Theory Explains In-Context Search Benefits for LLM Reasoning

This research delves into the theoretical underpinnings of "in-context search" within large language models (LLMs), a technique where models iteratively generate, evaluate, and refine their solution attempts. The study conceptualizes this process as an approximate inference mechanism operating over reasoning traces, with the base LLM providing an initial probability distribution and self-reflection offering feedback for subsequent updates. The primary focus is on understanding the sampling complexity—the number of sequential attempts required to achieve a high probability of success. The analysis reveals that when an LLM's reflections are effective at identifying and localizing early errors, in-context search can deliver exponential improvements in problem-solving capabilities. This means problems with extremely low zero-shot success rates can be solved with a manageable, polynomial number of sequential attempts. Furthermore, these significant gains are shown to be robust and learnable, suggesting that even approximate posterior updates are sufficient, and the necessary reflective behaviors can be acquired through training on search rollouts.