The Error You See Is Not the Error You Made: Progression-aware Reasoning Origin for Reasoning Error Localization

Multi-step reasoning with Chain-of-Thought (CoT) prompting remains fragile: logical errors or hallucinations in early steps silently propagate, producing confident but incorrect conclusions. This paper presents VeryTrace, a zero-shot verification-and-repair framework that formalizes natural-language reasoning traces into a structured, compilable representation. VeryTrace introduces a Domain-Specific Language (DSL) that (i) makes step dependencies explicit, (ii) mechanizes quantitative content as executable expressions, and (iii) structures semantic inferences via deduction schemas. Our hybrid verifier combines deterministic checks for computational correctness, dependency resolution, and constraint satisfaction with targeted LLM audits for non-mechanizable semantic judgments, enabling step-level error localization and repair. Across three diverse domains-competition mathematics (AIME 2025), robotics planning (LLM-BabyBench), and kinship reasoning (CLUTRR), VeryTrace improves accuracy over zero-shot baselines on state-of-the-art LLMs without requiring domain-specific training or in-context examples, demonstrating that formalized trace verification achieves both precision and generalization.

Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation offers a diagnostic signal, yet existing methods are restricted to final answers or require internal model access. In this paper, we introduce Stepwise Confidence Attribution (SCA), a framework for closed-source LLMs that assigns step-level confidence based only on generated reasoning traces. SCA applies the Information Bottleneck principle: steps aligning with consensus structures across correct solutions receive high confidence, while deviations are flagged as potentially erroneous. We propose two complementary methods: (1) NIBS, a non-parametric IB approach measuring consistency without graph structures, and (2) GIBS, a graph-based IB model that learns subgraphs through a differentiable mask to capture logical variability. Extensive experiments on mathematical reasoning and multi-hop question answering show that SCA reliably identifies low-confidence steps strongly correlated with reasoning errors. Moreover, using step-level confidence to guide self-correction improves the correction success rate by up to 13.5% over answer-level feedback.

Large Language Models (LLMs) using chain-of-thought have demonstrated great potential for solving complex reasoning and planning tasks. Despite these advances, LLM-generated outputs remain susceptible to errors, making verification important for reliable reasoning systems. Learned verifiers can increase trust, enforce safety constraints, and ensure alignment with personal preferences, while also providing feedback to improve generation. This raises a central challenge: when learned verifiers are used to guide generation, the feedback loop between generator and verifier may induce a distribution shift. This is particularly salient for process reward models, a prominent class of learned verifiers that score or classify individual steps in a chain-of-thought reasoning trace. Motivated by this challenge, we propose a new online learning framework for chain-of-thought verifiers that, given a problem statement and a reasoning trace, check the correctness of each reasoning step given the preceding steps. Highlighting the asymmetric role of soundness errors (accepting an incorrect reasoning step) and completeness errors (flagging a correct step as wrong), we introduce novel notions of dimension that characterize their optimal tradeoff. We then show how our learned verifiers can boost the accuracy of a weak generator. Assuming that the generator can produce a correct next step with a small success probability, we show how to learn a strong generator with small error and abstention rates. Our results also allow learning from offline data when queries to an expert verifier can be simulated from a small set of correct reasoning traces. However, we establish a separation between our approach and learning from offline expert demonstrations: we show that learning from offline demonstrations cannot in general achieve the soundness-completeness guarantees produced by our interactive learning approach.