasoning by generating multiple reasoning paths for a given input during inference. However, despite its practical success, the theoretical foundations remain underexplored. In this paper, we provide the first theoretical framework for analyzing sampling-based test-time scaling methods, grounded in the perspective of confidence estimation. Based on the framework, we analyze two dominant paradigms: self-consistency and perplexity, and reveal key limitations: self-consistency suffers from high estimation error while perplexity exhibits substantial modeling error and possible degradation of the estimation error convergence. To address these limitations, we introduce RPC, a hybrid method that leverages our theoretical insights through two key components: Perplexity Consistency and Reasoning Pruning. Perplexity Consistency combines the strengths of self-consistency and perplexity, boosting the convergence rate of estimation error from linear to exponential while preserving model error. Reasoning Pruning prevents degradation by eliminating low-probability reasoning paths. Both theoretical analysis and empirical results across seven benchmark datasets demonstrate that RPC has a strong potential for reducing reasoning error. Notably, RPC achieves reasoning performance comparable to self-consistency while not only enhancing confidence reliability but also reducing sampling costs by 50%. The code and resources are available at https://wnjxyk.github.io/RPC.

This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations (X_1, dots, X_n) with mean mu^star that are privatized into (Z_1, dots, Z_n), we present confidence intervals (CI) and time-uniform confidence sequences (CS) for mu^star when only given access to the privatized data. To achieve this, we introduce a nonparametric and sequentially interactive generalization of Warner's famous ``randomized response'' mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

It is well known that many open-released foundational diffusion models have difficulty in generating images that substantially depart from average brightness, despite such images being present in the training data. This is due to an inconsistency: while denoising starts from pure Gaussian noise during inference, the training noise schedule retains residual data even in the final timestep distribution, due to difficulties in numerical conditioning in mainstream formulation, leading to unintended bias during inference. To mitigate this issue, certain epsilon-prediction models are combined with an ad-hoc offset-noise methodology. In parallel, some contemporary models have adopted zero-terminal SNR noise schedules together with v-prediction, which necessitate major alterations to pre-trained models. However, such changes risk destabilizing a large multitude of community-driven applications anchored on these pre-trained models. In light of this, our investigation revisits the fundamental causes, leading to our proposal of an innovative and principled remedy, called One More Step (OMS). By integrating a compact network and incorporating an additional simple yet effective step during inference, OMS elevates image fidelity and harmonizes the dichotomy between training and inference, while preserving original model parameters. Once trained, various pre-trained diffusion models with the same latent domain can share the same OMS module.

As large language models gain widespread adoption, running them efficiently becomes crucial. Recent works on LLM inference use speculative decoding to achieve extreme speedups. However, most of these works implicitly design their algorithms for high-end datacenter hardware. In this work, we ask the opposite question: how fast can we run LLMs on consumer machines? Consumer GPUs can no longer fit the largest available models (50B+ parameters) and must offload them to RAM or SSD. When running with offloaded parameters, the inference engine can process batches of hundreds or thousands of tokens at the same time as just one token, making it a natural fit for speculative decoding. We propose SpecExec (Speculative Execution), a simple parallel decoding method that can generate up to 20 tokens per target model iteration for popular LLM families. It utilizes the high spikiness of the token probabilities distribution in modern LLMs and a high degree of alignment between model output probabilities. SpecExec takes the most probable tokens continuation from the draft model to build a "cache" tree for the target model, which then gets validated in a single pass. Using SpecExec, we demonstrate inference of 50B+ parameter LLMs on consumer GPUs with RAM offloading at 4-6 tokens per second with 4-bit quantization or 2-3 tokens per second with 16-bit weights.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Large language models (LLMs) often demonstrate inconsistencies with human preferences. Previous research gathered human preference data and then aligned the pre-trained models using reinforcement learning or instruction tuning, the so-called finetuning step. In contrast, aligning frozen LLMs without any extra data is more appealing. This work explores the potential of the latter setting. We discover that by integrating self-evaluation and rewind mechanisms, unaligned LLMs can directly produce responses consistent with human preferences via self-boosting. We introduce a novel inference method, Rewindable Auto-regressive INference (RAIN), that allows pre-trained LLMs to evaluate their own generation and use the evaluation results to guide backward rewind and forward generation for AI safety. Notably, RAIN operates without the need of extra data for model alignment and abstains from any training, gradient computation, or parameter updates; during the self-evaluation phase, the model receives guidance on which human preference to align with through a fixed-template prompt, eliminating the need to modify the initial prompt. Experimental results evaluated by GPT-4 and humans demonstrate the effectiveness of RAIN: on the HH dataset, RAIN improves the harmlessness rate of LLaMA 30B over vanilla inference from 82% to 97%, while maintaining the helpfulness rate. Under the leading adversarial attack llm-attacks on Vicuna 33B, RAIN establishes a new defense baseline by reducing the attack success rate from 94% to 19%.

Recent years have seen significant advancements in foundation models through generative pre-training, yet algorithmic innovation in this space has largely stagnated around autoregressive models for discrete signals and diffusion models for continuous signals. This stagnation creates a bottleneck that prevents us from fully unlocking the potential of rich multi-modal data, which in turn limits the progress on multimodal intelligence. We argue that an inference-first perspective, which prioritizes scaling efficiency during inference time across sequence length and refinement steps, can inspire novel generative pre-training algorithms. Using Inductive Moment Matching (IMM) as a concrete example, we demonstrate how addressing limitations in diffusion models' inference process through targeted modifications yields a stable, single-stage algorithm that achieves superior sample quality with over an order of magnitude greater inference efficiency.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer D for the total number of nestings. Standard Monte Carlo methods typically cost at least O(varepsilon^{-(2+D)}) and sometimes O(varepsilon^{-2(1+D)}) to obtain an estimator up to varepsilon-error. More advanced methods, such as multilevel Monte Carlo, currently only exist for D = 1. In this paper, we propose a novel Monte Carlo estimator called READ, which stands for "Recursive Estimator for Arbitrary Depth.'' Our estimator has an optimal computational cost of O(varepsilon^{-2}) for every fixed D under suitable assumptions, and a nearly optimal computational cost of O(varepsilon^{-2(1 + delta)}) for any 0 < delta < frac12 under much more general assumptions. Our estimator is also unbiased, which makes it easy to parallelize. The key ingredients in our construction are an observation of the problem's recursive structure and the recursive use of the randomized multilevel Monte Carlo method.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

While AI agents have shown remarkable performance at various tasks, they still struggle with complex multi-modal applications, structured generation and strategic planning. Improvements via standard fine-tuning is often impractical, as solving agentic tasks usually relies on black box API access without control over model parameters. Inference-time methods such as Best-of-N (BON) sampling offer a simple yet effective alternative to improve performance. However, BON lacks iterative feedback integration mechanism. Hence, we propose Iterative Agent Decoding (IAD) which combines iterative refinement with dynamic candidate evaluation and selection guided by a verifier. IAD differs in how feedback is designed and integrated, specifically optimized to extract maximal signal from reward scores. We conduct a detailed comparison of baselines across key metrics on Sketch2Code, Text2SQL, and Webshop where IAD consistently outperforms baselines, achieving 3--6% absolute gains on Sketch2Code and Text2SQL (with and without LLM judges) and 8--10% gains on Webshop across multiple metrics. To better understand the source of IAD's gains, we perform controlled experiments to disentangle the effect of adaptive feedback from stochastic sampling, and find that IAD's improvements are primarily driven by verifier-guided refinement, not merely sampling diversity. We also show that both IAD and BON exhibit inference-time scaling with increased compute when guided by an optimal verifier. Our analysis highlights the critical role of verifier quality in effective inference-time optimization and examines the impact of noisy and sparse rewards on scaling behavior. Together, these findings offer key insights into the trade-offs and principles of effective inference-time optimization.

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement learning (RL) holds promise for enabling self-exploration and learning from feedback, recent attempts yield only modest improvements in complex reasoning. In this paper, we present T1 to scale RL by encouraging exploration and understand inference scaling. We first initialize the LLM using synthesized chain-of-thought data that integrates trial-and-error and self-verification. To scale RL training, we promote increased sampling diversity through oversampling. We further employ an entropy bonus as an auxiliary loss, alongside a dynamic anchor for regularization to facilitate reward optimization. We demonstrate that T1 with open LLMs as its base exhibits inference scaling behavior and achieves superior performance on challenging math reasoning benchmarks. For example, T1 with Qwen2.5-32B as the base model outperforms the recent Qwen QwQ-32B-Preview model on MATH500, AIME2024, and Omni-math-500. More importantly, we present a simple strategy to examine inference scaling, where increased inference budgets directly lead to T1's better performance without any additional verification. We will open-source the T1 models and the data used to train them at https://github.com/THUDM/T1.

With few exceptions, neural networks have been relying on backpropagation and gradient descent as the inference engine in order to learn the model parameters, because the closed-form Bayesian inference for neural networks has been considered to be intractable. In this paper, we show how we can leverage the tractable approximate Gaussian inference's (TAGI) capabilities to infer hidden states, rather than only using it for inferring the network's parameters. One novel aspect it allows is to infer hidden states through the imposition of constraints designed to achieve specific objectives, as illustrated through three examples: (1) the generation of adversarial-attack examples, (2) the usage of a neural network as a black-box optimization method, and (3) the application of inference on continuous-action reinforcement learning. These applications showcase how tasks that were previously reserved to gradient-based optimization approaches can now be approached with analytically tractable inference

Modern machine learning models are sensitive to the manipulation of both the training data (poisoning attacks) and inference data (adversarial examples). Recognizing this issue, the community has developed many empirical defenses against both attacks and, more recently, provable certification methods against inference-time attacks. However, such guarantees are still largely lacking for training-time attacks. In this work, we present FullCert, the first end-to-end certifier with sound, deterministic bounds, which proves robustness against both training-time and inference-time attacks. We first bound all possible perturbations an adversary can make to the training data under the considered threat model. Using these constraints, we bound the perturbations' influence on the model's parameters. Finally, we bound the impact of these parameter changes on the model's prediction, resulting in joint robustness guarantees against poisoning and adversarial examples. To facilitate this novel certification paradigm, we combine our theoretical work with a new open-source library BoundFlow, which enables model training on bounded datasets. We experimentally demonstrate FullCert's feasibility on two different datasets.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to learn accurate approximations. In contrast, Neural Likelihood Estimation methods can handle multiple observations at inference time after learning from individual observations, but they rely on standard inference methods, such as MCMC or variational inference, which come with certain performance drawbacks. We introduce a new method based on conditional score modeling that enjoys the benefits of both approaches. We model the scores of the (diffused) posterior distributions induced by individual observations, and introduce a way of combining the learned scores to approximately sample from the target posterior distribution. Our approach is sample-efficient, can naturally aggregate multiple observations at inference time, and avoids the drawbacks of standard inference methods.

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as tau-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, tau-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the theta-trapezoidal method in KL divergence. Empirical evaluations on GPT-2 level text and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints.

