New PPT method trains LLMs to reason inductively from sparse data

A new paper from Liyi Zhang, Akshay K. Jagadish, Brenden M. Lake, and Thomas L. Griffiths introduces Program-based Posterior Training (PPT), a method that uses probabilistic programs to improve inductive reasoning in large language models. Unlike deductive reasoning tasks (e.g., math, coding) where answers are verifiable, inductive reasoning requires agents to infer uncertain beliefs from sparse, ambiguous observations—a common real-world scenario. The researchers generate diverse open-world scenarios as probabilistic programs, run probabilistic inference to produce distributional target responses, and fine-tune LLMs on these probabilistic soft labels.

PPT was trained on 10,000 programmatically generated scenarios and evaluated on held-out motifs, human-labeled judgments, and external benchmarks. Results show substantial improvements in estimation accuracy on inductive tasks, increased alignment with human judgment, and transferable gains to external estimation benchmarks. Notably, the calibration improvements go beyond what post-hoc temperature scaling can achieve, indicating that models internalize uncertainty more deeply. This work opens a new path for post-training LLMs to handle inductive inference reliably, addressing a critical gap in current fine-tuning approaches.