Training Chain-of-Thought via Latent-Variable Inference
Du Phan Matthew D. Hoffman David Dohan Sholto Douglas Tuan Anh Le Aaron Parisi Pavel Sountsov Charles Sutton Sharad Vikram Rif A. Saurous
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.