The recent surge of open-source large language models (LLMs) enables developers to create AI-based solutions while maintaining control over aspects such as privacy and compliance, thereby providing governance and ownership of the model deployment process. To utilize these LLMs, inference engines are needed. These engines load the model's weights onto available resources, such as GPUs, and process queries to generate responses. The speed of inference, or performance, of the LLM, is critical for real-time applications, as it computes millions or billions of floating point operations per inference. Recently, advanced inference engines such as vLLM have emerged, incorporating novel mechanisms such as efficient memory management to achieve state-of-the-art performance. In this paper, we analyze the performance, particularly the throughput (tokens generated per unit of time), of 20 LLMs using two inference libraries: vLLM and HuggingFace's pipelines. We investigate how various hyperparameters, which developers must configure, influence inference performance. Our results reveal that throughput landscapes are irregular, with distinct peaks, highlighting the importance of hyperparameter optimization to achieve maximum performance. We also show that applying hyperparameter optimization when upgrading or downgrading the GPU model used for inference can improve throughput from HuggingFace pipelines by an average of 9.16% and 13.7%, respectively.

Accelerating the inference of large language models (LLMs) is an important challenge in artificial intelligence. This paper introduces distributed speculative inference (DSI), a novel distributed inference algorithm that is provably faster than speculative inference (SI) [leviathan2023fast, chen2023accelerating, miao2023specinfer] and traditional autoregressive inference (non-SI). Like other SI algorithms, DSI works on frozen LLMs, requiring no training or architectural modifications, and it preserves the target distribution. Prior studies on SI have demonstrated empirical speedups (compared to non-SI) but require a fast and accurate drafter LLM. In practice, off-the-shelf LLMs often do not have matching drafters that are sufficiently fast and accurate. We show a gap: SI gets slower than non-SI when using slower or less accurate drafters. We close this gap by proving that DSI is faster than both SI and non-SI given any drafters. By orchestrating multiple instances of the target and drafters, DSI is not only faster than SI but also supports LLMs that cannot be accelerated with SI. Our simulations show speedups of off-the-shelf LLMs in realistic settings: DSI is 1.29-1.92x faster than SI.

We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.

In recent years, masked diffusion models (MDMs) have emerged as a promising alternative approach for generative modeling over discrete domains. Compared to autoregressive models (ARMs), MDMs trade off complexity at training time with flexibility at inference time. At training time, they must learn to solve an exponentially large number of infilling problems, but at inference time, they can decode tokens in essentially arbitrary order. In this work, we closely examine these two competing effects. On the training front, we theoretically and empirically demonstrate that MDMs indeed train on computationally intractable subproblems compared to their autoregressive counterparts. On the inference front, we show that a suitable strategy for adaptively choosing the token decoding order significantly enhances the capabilities of MDMs, allowing them to sidestep hard subproblems. On logic puzzles like Sudoku, we show that adaptive inference can boost solving accuracy in pretrained MDMs from <7% to approx 90%, even outperforming ARMs with 7times as many parameters and that were explicitly trained via teacher forcing to learn the right order of decoding.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the `conjugate priors' of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions, and (3) a logical description of conjugate priors that highlights the required closure of the priors under updating. The theory is illustrated with several standard examples, also covering multiple updating.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

The advent of 1-bit large language models (LLMs), led by BitNet b1.58, has spurred interest in ternary LLMs. Despite this, research and practical applications focusing on efficient edge inference for ternary LLMs remain scarce. To bridge this gap, we introduce Bitnet.cpp, an inference system optimized for BitNet b1.58 and ternary LLMs. Given that mixed-precision matrix multiplication (mpGEMM) constitutes the bulk of inference time in ternary LLMs, Bitnet.cpp incorporates a novel mpGEMM library to facilitate sub-2-bits-per-weight, efficient and lossless inference. The library features two core solutions: Ternary Lookup Table (TL), which addresses spatial inefficiencies of previous bit-wise methods, and Int2 with a Scale (I2_S), which ensures lossless edge inference, both enabling high-speed inference. Our experiments show that Bitnet.cpp achieves up to a 6.25x increase in speed over full-precision baselines and up to 2.32x over low-bit baselines, setting new benchmarks in the field. Additionally, we expand TL to element-wise lookup table (ELUT) for low-bit LLMs in the appendix, presenting both theoretical and empirical evidence of its considerable potential. Bitnet.cpp is publicly available at https://github.com/microsoft/BitNet/tree/paper , offering a sophisticated solution for the efficient and practical deployment of edge LLMs.

Large language models (LLMs) are widely applied in chatbots, code generators, and search engines. Workloads such as chain-of-thought, complex reasoning, and agent services significantly increase the inference cost by invoking the model repeatedly. Optimization methods such as parallelism, compression, and caching have been adopted to reduce costs, but the diverse service requirements make it hard to select the right method. Recently, specialized LLM inference engines have emerged as a key component for integrating the optimization methods into service-oriented infrastructures. However, a systematic study on inference engines is still lacking. This paper provides a comprehensive evaluation of 25 open-source and commercial inference engines. We examine each inference engine in terms of ease-of-use, ease-of-deployment, general-purpose support, scalability, and suitability for throughput- and latency-aware computation. Furthermore, we explore the design goals of each inference engine by investigating the optimization techniques it supports. In addition, we assess the ecosystem maturity of open source inference engines and handle the performance and cost policy of commercial solutions. We outline future research directions that include support for complex LLM-based services, support of various hardware, and enhanced security, offering practical guidance to researchers and developers in selecting and designing optimized LLM inference engines. We also provide a public repository to continually track developments in this fast-evolving field: https://github.com/sihyeong/Awesome-LLM-Inference-Engine

Diffusion models (DMs) excel in image generation, but suffer from slow inference and the training-inference discrepancies. Although gradient-based solvers like DPM-Solver accelerate the denoising inference, they lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers a reference-free way to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called EVODiff, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to 45.5\% (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by 25\% (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts. Code is available at https://github.com/ShiguiLi/EVODiff.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

Recent studies have indicated that effectively utilizing inference-time compute is crucial for attaining better performance from large language models (LLMs). In this work, we propose a novel inference-aware fine-tuning paradigm, in which the model is fine-tuned in a manner that directly optimizes the performance of the inference-time strategy. We study this paradigm using the simple yet effective Best-of-N (BoN) inference strategy, in which a verifier selects the best out of a set of LLM-generated responses. We devise the first imitation learning and reinforcement learning~(RL) methods for BoN-aware fine-tuning, overcoming the challenging, non-differentiable argmax operator within BoN. We empirically demonstrate that our BoN-aware models implicitly learn a meta-strategy that interleaves best responses with more diverse responses that might be better suited to a test-time input -- a process reminiscent of the exploration-exploitation trade-off in RL. Our experiments demonstrate the effectiveness of BoN-aware fine-tuning in terms of improved performance and inference-time compute. In particular, we show that our methods improve the Bo32 performance of Gemma 2B on Hendrycks MATH from 26.8% to 30.8%, and pass@32 from 60.0% to 67.0%, as well as the pass@16 on HumanEval from 61.6% to 67.1%.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a varphi-divergence to an empirical distribution. However, the use of varphi-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these deterministic uncertainty methods (DUMs) achieve strong performance on detecting out-of-distribution (OOD) data while adding negligible computational costs at inference time. However, it remains unclear whether DUMs are well calibrated and can seamlessly scale to real-world applications - both prerequisites for their practical deployment. To this end, we first provide a taxonomy of DUMs, and evaluate their calibration under continuous distributional shifts. Then, we extend them to semantic segmentation. We find that, while DUMs scale to realistic vision tasks and perform well on OOD detection, the practicality of current methods is undermined by poor calibration under distributional shifts.

This review paper is intended for the 2nd edition of the Handbook of Markov chain Monte Carlo. We provide an introduction to approximate inference techniques as Bayesian computation methods applied to deep learning models. We organize the chapter by presenting popular computational methods for Bayesian neural networks and deep generative models, explaining their unique challenges in posterior inference as well as the solutions.

This paper presents a case study of coding tasks by the latest reasoning models of OpenAI, i.e. o1-preview and o1-mini, in comparison with other frontier models. The o1 models deliver SOTA results for WebApp1K, a single-task benchmark. To this end, we introduce WebApp1K-Duo, a harder benchmark doubling number of tasks and test cases. The new benchmark causes the o1 model performances to decline significantly, falling behind Claude 3.5. Moreover, they consistently fail when confronted with atypical yet correct test cases, a trap non-reasoning models occasionally avoid. We hypothesize that the performance variability is due to instruction comprehension. Specifically, the reasoning mechanism boosts performance when all expectations are captured, meanwhile exacerbates errors when key expectations are missed, potentially impacted by input lengths. As such, we argue that the coding success of reasoning models hinges on the top-notch base model and SFT to ensure meticulous adherence to instructions.

We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed algorithms, state-free inference does not incur any significant memory or computational cost with an increase in state size. We achieve this using properties of the proposed frequency domain transfer function parametrization, which enables direct computation of its corresponding convolutional kernel's spectrum via a single Fast Fourier Transform. Our experimental results across multiple sequence lengths and state sizes illustrates, on average, a 35% training speed improvement over S4 layers -- parametrized in time-domain -- on the Long Range Arena benchmark, while delivering state-of-the-art downstream performances over other attention-free approaches. Moreover, we report improved perplexity in language modeling over a long convolutional Hyena baseline, by simply introducing our transfer function parametrization. Our code is available at https://github.com/ruke1ire/RTF.

Drafting-then-verifying decoding methods such as speculative decoding are widely adopted training-free methods to accelerate the inference of large language models (LLMs). Instead of employing an autoregressive process to decode tokens sequentially, speculative decoding initially creates drafts with an efficient small model. Then LLMs are required to conduct verification and correction in a non-autoregressive fashion to minimize time overhead. Generating longer drafts can lead to even more significant speedups once verified, but also incurs substantial trial and error costs if it fails. Suffering from the high verification failure probability, existing decoding methods cannot draft too much content for verification at one time, achieving sub-optimal inference acceleration. In this paper, we introduce Ouroboros, which constructs a phrase candidate pool from the verification process of LLMs to provide candidates for draft generation of the small model. Thereby, Ouroboros can further improve the efficiency and effectiveness of the initial drafts. The experimental results on typical text generation tasks show that Ouroboros achieves speedups of up to 1.9x and 2.8x compared to lookahead decoding and speculative decoding, respectively. The source code of Ouroboros is available at https://github.com/thunlp/Ouroboros.

We introduce a new analytical framework to quantify the changes in a machine learning algorithm's output distribution following the inclusion of a few data points in its training set, a notion we define as leave-one-out distinguishability (LOOD). This problem is key to measuring data **memorization** and **information leakage** in machine learning, and the **influence** of training data points on model predictions. We illustrate how our method broadens and refines existing empirical measures of memorization and privacy risks associated with training data. We use Gaussian processes to model the randomness of machine learning algorithms, and validate LOOD with extensive empirical analysis of information leakage using membership inference attacks. Our theoretical framework enables us to investigate the causes of information leakage and where the leakage is high. For example, we analyze the influence of activation functions, on data memorization. Additionally, our method allows us to optimize queries that disclose the most significant information about the training data in the leave-one-out setting. We illustrate how optimal queries can be used for accurate **reconstruction** of training data.

Machine learning models trained with differentially-private (DP) algorithms such as DP-SGD enjoy resilience against a wide range of privacy attacks. Although it is possible to derive bounds for some attacks based solely on an (varepsilon,delta)-DP guarantee, meaningful bounds require a small enough privacy budget (i.e., injecting a large amount of noise), which results in a large loss in utility. This paper presents a new approach to evaluate the privacy of machine learning models against specific record-level threats, such as membership and attribute inference, without the indirection through DP. We focus on the popular DP-SGD algorithm, and derive simple closed-form bounds. Our proofs model DP-SGD as an information theoretic channel whose inputs are the secrets that an attacker wants to infer (e.g., membership of a data record) and whose outputs are the intermediate model parameters produced by iterative optimization. We obtain bounds for membership inference that match state-of-the-art techniques, whilst being orders of magnitude faster to compute. Additionally, we present a novel data-dependent bound against attribute inference. Our results provide a direct, interpretable, and practical way to evaluate the privacy of trained models against specific inference threats without sacrificing utility.

