Title: Deciphering Self-Improvement: Large Language Models Can Take False First Steps
Primary area: applications to neuroscience & cognitive science
Keywords: Large Language Models, self-improvement, planning, Bayesian, MCMC

Abstract: One of the most striking capabilities of Large Language Models (LLMs) is their apparent ability to refine outputs through a process of self-improvement. Yet how an autoregressive model acquires such capability remains unclear. We propose a mechanistic model of LLM self-improvement grounded in a Bayesian perspective on token generation. In this view, LLMs maintain latent plans for future token generations, which gradually stabilize as more self-generated tokens are autoregressively incorporated back into the context. Across two single-dimensional random number generation experiments, we find evidence consistent with the dynamic patterns of planning and generation predicted by this Bayesian model. Building on these insights, we introduce self-play Markov Chain Monte Carlo (spMCMC), an extension of MCMC-with-LLMs designed to elicit reliable reward signals for self-improvement in open-ended text generation. Human evaluations show that spMCMC identifies higher-quality outputs that are often overlooked by both greedy decoding and other self-evaluation methods.