  A central piece in enabling intelligent agentic behavior in foundation models
is to make them capable of introspecting upon their behavior, reasoning, and
correcting their mistakes as more computation or interaction is available. Even
the strongest proprietary large language models (LLMs) do not quite exhibit the
ability of continually improving their responses sequentially, even in
scenarios where they are explicitly told that they are making a mistake. In
this paper, we develop RISE: Recursive IntroSpEction, an approach for
fine-tuning LLMs to introduce this capability, despite prior work hypothesizing
that this capability may not be possible to attain. Our approach prescribes an
iterative fine-tuning procedure, which attempts to teach the model how to alter
its response after having executed previously unsuccessful attempts to solve a
hard test-time problem, with optionally additional environment feedback. RISE
poses fine-tuning for a single-turn prompt as solving a multi-turn Markov
decision process (MDP), where the initial state is the prompt. Inspired by
principles in online imitation learning and reinforcement learning, we propose
strategies for multi-turn data collection and training so as to imbue an LLM
with the capability to recursively detect and correct its previous mistakes in
subsequent iterations. Our experiments show that RISE enables Llama2, Llama3,
and Mistral models to improve themselves with more turns on math reasoning
tasks, outperforming several single-turn strategies given an equal amount of
inference-time computation. We also find that RISE scales well, often attaining
larger benefits with more capable models. Our analysis shows that RISE makes
meaningful improvements to responses to arrive at the correct solution for
challenging prompts, without disrupting one-turn abilities as a result of
expressing more complex distributions.