Online inference is becoming a key service product for many businesses, deployed in cloud platforms to meet customer demands. Despite their revenue-generation capability, these services need to operate under tight Quality-of-Service (QoS) and cost budget constraints. This paper introduces KAIROS, a novel runtime framework that maximizes the query throughput while meeting QoS target and a cost budget. KAIROS designs and implements novel techniques to build a pool of heterogeneous compute hardware without online exploration overhead, and distribute inference queries optimally at runtime. Our evaluation using industry-grade deep learning (DL) models shows that KAIROS yields up to 2X the throughput of an optimal homogeneous solution, and outperforms state-of-the-art schemes by up to 70%, despite advantageous implementations of the competing schemes to ignore their exploration overhead.

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

Membership inference attacks aim to infer whether an individual record was used to train a model, serving as a key tool for disclosure auditing. While such evaluations are useful to demonstrate risk, they are computationally expensive and often make strong assumptions about potential adversaries' access to models and training environments, and thus do not provide very tight bounds on leakage from potential attacks. We show how prior claims around black-box access being sufficient for optimal membership inference do not hold for most useful settings such as stochastic gradient descent, and that optimal membership inference indeed requires white-box access. We validate our findings with a new white-box inference attack IHA (Inverse Hessian Attack) that explicitly uses model parameters by taking advantage of computing inverse-Hessian vector products. Our results show that both audits and adversaries may be able to benefit from access to model parameters, and we advocate for further research into white-box methods for membership privacy auditing.

Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models (43.4% rightarrow 46.3%, Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

Prior work on Private Inference (PI) -- inferences performed directly on encrypted input -- has focused on minimizing a network's ReLUs, which have been assumed to dominate PI latency rather than FLOPs. Recent work has shown that FLOPs for PI can no longer be ignored and incur high latency penalties. In this paper, we develop DeepReShape, a technique that optimizes neural network architectures under PI's constraints, optimizing for both ReLUs and FLOPs for the first time. The key insight is strategically allocating channels to position the network's ReLUs in order of their criticality to network accuracy, simultaneously optimizes ReLU and FLOPs efficiency. DeepReShape automates network development with an efficient process, and we call generated networks HybReNets. We evaluate DeepReShape using standard PI benchmarks and demonstrate a 2.1% accuracy gain with a 5.2times runtime improvement at iso-ReLU on CIFAR-100 and an 8.7times runtime improvement at iso-accuracy on TinyImageNet. Furthermore, we investigate the significance of network selection in prior ReLU optimizations and shed light on the key network attributes for superior PI performance.

Inference of Large Language Models (LLMs) across computer clusters has become a focal point of research in recent times, with many acceleration techniques taking inspiration from CPU speculative execution. These techniques reduce bottlenecks associated with memory bandwidth, but also increase end-to-end latency per inference run, requiring high speculation acceptance rates to improve performance. Combined with a variable rate of acceptance across tasks, speculative inference techniques can result in reduced performance. Additionally, pipeline-parallel designs require many user requests to maintain maximum utilization. As a remedy, we propose PipeInfer, a pipelined speculative acceleration technique to reduce inter-token latency and improve system utilization for single-request scenarios while also improving tolerance to low speculation acceptance rates and low-bandwidth interconnects. PipeInfer exhibits up to a 2.15times improvement in generation speed over standard speculative inference. PipeInfer achieves its improvement through Continuous Asynchronous Speculation and Early Inference Cancellation, the former improving latency and generation speed by running single-token inference simultaneously with several speculative runs, while the latter improves speed and latency by skipping the computation of invalidated runs, even in the middle of inference.

The optimal training configurations of large language models (LLMs) with respect to model sizes and compute budgets have been extensively studied. But how to optimally configure LLMs during inference has not been explored in sufficient depth. We study compute-optimal inference: designing models and inference strategies that optimally trade off additional inference-time compute for improved performance. As a first step towards understanding and designing compute-optimal inference methods, we assessed the effectiveness and computational efficiency of multiple inference strategies such as Greedy Search, Majority Voting, Best-of-N, Weighted Voting, and their variants on two different Tree Search algorithms, involving different model sizes and computational budgets. We found that a smaller language model with a novel tree search algorithm typically achieves a Pareto-optimal trade-off. These results highlight the potential benefits of deploying smaller models equipped with more sophisticated decoding algorithms in budget-constrained scenarios, e.g., on end-devices, to enhance problem-solving accuracy. For instance, we show that the Llemma-7B model can achieve competitive accuracy to a Llemma-34B model on MATH500 while using 2times less FLOPs. Our findings could potentially apply to any generation task with a well-defined measure of success.

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4times super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.

A membership inference attack allows an adversary to query a trained machine learning model to predict whether or not a particular example was contained in the model's training dataset. These attacks are currently evaluated using average-case "accuracy" metrics that fail to characterize whether the attack can confidently identify any members of the training set. We argue that attacks should instead be evaluated by computing their true-positive rate at low (e.g., <0.1%) false-positive rates, and find most prior attacks perform poorly when evaluated in this way. To address this we develop a Likelihood Ratio Attack (LiRA) that carefully combines multiple ideas from the literature. Our attack is 10x more powerful at low false-positive rates, and also strictly dominates prior attacks on existing metrics.

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code and further information is available at https://probabilistic-inference-scaling.github.io.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

In domains with high stakes such as law, recruitment, and healthcare, learning models frequently rely on sensitive user data for inference, necessitating the complete set of features. This not only poses significant privacy risks for individuals but also demands substantial human effort from organizations to verify information accuracy. This paper asks whether it is necessary to use all input features for accurate predictions at inference time. The paper demonstrates that, in a personalized setting, individuals may only need to disclose a small subset of their features without compromising decision-making accuracy. The paper also provides an efficient sequential algorithm to determine the appropriate attributes for each individual to provide. Evaluations across various learning tasks show that individuals can potentially report as little as 10\% of their information while maintaining the same accuracy level as a model that employs the full set of user information.

Diffusion models achieve high-quality sample generation at the cost of a lengthy multistep inference procedure. To overcome this, diffusion distillation techniques produce student generators capable of matching or surpassing the teacher in a single step. However, the student model's inference speed is limited by the size of the teacher architecture, preventing real-time generation for computationally heavy applications. In this work, we introduce Multi-Student Distillation (MSD), a framework to distill a conditional teacher diffusion model into multiple single-step generators. Each student generator is responsible for a subset of the conditioning data, thereby obtaining higher generation quality for the same capacity. MSD trains multiple distilled students, allowing smaller sizes and, therefore, faster inference. Also, MSD offers a lightweight quality boost over single-student distillation with the same architecture. We demonstrate MSD is effective by training multiple same-sized or smaller students on single-step distillation using distribution matching and adversarial distillation techniques. With smaller students, MSD gets competitive results with faster inference for single-step generation. Using 4 same-sized students, MSD significantly outperforms single-student baseline counterparts and achieves remarkable FID scores for one-step image generation: 1.20 on ImageNet-64x64 and 8.20 on zero-shot COCO2014.

Large Language Models (LLMs) have demonstrated the ability to tackle increasingly complex tasks through advanced reasoning, long-form content generation, and tool use. Solving these tasks often involves long inference-time computations. In human problem solving, a common strategy to expedite work is collaboration: by dividing the problem into sub-tasks, exploring different strategies concurrently, etc. Recent research has shown that LLMs can also operate in parallel by implementing explicit cooperation frameworks, such as voting mechanisms or the explicit creation of independent sub-tasks that can be executed in parallel. However, each of these frameworks may not be suitable for all types of tasks, which can hinder their applicability. In this work, we propose a different design approach: we run LLM "workers" in parallel , allowing them to synchronize via a concurrently-updated attention cache and prompt these workers to decide how best to collaborate. Our approach allows the instances to come up with their own collaboration strategy for the problem at hand, all the while "seeing" each other's partial progress in the concurrent cache. We implement this approach via Hogwild! Inference: a parallel LLM inference engine where multiple instances of the same LLM run in parallel with the same attention cache, with "instant" access to each other's generated tokens. Hogwild! inference takes advantage of Rotary Position Embeddings (RoPE) to avoid recomputation while improving parallel hardware utilization. We find that modern reasoning-capable LLMs can perform inference with shared Key-Value cache out of the box, without additional fine-tuning.

Recently, long-thought reasoning LLMs, such as OpenAI's O1, adopt extended reasoning processes similar to how humans ponder over complex problems. This reasoning paradigm significantly enhances the model's problem-solving abilities and has achieved promising results. However, long-thought reasoning process leads to a substantial increase in inference time. A pressing challenge is reducing the inference overhead of long-thought LLMs while ensuring accuracy. In this paper, we experimentally demonstrate that long-thought reasoning models struggle to effectively allocate token budgets based on problem difficulty and reasoning redundancies. To address this, we propose Length-Harmonizing Fine-Tuning (O1-Pruner), aiming at minimizing reasoning overhead while maintaining accuracy. This effective fine-tuning method first estimates the LLM's baseline performance through pre-sampling and then uses RL-style fine-tuning to encourage the model to generate shorter reasoning processes under accuracy constraints. This allows the model to achieve efficient reasoning with lower redundancy while maintaining accuracy. Experiments on various mathematical reasoning benchmarks show that O1-Pruner not only significantly reduces inference overhead but also achieves higher accuracy, providing a novel and promising solution to this challenge. Our code is coming soon at https://github.com/StarDewXXX/O1-Pruner

Self-awareness, i.e., the ability to assess and correct one's own generation, is a fundamental aspect of human intelligence, making its replication in large language models (LLMs) an important yet challenging task. Previous works tackle this by employing extensive reinforcement learning or rather relying on large external verifiers. In this work, we propose Refine via Intrinsic Self-Verification (ReVISE), an efficient and effective framework that enables LLMs to self-correct their outputs through self-verification. The core idea of ReVISE is to enable LLMs to verify their reasoning processes and continually rethink reasoning trajectories based on its verification. We introduce a structured curriculum based upon online preference learning to implement this efficiently. Specifically, as ReVISE involves two challenging tasks (i.e., self-verification and reasoning correction), we tackle each task sequentially using curriculum learning, collecting both failed and successful reasoning paths to construct preference pairs for efficient training. During inference, our approach enjoys natural test-time scaling by integrating self-verification and correction capabilities, further enhanced by our proposed confidence-aware decoding mechanism. Our experiments on various reasoning tasks demonstrate that ReVISE achieves efficient self-correction and significantly improves reasoning performance.

Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in programming languages, type-and-effect systems did not yet gain widespread adoption. One reason for this is that type-and-effect systems are more complex and the existing inference algorithms make compromises between expressiveness, intuitiveness, and decidability. In this work, we present an effect inference algorithm for a type-and-effect system with subtyping, expressive higher-rank polymorphism, and intuitive set-like semantics of effects. In order to deal with scoping issues of higher-rank polymorphism, we delay solving of effect constraints by transforming them into formulae of propositional logic. We prove soundness and completeness of our algorithm with respect to a declarative type-and-effect system. All the presented results have been formalized in the Rocq proof assistant, and the algorithm has been successfully implemented in a realistic programming language.

