Correct Reasoning Paths Visit Shared Decision Pivots
This addresses the challenge of scalable verification for reasoning in LLMs, which is crucial for improving reliability in applications like question-answering, though it appears incremental as it builds on existing CoT methods.
The paper tackles the problem of verifying chain-of-thought reasoning traces in large language models by introducing decision pivots—minimal checkpoints that correct reasoning paths must share—and proposes a self-training pipeline that mines and uses these pivots to align reasoning without ground truth data. Experiments on LogiQA, MedQA, and MATH500 benchmarks demonstrate its effectiveness.
Chain-of-thought (CoT) reasoning exposes the intermediate thinking process of large language models (LLMs), yet verifying those traces at scale remains unsolved. In response, we introduce the idea of decision pivots-minimal, verifiable checkpoints that any correct reasoning path must visit. We hypothesize that correct reasoning, though stylistically diverse, converge on the same pivot set, while incorrect ones violate at least one pivot. Leveraging this property, we propose a self-training pipeline that (i) samples diverse reasoning paths and mines shared decision pivots, (ii) compresses each trace into pivot-focused short-path reasoning using an auxiliary verifier, and (iii) post-trains the model using its self-generated outputs. The proposed method aligns reasoning without ground truth reasoning data or external metrics. Experiments on standard benchmarks such as LogiQA, MedQA, and MATH500 show the effectiveness of our method.