Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference.

Our work makes one of the first attempts at highlighting the potential of post hoc explanations as valuable tools for enhancing the effectiveness of LLMs.

These methods, while effective, often involve manually intensive prompt engineering.

Chain-of-thought (CoT) is a method that enables language models to handle complex reasoning tasks by decomposing them into simpler steps.

This parameter prompting, 5. Tobe t, instruction I: {Ii}n,It intoate{Ii}n refers in-conte It denotes wherethe54], we I into 6

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a chain-of-thought (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the \emph{marginal} log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.