Chain-of-Thought (CoT) prompting in large language models (LLMs) has shown promising performance on mathematical reasoning tasks. Recently, Self-Consistency samples a diverse set of reasoning chains with different answers and chooses the answer by majority voting. Though effective, its performance cannot be further improved by sampling more reasoning chains. To address this problem, we propose to integrate backward reasoning into answer verification. We first mask a number in the question by {bf x}. The LLM is then asked to predict the masked number with a candidate answer A embedded in the template: ``If we know the answer to the above question is {A}, what is the value of unknown variable {bf x}?'' The LLM is expected to predict the masked number successfully if the provided candidate answer is correct. To further improve performance, we propose FOBAR (FOrward-BAckward Reasoning) to combine forward and backward reasoning for verifying candidate answers. Experiments are performed on six standard mathematical data sets and three LLMs (text-davinci-003, GPT-3.5-Turbo, GPT-4). Results show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency which uses forward reasoning alone, demonstrating that combining forward and forward reasoning is better. It also outperforms existing verification methods, verifying the effectiveness of using the simple template in backward reasoning and the proposed combination.

With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance reasoning performance without modifying model parameters or requiring additional training. However, these techniques come with implementation challenges, and most existing methods remain at the proof-of-concept stage with limited practical adoption due to their computational complexity and varying effectiveness across different tasks. In this paper, we investigate and benchmark diverse inference-time computation strategies across reasoning tasks of varying complexity. Since most current methods rely on a proposer-verifier pipeline that first generates candidate solutions (e.g., reasoning solutions) and then selects the best one based on reward signals (e.g., RLHF rewards, process rewards), our research focuses on optimizing both candidate solution generation (e.g., instructing prompts, hyperparameters such as temperature and top-p) and reward mechanisms (e.g., self-evaluation, reward types). Through extensive experiments (more than 20,000 A100-80G GPU hours with over 1,000 experiments) across a variety of models (e.g., Llama, Qwen, and Mistral families) of various sizes, our ablation studies reveal that previously overlooked strategies can significantly enhance performance (e.g., tuning temperature can improve reasoning task performance by up to 5%). Furthermore, we establish a standardized benchmark for inference-time computation by systematically evaluating six representative methods across eight reasoning tasks. These findings provide a stronger foundation for future research. The code is available at https://github.com/usail-hkust/benchmark_inference_time_computation_LLM

Despite their remarkable success in complex tasks propelling widespread adoption, large language-model-based agents still face critical deployment challenges due to prohibitive latency and inference costs. While recent work has explored various methods to accelerate inference, existing approaches suffer from significant limitations: they either fail to preserve performance fidelity, require extensive offline training of router modules, or incur excessive operational costs. Moreover, they provide minimal user control over the tradeoff between acceleration and other performance metrics. To address these gaps, we introduce Dynamic Speculative Planning (DSP), an asynchronous online reinforcement learning framework that provides lossless acceleration with substantially reduced costs without requiring additional pre-deployment preparation. DSP explicitly optimizes a joint objective balancing end-to-end latency against dollar cost, allowing practitioners to adjust a single parameter that steers the system toward faster responses, cheaper operation, or any point along this continuum. Experiments on two standard agent benchmarks demonstrate that DSP achieves comparable efficiency to the fastest lossless acceleration method while reducing total cost by 30% and unnecessary cost up to 60%. Our code and data are available through https://github.com/guanyilin428/Dynamic-Speculative-Planning.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.

Privacy estimation techniques for differentially private (DP) algorithms are useful for comparing against analytical bounds, or to empirically measure privacy loss in settings where known analytical bounds are not tight. However, existing privacy auditing techniques usually make strong assumptions on the adversary (e.g., knowledge of intermediate model iterates or the training data distribution), are tailored to specific tasks, model architectures, or DP algorithm, and/or require retraining the model many times (typically on the order of thousands). These shortcomings make deploying such techniques at scale difficult in practice, especially in federated settings where model training can take days or weeks. In this work, we present a novel ``one-shot'' approach that can systematically address these challenges, allowing efficient auditing or estimation of the privacy loss of a model during the same, single training run used to fit model parameters, and without requiring any a priori knowledge about the model architecture, task, or DP training algorithm. We show that our method provides provably correct estimates for the privacy loss under the Gaussian mechanism, and we demonstrate its performance on well-established FL benchmark datasets under several adversarial threat models.

The goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees for generalization without further assumptions, in practice we observe that simple models which explain the training data generalize best: a principle called Occam's razor. Despite the need for simple models, most current approaches in machine learning only minimize the training error, and at best indirectly promote simplicity through regularization or architecture design. Here, we draw a connection between Occam's razor and in-context learning: an emergent ability of certain sequence models like Transformers to learn at inference time from past observations in a sequence. In particular, we show that the next-token prediction loss used to train in-context learners is directly equivalent to a data compression technique called prequential coding, and that minimizing this loss amounts to jointly minimizing both the training error and the complexity of the model that was implicitly learned from context. Our theory and the empirical experiments we use to support it not only provide a normative account of in-context learning, but also elucidate the shortcomings of current in-context learning methods, suggesting ways in which they can be improved. We make our code available at https://github.com/3rdCore/PrequentialCode.

While inference-time scaling enables LLMs to carry out increasingly long and capable reasoning traces, the patterns and insights uncovered during these traces are immediately discarded once the context window is reset for a new query. External memory is a natural way to persist these discoveries, and recent work has shown clear benefits for reasoning-intensive tasks. We see an opportunity to make such memories more broadly reusable and scalable by moving beyond instance-based memory entries (e.g. exact query/response pairs, or summaries tightly coupled with the original problem context) toward concept-level memory: reusable, modular abstractions distilled from solution traces and stored in natural language. For future queries, relevant concepts are selectively retrieved and integrated into the prompt, enabling test-time continual learning without weight updates. Our design introduces new strategies for abstracting takeaways from rollouts and retrieving entries for new queries, promoting reuse and allowing memory to expand with additional experiences. We evaluate on ARC-AGI, a benchmark that stresses compositional generalization and abstract reasoning, making it a natural fit for concept memory. Our method yields a 7.5% relative gain over a strong no-memory baseline with performance continuing to scale with inference compute. We find abstract concepts to be the most consistent memory design, outscoring the baseline at all tested inference compute scales. Moreover, dynamically updating memory during test-time outperforms fixed settings, supporting the hypothesis that accumulating and abstracting patterns enables further solutions in a form of self-improvement. Code is available at https://github.com/matt-seb-ho/arc_memo.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Diffusion-based Large Language Models (dLLMs) have emerged as a competitive alternative to autoregressive models, offering unique advantages through bidirectional attention and parallel generation paradigms. However, the generation results of current parallel decoding methods deviate from stepwise decoding, introducing potential performance degradation, which limits their practical deployment. To address this problem, we propose Self Speculative Decoding (SSD), a lossless inference acceleration method that leverages the dLLM itself as both speculative decoding drafter and verifier without auxiliary modules. SSD introduces a self-drafting mechanism where the model generates predictions for multiple positions, then verifies them through hierarchical verification trees in a single forward pass. Unlike traditional speculative decoding that requires separate draft models, SSD eliminates model redundancy and memory overhead by exploiting the dLLM's inherent parallel prediction capability for multiple positions. This self-speculative approach allows the model to progressively verify and accept multiple tokens in a single forward pass. Our experiments demonstrate that SSD achieves up to 3.46times speedup while keeping the output identical to stepwise decoding on open source models such as LLaDA and Dream. Code will be made publicly available on GitHub.

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

Transferring reasoning capabilities from larger language models to smaller ones through supervised fine-tuning often fails counterintuitively, with performance degrading despite access to high-quality teacher demonstrations. We identify that this failure stems from distributional misalignment: reasoning traces from larger models contain tokens that are low probability under the student's distribution, exceeding the internal representation capacity of smaller architectures and creating learning barriers rather than helpful guidance. We propose Reverse Speculative Decoding (RSD), a mechanism for generating student-friendly reasoning traces in which the teacher model proposes candidate tokens but the student model determines acceptance based on its own probability distributions, filtering low probability tokens. When applied to Qwen3-0.6B, direct distillation of s1K-1.1 reasoning trace data degrades average performance across major reasoning benchmarks by 20.5\%, while the same model trained on RSD-generated reasoning traces achieves meaningful improvements of 4.9\%. Our analysis reveals that low probability tokens constitute the critical bottleneck in reasoning ability transfer. However, cross-model experiments demonstrate that RSD traces are model-specific rather than universally applicable, indicating that distributional alignment must be tailored for each student architecture's unique internal representation.

The largest experiments in machine learning now require resources far beyond the budget of all but a few institutions. Fortunately, it has recently been shown that the results of these huge experiments can often be extrapolated from the results of a sequence of far smaller, cheaper experiments. In this work, we show that not only can the extrapolation be done based on the size of the model, but on the size of the problem as well. By conducting a sequence of experiments using AlphaZero and Hex, we show that the performance achievable with a fixed amount of compute degrades predictably as the game gets larger and harder. Along with our main result, we further show that the test-time and train-time compute available to an agent can be traded off while maintaining performance.

Diffusion language models, as a promising alternative to traditional autoregressive (AR) models, enable faster generation and richer conditioning on bidirectional context. However, they suffer from a key discrepancy between training and inference: during inference, MDLMs progressively reveal the structure of the generated sequence by producing fewer and fewer masked tokens, whereas this structure is ignored in training as tokens are masked at random. Although this discrepancy between training and inference can lead to suboptimal performance, it has been largely overlooked by previous works, leaving closing this gap between the two stages an open problem. To address this, we frame the problem of learning effective denoising trajectories as a sequential decision-making problem and use the resulting framework to apply reinforcement learning. We propose a novel Masked Diffusion Policy Optimization (MDPO) to exploit the Markov property diffusion possesses and explicitly train the model under the same progressive refining schedule used at inference. MDPO matches the performance of the previous state-of-the-art (SOTA) method with 60x fewer gradient updates, while achieving average improvements of 9.6% on MATH500 and 54.2% on Countdown over SOTA when trained within the same number of weight updates. Additionally, we improve the remasking strategy of MDLMs as a plug-in inference replacement to overcome the limitation that the model cannot refine tokens flexibly. This simple yet effective training-free strategy, what we refer to as RCR, consistently improves performance and yields additional gains when combined with MDPO. Our findings establish great potential for investigating the discrepancy between pre-training and inference of MDLMs. Code: https://github.com/autonomousvision/mdpo. Project Page: https://cli212.github.io/MDPO/.

Although Large Vision-Language Models (LVLMs) have achieved impressive results, their high computational cost poses a significant barrier to wider application. To enhance inference efficiency, most existing approaches depend on parameter-dependent or token-dependent strategies to reduce computational demands. However, these methods typically require complex training processes and struggle to consistently select the most relevant tokens. In this paper, we systematically analyze the above challenges and provide a series of valuable insights for inference acceleration. Based on these findings, we propose a novel framework, the Pruning All-Rounder (PAR). Different from previous works, PAR develops a meta-router to adaptively organize pruning flows across both tokens and layers. With a self-supervised learning manner, our method achieves a superior balance between performance and efficiency. Notably, PAR is highly flexible, offering multiple pruning versions to address a range of pruning scenarios. The code for this work will be made publicly available.

