Correct Reasoning Paths Visit Shared Decision Pivots

Dongkyu Cho, Amy B.Z. Zhang, Bilel Fehri, Sheng Wang, Rumi Chunara, Hengrui Cai, Rui Song

Keywords: post training, large language models, reasoning

TL;DR: We introduce the concept of decision pivots, a key reasoning step that must be visited to reach a correct decision.

Abstract: 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; 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.

Submission Number: 64