Probabilistic Program Training Enhances Inductive Reasoning in LLMs
This paper introduces Program-based Posterior Training (PPT), a novel method for enhancing the inductive reasoning capabilities of Large Language Models (LLMs). PPT leverages generative LLMs to create scenarios as probabilistic programs, which are then used for probabilistic inference to generate distributional target responses. Fine-tuning LLMs on these synthetic, soft labels shows significant improvements in estimation accuracy, human alignment, and calibration on inductive tasks, outperforming traditional methods and demonstrating deeper internalization of uncertainty than post-hoc scaling.