Inference-Time Scaling (ITS) improves language models by allocating more computation at generation time. Particle Filtering (PF) has emerged as a strong ITS method for complex mathematical reasoning tasks, but it is vulnerable when guided by process reward models, which often assign overconfident scores early in the reasoning process. This causes PF to suffer from premature exploitation: it myopically commits to locally promising trajectories, prunes potentially correct hypotheses, and converges to suboptimal solutions. This failure mode, known as particle impoverishment, is especially severe under constrained computational budgets. To address this, we analyze the problem and identify two root causes: a lack of diversity in the particle set due to overconfident resampling and consequent inability to assess the potential of a reasoning path. We introduce Entropic Particle Filtering (ePF), an algorithm that integrates two new techniques to solve these issues. The first technique, Entropic Annealing (EA), directly mitigates particle impoverishment by monitoring search diversity via entropy; when diversity drops, it intervenes by dynamically annealing the resampling distribution to preserve exploration. The second, an enhancement called Look-ahead Modulation (LaM), adds a predictive guide to evaluate a state's potential based on its successors. On several challenging math benchmarks, ePF significantly outperforms strong baselines and achieves up to a 50 % relative improvement in task reward. Together, these methods improve PF's resilience by balancing the exploration of diverse solution spaces with the exploitation of high-reward regions, ultimately leading to higher-quality solutions.

Despite their strong performance on reasoning tasks, large reasoning models (LRMs) often suffer from overthinking, producing unnecessarily long outputs and incurring high end-to-end latency, a significant limitation to their real-world deployment. To address overthinking, early-exit mechanisms have been proposed to terminate reasoning before typical completion, showing that this approach can effectively shorten generation length with minimal impact on accuracy. However, their reliance on probing mechanisms introduces a detection overhead that limits their end-to-end latency gains and compromises their generalizability across diverse problems. Inspired by the use of hidden states in speculative decoding, we propose SpecExit, a novel framework that predicts both future tokens and an early-exit signal directly from a lightweight draft model without probing overhead. Our method offers significant improvements, reducing average generation length by 66\% and achieving a 2.5x speedup in end-to-end latency compared to the speculative decoding baseline, without compromising accuracy. Our method leverages the inherent signals from hidden states to provide effective early-exit signals, suggesting broader use of hidden states for efficient reasoning. Our code is available at https://github.com/Tencent/AngelSlim.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

We introduce a deterministic variational formulation for training Bayesian last layer neural networks. This yields a sampling-free, single-pass model and loss that effectively improves uncertainty estimation. Our variational Bayesian last layer (VBLL) can be trained and evaluated with only quadratic complexity in last layer width, and is thus (nearly) computationally free to add to standard architectures. We experimentally investigate VBLLs, and show that they improve predictive accuracy, calibration, and out of distribution detection over baselines across both regression and classification. Finally, we investigate combining VBLL layers with variational Bayesian feature learning, yielding a lower variance collapsed variational inference method for Bayesian neural networks.

Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model is complex. This paper uses iterates of a specially designed stochastic optimization algorithm as draws from which both point estimates and bootstrap standard errors can be computed in a single run. The draws are generated by the gradient and Hessian computed from batches of data that are resampled at each iteration. We show that these draws yield consistent estimates and asymptotically valid frequentist inference for a large class of regular problems. The algorithm provides accurate standard errors in simulation examples and empirical applications at low computational costs. The draws from the algorithm also provide a convenient way to detect data irregularities.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

Diffusion-based large language models (dLLMs) are trained flexibly to model extreme dependence in the data distribution; however, how to best utilize this information at inference time remains an open problem. In this work, we uncover an interesting property of these models: dLLMs trained on textual data implicitly learn a mixture of semi-autoregressive experts, where different generation orders reveal different specialized behaviors. We show that committing to any single, fixed inference time schedule, a common practice, collapses performance by failing to leverage this latent ensemble. To address this, we introduce HEX (Hidden semiautoregressive EXperts for test-time scaling), a training-free inference method that ensembles across heterogeneous block schedules. By doing a majority vote over diverse block-sized generation paths, HEX robustly avoids failure modes associated with any single fixed schedule. On reasoning benchmarks such as GSM8K, it boosts accuracy by up to 3.56X (from 24.72% to 88.10%), outperforming top-K margin inference and specialized fine-tuned methods like GRPO, without additional training. HEX even yields significant gains on MATH benchmark from 16.40% to 40.00%, scientific reasoning on ARC-C from 54.18% to 87.80%, and TruthfulQA from 28.36% to 57.46%. Our results establish a new paradigm for test-time scaling in diffusion-based LLMs (dLLMs), revealing that the sequence in which masking is performed plays a critical role in determining performance during inference.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning. Our method first trains an unconditional discretization-agnostic denoising model using neural operator architectures. At inference, we refine the samples to satisfy sparse observation data via a gradient-based guidance mechanism. Through rigorous mathematical analysis, we extend Tweedie's formula to infinite-dimensional Hilbert spaces, providing the theoretical foundation for our posterior sampling approach. Our method (FunDPS) accurately captures posterior distributions in function spaces under minimal supervision and severe data scarcity. Across five PDE tasks with only 3% observation, our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https://github.com/neuraloperator/FunDPS

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Inference-time scaling techniques have significantly bolstered the reasoning capabilities of large language models (LLMs) by harnessing additional computational effort at inference without retraining. Similarly, Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy by generating rich intermediate reasoning trajectories, but these approaches incur substantial token costs that impede their deployment in latency-sensitive settings. In this work, we first show that truncated CoT, which stops reasoning before completion and directly generates the final answer, often matches full CoT sampling while using dramatically fewer tokens. Building on this insight, we introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling along three orthogonal axes: (1) the number of reasoning trajectories, (2) the number of final solutions per trajectory, and (3) the depth at which reasoning traces are truncated. Through extensive experiments on five diverse reasoning benchmarks and several model scales, we demonstrate that Fractured Sampling consistently achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling gains in Pass@k versus token budget. Our analysis reveals how to allocate computation across these dimensions to maximize performance, paving the way for more efficient and scalable LLM reasoning.

We present Klear-Reasoner, a model with long reasoning capabilities that demonstrates careful deliberation during problem solving, achieving outstanding performance across multiple benchmarks. Although there are already many excellent works related to inference models in the current community, there are still many problems with reproducing high-performance inference models due to incomplete disclosure of training details. This report provides an in-depth analysis of the reasoning model, covering the entire post-training workflow from data preparation and long Chain-of-Thought supervised fine-tuning (long CoT SFT) to reinforcement learning (RL), along with detailed ablation studies for each experimental component. For SFT data, our experiments show that a small number of high-quality data sources are more effective than a large number of diverse data sources, and that difficult samples can achieve better results without accuracy filtering. In addition, we investigate two key issues with current clipping mechanisms in RL: Clipping suppresses critical exploration signals and ignores suboptimal trajectories. To address these challenges, we propose Gradient-Preserving clipping Policy Optimization (GPPO) that gently backpropagates gradients from clipped tokens. GPPO not only enhances the model's exploration capacity but also improves its efficiency in learning from negative samples. Klear-Reasoner exhibits exceptional reasoning abilities in mathematics and programming, scoring 90.5\% on AIME 2024, 83.2\% on AIME 2025, 66.0\% on LiveCodeBench V5 and 58.1\% on LiveCodeBench V6.

Recent advances in inference-time compute have significantly improved performance on complex tasks by generating long chains of thought (CoTs) using Large Reasoning Models (LRMs). However, this improved accuracy comes at the cost of high inference latency due to the length of generated reasoning sequences and the autoregressive nature of decoding. Our key insight in tackling these overheads is that LRM inference, and the reasoning that it embeds, is highly tolerant of approximations: complex tasks are typically broken down into simpler steps, each of which brings utility based on the semantic insight it provides for downstream steps rather than the exact tokens it generates. Accordingly, we introduce SpecReason, a system that automatically accelerates LRM inference by using a lightweight model to (speculatively) carry out simpler intermediate reasoning steps and reserving the costly base model only to assess (and potentially correct) the speculated outputs. Importantly, SpecReason's focus on exploiting the semantic flexibility of thinking tokens in preserving final-answer accuracy is complementary to prior speculation techniques, most notably speculative decoding, which demands token-level equivalence at each step. Across a variety of reasoning benchmarks, SpecReason achieves 1.5-2.5times speedup over vanilla LRM inference while improving accuracy by 1.0-9.9\%. Compared to speculative decoding without SpecReason, their combination yields an additional 19.4-44.2\% latency reduction. We open-source SpecReason at https://github.com/ruipeterpan/specreason.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

Large Language Models (LLMs) are increasingly being used to simulate human-like decision making in agent-based financial market models (ABMs). As models become more powerful and accessible, researchers can now incorporate individual LLM decisions into ABM environments. However, integration may introduce inherent biases that need careful evaluation. In this paper we test three state-of-the-art GPT models for bias using two model sampling approaches: one-shot and few-shot API queries. We observe significant variations in distributions of outputs between specific models, and model sub versions, with GPT-4o-Mini-2024-07-18 showing notably better performance (32-43% yes responses) compared to GPT-4-0125-preview's extreme bias (98-99% yes responses). We show that sampling methods and model sub-versions significantly impact results: repeated independent API calls produce different distributions compared to batch sampling within a single call. While no current GPT model can simultaneously achieve a uniform distribution and Markovian properties in one-shot testing, few-shot sampling can approach uniform distributions under certain conditions. We explore the Temperature parameter, providing a definition and comparative results. We further compare our results to true random binary series and test specifically for the common human bias of Negative Recency - finding LLMs have a mixed ability to 'beat' humans in this one regard. These findings emphasise the critical importance of careful LLM integration into ABMs for financial markets and more broadly.

Large Reasoning Models (LRMs) have demonstrated remarkable performance on tasks such as mathematics and code generation. Motivated by these strengths, recent work has empirically demonstrated the effectiveness of LRMs as guard models in improving harmful query detection. However, LRMs typically generate long reasoning traces during inference, causing substantial computational overhead. In this paper, we introduce PSRT, a method that replaces the model's reasoning process with a Prefilled Safe Reasoning Trace, thereby significantly reducing the inference cost of LRMs. Concretely, PSRT prefills "safe reasoning virtual tokens" from a constructed dataset and learns over their continuous embeddings. With the aid of indicator tokens, PSRT enables harmful-query detection in a single forward pass while preserving the classification effectiveness of LRMs. We evaluate PSRT on 7 models, 13 datasets, and 8 jailbreak methods. In terms of efficiency, PSRT completely removes the overhead of generating reasoning tokens during inference. In terms of classification performance, PSRT achieves nearly identical accuracy, with only a minor average F1 drop of 0.015 across 7 models and 5 datasets.

Variational inference (VI) seeks to approximate a target distribution pi by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates pi by minimizing the Kullback-Leibler (KL) divergence to pi over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when pi is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when pi is only log-smooth.

The integration of machine learning (ML) in numerous critical applications introduces a range of privacy concerns for individuals who provide their datasets for model training. One such privacy risk is Membership Inference (MI), in which an attacker seeks to determine whether a particular data sample was included in the training dataset of a model. Current state-of-the-art MI attacks capitalize on access to the model's predicted confidence scores to successfully perform membership inference, and employ data poisoning to further enhance their effectiveness. In this work, we focus on the less explored and more realistic label-only setting, where the model provides only the predicted label on a queried sample. We show that existing label-only MI attacks are ineffective at inferring membership in the low False Positive Rate (FPR) regime. To address this challenge, we propose a new attack Chameleon that leverages a novel adaptive data poisoning strategy and an efficient query selection method to achieve significantly more accurate membership inference than existing label-only attacks, especially at low FPRs.

