“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. Saurous2023-11-28 (inner monologue (AI), math)⁠:

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, ie. 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 marginal log-likelihood of generating a correct answer using CoT prompting, 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.