Training Chain-of-Thought via Latent-Variable Inference

TL;DR

This paper introduces a novel fine-tuning method for large language models that maximizes the marginal likelihood of correct answers using chain-of-thought prompting, effectively averaging over possible rationales without requiring expensive rationale annotations.

Contribution

It proposes an MCMC-EM fine-tuning approach that improves LLM performance on reasoning tasks by marginalizing over rationales, avoiding the need for detailed rationale supervision.

Findings

Improves accuracy on GSM8K and BIG-Bench Hard tasks

Outperforms STaR and prompt-tuning methods

Uses a variance-reduction control variate technique

Abstract

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.