Large language models (LLMs) have proven to be very capable, but access to the best models currently rely on inference providers which introduces trust challenges -- how can we be sure that the provider is using the model configuration they claim? We propose TOPLOC, a novel method for verifiable inference that addresses this problem. TOPLOC leverages a compact locality sensitive hashing mechanism for intermediate activations which can detect unauthorized modifications to models, prompts, or precision with 100% accuracy, achieving no false positives or negatives in our empirical evaluations. Our approach is robust across diverse hardware configurations, GPU types, and algebraic reorderings, which allows for validation speeds significantly faster than the original inference. By introducing a polynomial encoding scheme, TOPLOC minimizes memory overhead of the generated commits by 1000times, requiring only 258 bytes of storage per 32 new tokens compared to the 262KB requirement of storing the token embeddings directly for Llama-3.1-8B-Instruct. Our method empowers users to verify LLM inference computations efficiently, fostering greater trust and transparency in open ecosystems and lays a foundation for decentralized and verifiable AI services.

We introduce and study the problem of detecting whether an agent is updating their prior beliefs given new evidence in an optimal way that is Bayesian, or whether they are biased towards their own prior. In our model, biased agents form posterior beliefs that are a convex combination of their prior and the Bayesian posterior, where the more biased an agent is, the closer their posterior is to the prior. Since we often cannot observe the agent's beliefs directly, we take an approach inspired by information design. Specifically, we measure an agent's bias by designing a signaling scheme and observing the actions they take in response to different signals, assuming that they are maximizing their own expected utility; our goal is to detect bias with a minimum number of signals. Our main results include a characterization of scenarios where a single signal suffices and a computationally efficient algorithm to compute optimal signaling schemes.

In this paper, we introduce a conformal prediction method to construct prediction sets in a oneshot federated learning setting. More specifically, we define a quantile-of-quantiles estimator and prove that for any distribution, it is possible to output prediction sets with desired coverage in only one round of communication. To mitigate privacy issues, we also describe a locally differentially private version of our estimator. Finally, over a wide range of experiments, we show that our method returns prediction sets with coverage and length very similar to those obtained in a centralized setting. Overall, these results demonstrate that our method is particularly well-suited to perform conformal predictions in a one-shot federated learning setting.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

Membership Inference Attacks (MIAs) have emerged as a valuable framework for evaluating privacy leakage by machine learning models. Score-based MIAs are distinguished, in particular, by their ability to exploit the confidence scores that the model generates for particular inputs. Existing score-based MIAs implicitly assume that the adversary has access to the target model's hyperparameters, which can be used to train the shadow models for the attack. In this work, we demonstrate that the knowledge of target hyperparameters is not a prerequisite for MIA in the transfer learning setting. Based on this, we propose a novel approach to select the hyperparameters for training the shadow models for MIA when the attacker has no prior knowledge about them by matching the output distributions of target and shadow models. We demonstrate that using the new approach yields hyperparameters that lead to an attack near indistinguishable in performance from an attack that uses target hyperparameters to train the shadow models. Furthermore, we study the empirical privacy risk of unaccounted use of training data for hyperparameter optimization (HPO) in differentially private (DP) transfer learning. We find no statistically significant evidence that performing HPO using training data would increase vulnerability to MIA.

Decoder-only Transformers often struggle with complex reasoning tasks, particularly arithmetic reasoning requiring multiple sequential operations. In this work, we identify representation collapse in the model's intermediate layers as a key factor limiting their reasoning capabilities. To address this, we propose Sequential Variance-Covariance Regularization (Seq-VCR), which enhances the entropy of intermediate representations and prevents collapse. Combined with dummy pause tokens as substitutes for chain-of-thought (CoT) tokens, our method significantly improves performance in arithmetic reasoning problems. In the challenging 5 times 5 integer multiplication task, our approach achieves 99.5% exact match accuracy, outperforming models of the same size (which yield 0% accuracy) and GPT-4 with five-shot CoT prompting (44%). We also demonstrate superior results on arithmetic expression and longest increasing subsequence (LIS) datasets. Our findings highlight the importance of preventing intermediate layer representation collapse to enhance the reasoning capabilities of Transformers and show that Seq-VCR offers an effective solution without requiring explicit CoT supervision.

Reasoning and inference are central to human and artificial intelligence. Modeling inference in human language is very challenging. With the availability of large annotated data (Bowman et al., 2015), it has recently become feasible to train neural network based inference models, which have shown to be very effective. In this paper, we present a new state-of-the-art result, achieving the accuracy of 88.6% on the Stanford Natural Language Inference Dataset. Unlike the previous top models that use very complicated network architectures, we first demonstrate that carefully designing sequential inference models based on chain LSTMs can outperform all previous models. Based on this, we further show that by explicitly considering recursive architectures in both local inference modeling and inference composition, we achieve additional improvement. Particularly, incorporating syntactic parsing information contributes to our best result---it further improves the performance even when added to the already very strong model.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

The growth of the Machine-Learning-As-A-Service (MLaaS) market has highlighted clients' data privacy and security issues. Private inference (PI) techniques using cryptographic primitives offer a solution but often have high computation and communication costs, particularly with non-linear operators like ReLU. Many attempts to reduce ReLU operations exist, but they may need heuristic threshold selection or cause substantial accuracy loss. This work introduces AutoReP, a gradient-based approach to lessen non-linear operators and alleviate these issues. It automates the selection of ReLU and polynomial functions to speed up PI applications and introduces distribution-aware polynomial approximation (DaPa) to maintain model expressivity while accurately approximating ReLUs. Our experimental results demonstrate significant accuracy improvements of 6.12% (94.31%, 12.9K ReLU budget, CIFAR-10), 8.39% (74.92%, 12.9K ReLU budget, CIFAR-100), and 9.45% (63.69%, 55K ReLU budget, Tiny-ImageNet) over current state-of-the-art methods, e.g., SNL. Morever, AutoReP is applied to EfficientNet-B2 on ImageNet dataset, and achieved 75.55% accuracy with 176.1 times ReLU budget reduction.

We study privacy leakage in the reasoning traces of large reasoning models used as personal agents. Unlike final outputs, reasoning traces are often assumed to be internal and safe. We challenge this assumption by showing that reasoning traces frequently contain sensitive user data, which can be extracted via prompt injections or accidentally leak into outputs. Through probing and agentic evaluations, we demonstrate that test-time compute approaches, particularly increased reasoning steps, amplify such leakage. While increasing the budget of those test-time compute approaches makes models more cautious in their final answers, it also leads them to reason more verbosely and leak more in their own thinking. This reveals a core tension: reasoning improves utility but enlarges the privacy attack surface. We argue that safety efforts must extend to the model's internal thinking, not just its outputs.

Can a mere next-token predictor faithfully model human intelligence? We crystallize this intuitive concern, which is fragmented in the literature. As a starting point, we argue that the two often-conflated phases of next-token prediction -- autoregressive inference and teacher-forced training -- must be treated distinctly. The popular criticism that errors can compound during autoregressive inference, crucially assumes that teacher-forcing has learned an accurate next-token predictor. This assumption sidesteps a more deep-rooted problem we expose: in certain classes of tasks, teacher-forcing can simply fail to learn an accurate next-token predictor in the first place. We describe a general mechanism of how teacher-forcing can fail, and design a minimal planning task where both the Transformer and the Mamba architecture empirically fail in that manner -- remarkably, despite the task being straightforward to learn. We provide preliminary evidence that this failure can be resolved when training to predict multiple tokens in advance. We hope this finding can ground future debates and inspire explorations beyond the next-token prediction paradigm. We make our code available under https://github.com/gregorbachmann/Next-Token-Failures

Existing chain-of-thought (CoT) distillation methods can effectively transfer reasoning abilities to base models but suffer from two major limitations: excessive verbosity of reasoning traces and inadequate adaptability to problem difficulty. Long reasoning traces significantly increase inference costs, and uniform-length solutions prevent base models from learning adaptive reasoning strategies. To address these issues, we propose a difficulty-aware prompting (DAP) method to dynamically shorten reasoning traces without performance loss. In our approach, a large teacher model first judges each problem's difficulty and then rewrites its reasoning traces to an appropriate shorter length, yielding concise yet complete reasoning traces. Leveraging the DAP pipeline, we curate a distilled dataset called LiteCoT consisting of 100K concise reasoning examples, with solutions averaging only 720 tokens (an order of magnitude shorter than typical CoTs). Using LiteCoT, we distilled a new family of reasoning models called Liter (1.5B, 7B, and 32B) based on the Qwen2.5 architecture. Experiments show that a student model fine-tuned on just 100K of these difficulty-pruned CoT samples outperforms a model distilled on 800K original Long CoT samples, while significantly reducing training and inference costs. Our method also generalizes well: across 11 diverse benchmarks, the shorter difficulty-aware CoTs achieve equal or better accuracy than Long chains, using far fewer tokens. For example, on the challenging AIME24 exam, our approach reaches 74.2% Pass@1 using only about 5K inference tokens, surpassing other methods that consume many more tokens. Our code and data are available at https://github.com/Evanwu1125/LiteCoT.

Large Language Models (LLMs) have showcased remarkable capabilities across various domains. Accompanying the evolving capabilities and expanding deployment scenarios of LLMs, their deployment challenges escalate due to their sheer scale and the advanced yet complex activation designs prevalent in notable model series, such as Llama, Gemma, and Mistral. These challenges have become particularly pronounced in resource-constrained deployment scenarios, where mitigating inference efficiency bottlenecks is imperative. Among various recent efforts, activation approximation has emerged as a promising avenue for pursuing inference efficiency, sometimes considered indispensable in applications such as private inference. Despite achieving substantial speedups with minimal impact on utility, even appearing sound and practical for real-world deployment, the safety implications of activation approximations remain unclear. In this work, we fill this critical gap in LLM safety by conducting the first systematic safety evaluation of activation approximations. Our safety vetting spans seven sota techniques across three popular categories, revealing consistent safety degradation across ten safety-aligned LLMs.

Recent advances in synthetic data generation (SDG) have been hailed as a solution to the difficult problem of sharing sensitive data while protecting privacy. SDG aims to learn statistical properties of real data in order to generate "artificial" data that are structurally and statistically similar to sensitive data. However, prior research suggests that inference attacks on synthetic data can undermine privacy, but only for specific outlier records. In this work, we introduce a new attribute inference attack against synthetic data. The attack is based on linear reconstruction methods for aggregate statistics, which target all records in the dataset, not only outliers. We evaluate our attack on state-of-the-art SDG algorithms, including Probabilistic Graphical Models, Generative Adversarial Networks, and recent differentially private SDG mechanisms. By defining a formal privacy game, we show that our attack can be highly accurate even on arbitrary records, and that this is the result of individual information leakage (as opposed to population-level inference). We then systematically evaluate the tradeoff between protecting privacy and preserving statistical utility. Our findings suggest that current SDG methods cannot consistently provide sufficient privacy protection against inference attacks while retaining reasonable utility. The best method evaluated, a differentially private SDG mechanism, can provide both protection against inference attacks and reasonable utility, but only in very specific settings. Lastly, we show that releasing a larger number of synthetic records can improve utility but at the cost of making attacks far more effective.

