# Verifying Chain-of-Thought Reasoning via Its Computational Graph

arXiv: https://arxiv.org/abs/2510.09312 · HTML: https://mlsanity.com/paper/2510.09312/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety](https://mlsanity.com/paper/2507.11473/) (2025)
- [Thought Anchors: Which LLM Reasoning Steps Matter?](https://mlsanity.com/paper/2506.19143/) (2025)
- [When Thinking Fails: The Pitfalls of Reasoning for Instruction-Following in LLMs](https://mlsanity.com/paper/2505.11423/) (2025)
- [CoT-Kinetics: A Theoretical Modeling Assessing LRM Reasoning Process](https://mlsanity.com/paper/2505.13408/) (2025)
- [Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations](https://mlsanity.com/paper/2503.14477/) (2025)
- [Measuring Chain of Thought Faithfulness by Unlearning Reasoning Steps](https://mlsanity.com/paper/2502.14829/) (2025)
- [Base Models Know How to Reason, Thinking Models Learn When](https://mlsanity.com/paper/2510.07364/) (2025)
- [Reasoning-Finetuning Repurposes Latent Representations in Base Models](https://mlsanity.com/paper/2507.12638/) (2025)
- [Long Horizon Temperature Scaling](https://mlsanity.com/paper/2302.03686/) (2023)
- [The Geometry of Self-Verification in a Task-Specific Reasoning Model](https://mlsanity.com/paper/2504.14379/) (2025)
- [Diversity-driven Data Selection for Language Model Tuning through Sparse Autoencoder](https://mlsanity.com/paper/2502.14050/) (2025)

## Built on by (most cited first, 20 of 20)

- [State over Tokens: Characterizing the Role of Reasoning Tokens](https://mlsanity.com/paper/2512.12777/) (2025)
- [Certified Circuits: Stability Guarantees for Mechanistic Circuits](https://mlsanity.com/paper/2602.22968/) (2026)
- [Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability](https://mlsanity.com/paper/2603.10384/) (2026)
- [ReasonOps: Operator Segmentation for LLM Reasoning Traces](https://mlsanity.com/paper/2605.29192/) (2026)
- [CodeCircuit: Toward Inferring LLM-Generated Code Correctness via Attribution Graphs](https://mlsanity.com/paper/2602.07080/) (2026)
- [CoTJudger: A Graph-Driven Framework for Automatic Evaluation of Chain-of-Thought Efficiency and Redundancy in LRMs](https://mlsanity.com/paper/2603.07078/) (2026)
- [Detecting Unfaithful Chain-of-Thought via Circuit-Guided Internal-External Discrepancy](https://mlsanity.com/paper/2605.25603/) (2026)
- [Contrastive Attribution in the Wild: An Interpretability Analysis of LLM Failures on Realistic Benchmarks](https://mlsanity.com/paper/2604.17761/) (2026)
- [Conformal Certification of Reasoning Trace Prefixes](https://mlsanity.com/paper/2605.30085/) (2026)
- [The Past Is Not Past: Memory-Enhanced Dynamic Reward Shaping](https://mlsanity.com/paper/2604.11297/) (2026)
- [Playing Psychic: Using Thought Trees to Predict Reasoning Models Accuracy on Coding Tasks](https://mlsanity.com/paper/2604.16931/) (2026)
- [Tracing Uncertainty in Language Model "Reasoning"](https://mlsanity.com/paper/2605.07776/) (2026)
- [VeryTrace: Verifying Reasoning Traces through Compilable Formalism and Structured Verification](https://mlsanity.com/paper/2606.24124/) (2026)
- [Mechanistic Interpretability of Chain-of-Thought Reasoning via Sequential Activation Patching](https://mlsanity.com/paper/2608.22332/) (2026)
- [SCAN: Sparse Circuit Anchor Interpretable Neuron for Lifelong Knowledge Editing](https://mlsanity.com/paper/2603.15226/) (2026)
- [Graph-Based Chain-of-Thought Pruning for Reducing Redundant Reflections in Reasoning LLMs](https://mlsanity.com/paper/2604.05643/) (2026)
- [Why Retrieval-Augmented Generation Fails: A Graph Perspective](https://mlsanity.com/paper/2605.14192/) (2026)
- [Context-Masked Truncated Reasoning Audits for Answer-Key Dependence in LLM Tutors](https://mlsanity.com/paper/2607.04572/) (2026)
- [How Do Linear Probes Emerge? A Circuit-Tracing Framework with Concept-Targeted Attribution](https://mlsanity.com/paper/2608.27510/) (2026)
- [Medical AI Encodes a "Feeling of Error": Verifying Cancer Segmentation via Internal Concepts](https://mlsanity.com/paper/2609.08879/) (2026)

## Abstract (arXiv)

Current Chain-of-Thought (CoT) verification methods predict reasoning correctness based on outputs (black-box) or activations (gray-box), but offer limited insight into why a computation fails. We introduce a white-box method: Circuit-based Reasoning Verification (CRV). We hypothesize that attribution graphs of correct CoT steps, viewed as execution traces of the model's latent reasoning circuits, possess distinct structural fingerprints from those of incorrect steps. By training a classifier on structural features of these graphs, we show that these traces contain a powerful signal of reasoning errors. Our white-box approach yields novel scientific insights unattainable by other methods. (1) We demonstrate that structural signatures of error are highly predictive, establishing the viability of verifying reasoning directly via its computational graph. (2) We find these signatures to be highly domain-specific, revealing that failures in different reasoning tasks manifest as distinct computational patterns. (3) We provide evidence that these signatures are not merely correlational; by using our analysis to guide targeted interventions on individual transcoder features, we successfully correct the model's faulty reasoning. Our work shows that, by scrutinizing a model's computational process, we can move from simple error detection to a deeper, causal understanding of LLM reasoning.