  Large language models (LLMs) have shown impressive performance on language
tasks but face challenges when deployed on resource-constrained devices due to
their extensive parameters and reliance on dense multiplications, resulting in
high memory demands and latency bottlenecks. Shift-and-add reparameterization
offers a promising solution by replacing costly multiplications with
hardware-friendly primitives in both the attention and multi-layer perceptron
(MLP) layers of an LLM. However, current reparameterization techniques require
training from scratch or full parameter fine-tuning to restore accuracy, which
is resource-intensive for LLMs. To address this, we propose accelerating
pretrained LLMs through post-training shift-and-add reparameterization,
creating efficient multiplication-free models, dubbed ShiftAddLLM.
Specifically, we quantize each weight matrix into binary matrices paired with
group-wise scaling factors. The associated multiplications are reparameterized
into (1) shifts between activations and scaling factors and (2) queries and
adds according to the binary matrices. To reduce accuracy loss, we present a
multi-objective optimization method to minimize both weight and output
activation reparameterization errors. Additionally, based on varying
sensitivity across layers to reparameterization, we develop an automated bit
allocation strategy to further reduce memory usage and latency. Experiments on
five LLM families and eight tasks consistently validate the effectiveness of
ShiftAddLLM, achieving average perplexity improvements of 5.6 and 22.7 points
at comparable or lower latency compared to the most competitive quantized LLMs
at 3 and 2 bits, respectively, and more than 80% memory and energy reductions
over the original LLMs. Codes and models are available at
https://github.com/GATECH-EIC/ShiftAddLLM.