Large language models (LLMs) are typically prompted to follow a single instruction per inference call. In this work, we analyze whether LLMs also hold the capability to handle multiple instructions simultaneously, denoted as Multi-Task Inference. For this purpose, we introduce the MTI Bench(Multi-Task Inference Benchmark), a comprehensive evaluation benchmark encompassing 5,000 instances across 25 tasks. Each task in the MTI Bench involves 2 to 3 sub-tasks. As expected, we first demonstrate that Multi-Task Inference reduces the total inference time by 1.46 times in average since it does not require multiple inference calls. Interestingly, contrary to the expectation that LLMs would perform better when tasks are divided, we find that state-of-the-art LLMs, such as Llama-2-Chat-70B and GPT-4, show up to 7.3% and 12.4% improved performance with Multi-Task Inference compared to Single-Task Inference on the MTI Bench. We release the MTI Bench dataset and our code at this link https://github.com/guijinSON/MTI-Bench.

Large reasoning models (LRMs) generate intermediate reasoning traces before producing final answers, yielding strong gains on multi-step and mathematical tasks. Yet aligning LRMs with human preferences, a crucial prerequisite for model deployment, remains underexplored. The statistically correct objective for preference alignment requires marginalizing over reasoning traces, but this computation is intractable in practice. A common workaround optimizes a single sampled trajectory, which introduces substantial gradient variance from stochastic trace sampling. To address this challenge, we frame preference optimization for LRMs through the lens of the bias--variance trade-off and propose Bias--Variance Optimized Preference Optimization (BVPO), a simple, drop-in method that mixes two gradient estimators: a high-variance trace-based estimator and a low-variance empty-trace estimator obtained by disabling reasoning trace generation. Our theory shows that BVPO strictly reduces trace-induced variance for any nontrivial mixture, provides a closed-form choice of the mixing weight that minimizes mean-squared error relative to the true marginal gradient, and under standard smoothness and step-size conditions, tightens classical convergence bounds for stochastic gradient descent. Empirically, BVPO improves alignment over the best baseline by up to 7.8 points on AlpacaEval~2 and 6.8 points on Arena-Hard. Despite being trained only on general conversational data, BVPO also boosts reasoning performance for base models by up to 4.0 points on the average of six math reasoning benchmarks. These results identify variance from trace sampling as a key bottleneck and demonstrate that directly optimizing the bias--variance trade-off yields more stable training and stronger overall performance.

Recent advances in one-step generative models typically follow a two-stage process: first training a teacher diffusion model and then distilling it into a one-step student model. This distillation process traditionally relies on both the teacher model's score function to compute the distillation loss and its weights for student initialization. In this paper, we explore whether one-step generative models can be trained directly without this distillation process. First, we show that the teacher's score function is not essential and propose a family of distillation methods that achieve competitive results without relying on score estimation. Next, we demonstrate that initialization from teacher weights is indispensable in successful training. Surprisingly, we find that this benefit is not due to improved ``input-output" mapping but rather the learned feature representations, which dominate distillation quality. Our findings provide a better understanding of the role of initialization in one-step model training and its impact on distillation quality.

Recent advancements in large language models (LLMs) have shifted focus toward scaling inference-time compute, improving performance without retraining the model. A common approach is to sample multiple outputs in parallel, and select one of these as the final output. However, work to date has focused on English and a handful of domains such as math and code. In contrast, we are most interested in techniques that generalize across open-ended tasks, formally verifiable tasks, and across languages. In this work, we study how to robustly scale inference-time compute for open-ended generative tasks in a multilingual, multi-task setting. Our findings show that both sampling strategy based on temperature variation and selection strategy must be adapted to account for diverse domains and varied language settings. We evaluate existing selection methods, revealing that strategies effective in English often fail to generalize across languages. We propose novel sampling and selection strategies specifically adapted for multilingual and multi-task inference scenarios, and show they yield notable gains across languages and tasks. In particular, our combined sampling and selection methods lead to an average +6.8 jump in win-rates for our 8B models on m-ArenaHard-v2.0 prompts, against proprietary models such as Gemini. At larger scale, Command-A (111B model) equipped with our methods, shows +9.0 improvement in win-rates on the same benchmark with just five samples against single-sample decoding, a substantial increase at minimal cost. Our results underscore the need for language- and task-aware approaches to inference-time compute, aiming to democratize performance improvements in underrepresented languages.

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state rho and M unknown quantum measurements M_1,...,M_M with Kgeq 2 outcomes, estimating the probability distribution for applying M_i on rho to within total variation distance epsilon. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring O(Klog^2Mlog d/epsilon^4) copies of rho. We further prove an information-theoretic lower bound that at least Omega(min{d^2,K+log M}/epsilon^2) copies of rho are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

With increasing demands for efficiency, information retrieval has developed a branch of sparse retrieval, further advancing towards inference-free retrieval where the documents are encoded during indexing time and there is no model-inference for queries. Existing sparse retrieval models rely on FLOPS regularization for sparsification, while this mechanism was originally designed for Siamese encoders, it is considered to be suboptimal in inference-free scenarios which is asymmetric. Previous attempts to adapt FLOPS for inference-free scenarios have been limited to rule-based methods, leaving the potential of sparsification approaches for inference-free retrieval models largely unexplored. In this paper, we explore ell_0 inspired sparsification manner for inference-free retrievers. Through comprehensive out-of-domain evaluation on the BEIR benchmark, our method achieves state-of-the-art performance among inference-free sparse retrieval models and is comparable to leading Siamese sparse retrieval models. Furthermore, we provide insights into the trade-off between retrieval effectiveness and computational efficiency, demonstrating practical value for real-world applications.

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.

Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support embodied, adaptable, and energy-efficient autonomous agents. A central theory in this domain is predictive coding, which posits that learning and behaviour are driven by hierarchical probabilistic inferences about the causes of sensory inputs. Biological realism constrains these networks to rely on simple local computations in the form of precision-weighted predictions and prediction errors. This can make this framework highly efficient, but its implementation comes with unique challenges on the software development side. Embedding such models in standard neural network libraries often becomes limiting, as these libraries' compilation and differentiation backends can force a conceptual separation between optimization algorithms and the systems being optimized. This critically departs from other biological principles such as self-monitoring, self-organisation, cellular growth and functional plasticity. In this paper, we introduce pyhgf: a Python package backed by JAX and Rust for creating, manipulating and sampling dynamic networks for predictive coding. We improve over other frameworks by enclosing the network components as transparent, modular and malleable variables in the message-passing steps. The resulting graphs can implement arbitrary computational complexities as beliefs propagation. But the transparency of core variables can also translate into inference processes that leverage self-organisation principles, and express structure learning, meta-learning or causal discovery as the consequence of network structural adaptation to surprising inputs. The code, tutorials and documentation are hosted at: https://github.com/ilabcode/pyhgf.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

Speculative Decoding (SD) is a widely used approach to accelerate the inference of large language models (LLMs) without reducing generation quality. It operates by first using a compact model to draft multiple tokens efficiently, followed by parallel verification using the target LLM. This approach leads to faster inference compared to auto-regressive decoding. While there are multiple approaches to create a draft model, one promising approach is to use early-exit methods. These methods draft candidate tokens by using a subset of layers of the primary model and applying the remaining layers for verification, allowing a single model to handle both drafting and verification. While this technique reduces memory usage and computational cost, its performance relies on the choice of the exit layer for drafting and the number of tokens drafted (speculation length) in each SD round. Prior works use hyperparameter exploration to statically select these values. However, our evaluations show that these hyperparameter values are task-specific, and even within a task they are dependent on the current sequence context. We introduce DEL, a plug-and-play method that adaptively selects the exit layer and speculation length during inference. DEL dynamically tracks the token acceptance rate if the tokens are drafted at each layer of an LLM and uses that knowledge to heuristically select the optimal exit layer and speculation length. Our experiments across a broad range of models and downstream tasks show that DEL achieves overall speedups of 2.16timessim2.50times over vanilla auto-regressive decoding and improves upon the state-of-the-art SD methods by up to 0.27times.

Reasoning large language models (LLMs) have demonstrated superior capacities in solving complicated problems by generating long chain-of-thoughts (CoT), but such a lengthy CoT incurs high inference costs. In this study, we introduce ES-CoT, an inference-time method that shortens CoT generation by detecting answer convergence and stopping early with minimal performance loss. At the end of each reasoning step, we prompt the LLM to output its current final answer, denoted as a step answer. We then track the run length of consecutive identical step answers as a measure of answer convergence. Once the run length exhibits a sharp increase and exceeds a minimum threshold, the generation is terminated. We provide both empirical and theoretical support for this heuristic: step answers steadily converge to the final answer, and large run-length jumps reliably mark this convergence. Experiments on five reasoning datasets across three LLMs show that ES-CoT reduces the number of inference tokens by about 41\% on average while maintaining accuracy comparable to standard CoT. Further, ES-CoT integrates seamlessly with self-consistency prompting and remains robust across hyperparameter choices, highlighting it as a practical and effective approach for efficient reasoning.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

Pruning generates sparse networks by setting parameters to zero. In this work we improve one-shot pruning methods, applied before training, without adding any additional storage costs while preserving the sparse gradient computations. The main difference to pruning is that we do not sparsify the network's weights but learn just a few key parameters and keep the other ones fixed at their random initialized value. This mechanism is called freezing the parameters. Those frozen weights can be stored efficiently with a single 32bit random seed number. The parameters to be frozen are determined one-shot by a single for- and backward pass applied before training starts. We call the introduced method FreezeNet. In our experiments we show that FreezeNets achieve good results, especially for extreme freezing rates. Freezing weights preserves the gradient flow throughout the network and consequently, FreezeNets train better and have an increased capacity compared to their pruned counterparts. On the classification tasks MNIST and CIFAR-10/100 we outperform SNIP, in this setting the best reported one-shot pruning method, applied before training. On MNIST, FreezeNet achieves 99.2% performance of the baseline LeNet-5-Caffe architecture, while compressing the number of trained and stored parameters by a factor of x 157.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is challenging and requires restrictive approximations. Monte Carlo Dropout has been widely used as a relatively cheap way for approximate Inference and to estimate uncertainty with deep neural networks. Traditionally, the dropout mask is sampled independently from a fixed distribution. Recent works show that the dropout mask can be viewed as a latent variable, which can be inferred with variational inference. These methods face two important challenges: (a) the posterior distribution over masks can be highly multi-modal which can be difficult to approximate with standard variational inference and (b) it is not trivial to fully utilize sample-dependent information and correlation among dropout masks to improve posterior estimation. In this work, we propose GFlowOut to address these issues. GFlowOut leverages the recently proposed probabilistic framework of Generative Flow Networks (GFlowNets) to learn the posterior distribution over dropout masks. We empirically demonstrate that GFlowOut results in predictive distributions that generalize better to out-of-distribution data, and provide uncertainty estimates which lead to better performance in downstream tasks.

Deploying machine learning models in production may allow adversaries to infer sensitive information about training data. There is a vast literature analyzing different types of inference risks, ranging from membership inference to reconstruction attacks. Inspired by the success of games (i.e., probabilistic experiments) to study security properties in cryptography, some authors describe privacy inference risks in machine learning using a similar game-based style. However, adversary capabilities and goals are often stated in subtly different ways from one presentation to the other, which makes it hard to relate and compose results. In this paper, we present a game-based framework to systematize the body of knowledge on privacy inference risks in machine learning. We use this framework to (1) provide a unifying structure for definitions of inference risks, (2) formally establish known relations among definitions, and (3) to uncover hitherto unknown relations that would have been difficult to spot otherwise.

A Membership Inference Attack (MIA) assesses how much a trained machine learning model reveals about its training data by determining whether specific query instances were included in the dataset. We classify existing MIAs into adaptive or non-adaptive, depending on whether the adversary is allowed to train shadow models on membership queries. In the adaptive setting, where the adversary can train shadow models after accessing query instances, we highlight the importance of exploiting membership dependencies between instances and propose an attack-agnostic framework called Cascading Membership Inference Attack (CMIA), which incorporates membership dependencies via conditional shadow training to boost membership inference performance. In the non-adaptive setting, where the adversary is restricted to training shadow models before obtaining membership queries, we introduce Proxy Membership Inference Attack (PMIA). PMIA employs a proxy selection strategy that identifies samples with similar behaviors to the query instance and uses their behaviors in shadow models to perform a membership posterior odds test for membership inference. We provide theoretical analyses for both attacks, and extensive experimental results demonstrate that CMIA and PMIA substantially outperform existing MIAs in both settings, particularly in the low false-positive regime, which is crucial for evaluating privacy risks.

Existing benchmarks for frontier models often test specialized, ``PhD-level'' knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark based on the NPR Sunday Puzzle Challenge that requires only general knowledge. Our benchmark is challenging for both humans and models, however correct solutions are easy to verify, and models' mistakes are easy to spot. Our work reveals capability gaps that are not evident in existing benchmarks: OpenAI o1 significantly outperforms other reasoning models that are on par on benchmarks that test specialized knowledge. Furthermore, our analysis of reasoning outputs uncovers new kinds of failures. DeepSeek R1, for instance, often concedes with ``I give up'' before providing an answer that it knows is wrong. R1 can also be remarkably ``uncertain'' in its output and in rare cases, it does not ``finish thinking,'' which suggests the need for an inference-time technique to ``wrap up'' before the context window limit is reached. We also quantify the effectiveness of reasoning longer with R1 and Gemini Thinking to identify the point beyond which more reasoning is unlikely to improve accuracy on our benchmark.

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Inferring unbiased treatment effects has received widespread attention in the machine learning community. In recent years, our community has proposed numerous solutions in standard settings, high-dimensional treatment settings, and even longitudinal settings. While very diverse, the solution has mostly relied on neural networks for inference and simultaneous correction of assignment bias. New approaches typically build on top of previous approaches by proposing new (or refined) architectures and learning algorithms. However, the end result -- a neural-network-based inference machine -- remains unchallenged. In this paper, we introduce a different type of solution in the longitudinal setting: a closed-form ordinary differential equation (ODE). While we still rely on continuous optimization to learn an ODE, the resulting inference machine is no longer a neural network. Doing so yields several advantages such as interpretability, irregular sampling, and a different set of identification assumptions. Above all, we consider the introduction of a completely new type of solution to be our most important contribution as it may spark entirely new innovations in treatment effects in general. We facilitate this by formulating our contribution as a framework that can transform any ODE discovery method into a treatment effects method.

As the usage of large language models (LLMs) grows, performing efficient inference with these models becomes increasingly important. While speculative decoding has recently emerged as a promising direction for speeding up inference, existing methods are limited in their ability to scale to larger speculation budgets, and adapt to different hyperparameters and hardware. This paper introduces Sequoia, a scalable, robust, and hardware-aware algorithm for speculative decoding. To attain better scalability, Sequoia introduces a dynamic programming algorithm to find the optimal tree structure for the speculated tokens. To achieve robust speculative performance, Sequoia uses a novel sampling and verification method that outperforms prior work across different decoding temperatures. Finally, Sequoia introduces a hardware-aware tree optimizer that maximizes speculative performance by automatically selecting the token tree size and depth for a given hardware platform. Evaluation shows that Sequoia improves the decoding speed of Llama2-7B, Llama2-13B, and Vicuna-33B on an A100 by up to 4.04times, 3.84times, and 2.37times, and Llama2-70B offloading by up to 10.33times on L40.

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called "data-copying," was proposed by Meehan et. al. (2020). We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect data-copying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection.

Differential privacy (DP) is by far the most widely accepted framework for mitigating privacy risks in machine learning. However, exactly how small the privacy parameter epsilon needs to be to protect against certain privacy risks in practice is still not well-understood. In this work, we study data reconstruction attacks for discrete data and analyze it under the framework of multiple hypothesis testing. We utilize different variants of the celebrated Fano's inequality to derive upper bounds on the inferential power of a data reconstruction adversary when the model is trained differentially privately. Importantly, we show that if the underlying private data takes values from a set of size M, then the target privacy parameter epsilon can be O(log M) before the adversary gains significant inferential power. Our analysis offers theoretical evidence for the empirical effectiveness of DP against data reconstruction attacks even at relatively large values of epsilon.

Machine unlearning methods seek to revise pretrained models such that effects of certain training samples can be removed. In addition to effective erasure, low computational cost and general utility retention are also highly desirable. Existing unlearning methods usually involve iterative updates over the model parameters, which incurs a high computational cost. In this work, we propose an efficient method that only requires a one-time gradient computation, with which we modify only a single layer of model parameters. Specifically, we first identify a small number of model layers that lie on the Pareto front of high forget importance and low retain influence as critical layers. Then we search for a suitable step size and take a step along the gradient direction of a single critical layer while keeping other layers frozen. This method is highly modular and can be used to unlearn multiple concepts simultaneously in a controllable manner. We demonstrate the effectiveness and efficiency of this method on various models including CLIP, stable diffusion, and VLMs, surpassing other state-of-the-art methods.

Inference-time computation is a powerful paradigm to enhance the performance of large language models (LLMs), with Best-of-N sampling being a widely used technique. However, this method is computationally expensive, requiring both (1) an external reward model and (2) the generation of multiple samples. In this work, we introduce a new generative self-evaluation scheme designed to adaptively reduce the number of generated samples while maintaining or even improving performance. We use a generative reward model formulation, allowing the LLM to predict mid-generation the probability that restarting the generation will yield a better response. These predictions are obtained without an external reward model and can be used to decide whether or not to generate more samples, prune unpromising samples early on, or to pick the best sample. This capability is very inexpensive as it involves generating a single predefined token. Trained using a dataset constructed with real unfiltered LMSYS user prompts, Llama 3.1 8B's win rate against GPT-4 on AlpacaEval increases from 21% to 34% with 16 samples and math performance on GSM8K improves from 84% to 91%. By sampling only when the LLM determines that it is beneficial to do so and adaptively adjusting temperature annealing, we demonstrate that 74% of the improvement from using 16 samples can be achieved with only 1.2 samples on average. We further demonstrate that 50-75% of samples can be pruned early in generation with minimal degradation in performance. Overall, our methods enable more efficient and scalable compute utilization during inference for LLMs.

Test-Time Scaling (TTS) is a promising approach to progressively elicit the model's intelligence during inference. Recently, training-based TTS methods, such as continued reinforcement learning (RL), have further surged in popularity, while training-free TTS methods are gradually fading from prominence. However, the additional computation overhead of training amplifies the burden on test-time scaling. In this paper, we focus on training-free TTS methods for reasoning. We first design Conditional Step-level Self-refinement, a fine-grained sequential scaling method guided by process verification. On top of its effectiveness, we further combine it with other classical parallel scaling methods at the step level, to introduce a novel inference paradigm called Hybrid Test-Time Scaling. Extensive experiments on five instruction-tuned LLMs across different scales (3B-14B) and families demonstrate that hybrid strategy incorporating various training-free TTS methods at a fine granularity has considerable potential for expanding the reasoning performance boundaries of LLMs.

Backpropagation provides a generalized configuration for overcoming catastrophic forgetting. Like, SGD and Adam are commonly used for weight updates in continual learning and continual pre-training. In practice, permission to access gradient information is not always granted (the gradient ban), such as black-box APIs, hardware limitations, and non-differentiable systems. To bridge this gap, we introduce the first benchmark ZeroFlow to evaluate gradient-free optimization algorithms for overcoming forgetting. This benchmark examines a suite of forward pass methods across multiple methods, forgetting scenarios, and datasets. We find that forward passes alone are enough to overcome forgetting. Our findings reveal new optimization principles that highlight the potential of forward-pass in mitigating forgetting, managing task conflicts, and reducing memory demands, alongside novel enhancements that further mitigate forgetting with just one forward pass. This work provides essential insights and tools for advancing forward pass methods to overcome forgetting.

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

With increasingly more data and computation involved in their training, machine learning models constitute valuable intellectual property. This has spurred interest in model stealing, which is made more practical by advances in learning with partial, little, or no supervision. Existing defenses focus on inserting unique watermarks in a model's decision surface, but this is insufficient: the watermarks are not sampled from the training distribution and thus are not always preserved during model stealing. In this paper, we make the key observation that knowledge contained in the stolen model's training set is what is common to all stolen copies. The adversary's goal, irrespective of the attack employed, is always to extract this knowledge or its by-products. This gives the original model's owner a strong advantage over the adversary: model owners have access to the original training data. We thus introduce dataset inference, the process of identifying whether a suspected model copy has private knowledge from the original model's dataset, as a defense against model stealing. We develop an approach for dataset inference that combines statistical testing with the ability to estimate the distance of multiple data points to the decision boundary. Our experiments on CIFAR10, SVHN, CIFAR100 and ImageNet show that model owners can claim with confidence greater than 99% that their model (or dataset as a matter of fact) was stolen, despite only exposing 50 of the stolen model's training points. Dataset inference defends against state-of-the-art attacks even when the adversary is adaptive. Unlike prior work, it does not require retraining or overfitting the defended model.

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.

Bayesian inference provides a principled framework for learning from complex data and reasoning under uncertainty. It has been widely applied in machine learning tasks such as medical diagnosis, drug design, and policymaking. In these common applications, data can be highly sensitive. Differential privacy (DP) offers data analysis tools with powerful worst-case privacy guarantees and has been developed as the leading approach in privacy-preserving data analysis. In this paper, we study Metropolis-Hastings (MH), one of the most fundamental MCMC methods, for large-scale Bayesian inference under differential privacy. While most existing private MCMC algorithms sacrifice accuracy and efficiency to obtain privacy, we provide the first exact and fast DP MH algorithm, using only a minibatch of data in most iterations. We further reveal, for the first time, a three-way trade-off among privacy, scalability (i.e. the batch size), and efficiency (i.e. the convergence rate), theoretically characterizing how privacy affects the utility and computational cost in Bayesian inference. We empirically demonstrate the effectiveness and efficiency of our algorithm in various experiments.

Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of NNGPs for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. With certain scale priors, we obtain heavy-tailed stochastic processes, and in the case of inverse gamma priors, we recover Student's t processes. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for NNGPs. We present a practical posterior-inference algorithm for the scale mixture of NNGPs and empirically demonstrate its usefulness on regression and classification tasks. In particular, we show that in both tasks, the heavy-tailed stochastic processes obtained from our framework are robust to out-of-distribution data.

We describe nonparametric deconvolution models (NDMs), a family of Bayesian nonparametric models for collections of data in which each observation is the average over the features from heterogeneous particles. For example, these types of data are found in elections, where we observe precinct-level vote tallies (observations) of individual citizens' votes (particles) across each of the candidates or ballot measures (features), where each voter is part of a specific voter cohort or demographic (factor). Like the hierarchical Dirichlet process, NDMs rely on two tiers of Dirichlet processes to explain the data with an unknown number of latent factors; each observation is modeled as a weighted average of these latent factors. Unlike existing models, NDMs recover how factor distributions vary locally for each observation. This uniquely allows NDMs both to deconvolve each observation into its constituent factors, and also to describe how the factor distributions specific to each observation vary across observations and deviate from the corresponding global factors. We present variational inference techniques for this family of models and study its performance on simulated data and voting data from California. We show that including local factors improves estimates of global factors and provides a novel scaffold for exploring data.