Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

NCV: A Node-Wise Consistency Verification Approach for Low-Cost Structured Error Localization in LLM Reasoning

Yulong Zhang, Li Wang, Wei Du, Peilin Li, Yuqin Dai Zhiyuan Zhao, Lingyong Fang, Ziniu Liu, Ru Zhang, Huijia Zhu, Gongshen Liu

TL;DR

NCV tackles the challenge of verifying long multi-step reasoning by converting chain-of-thought into a structured set of atomic verification nodes, enabling lightweight binary judgments. It eliminates attention dilution and reduces token costs compared to end-to-end CoT-based verifiers, achieving 10-25% F1 gains across four ProcessBench datasets. The approach demonstrates strong error localization, outperforming baselines while using 6-58× fewer tokens, and provides a scalable, training-free verification framework. The results suggest NCV as a practical method for reliable reasoning verification in real-time or large-scale deployments.

Abstract

Verifying multi-step reasoning in large language models is difficult due to imprecise error localization and high token costs. Existing methods either assess entire reasoning chains, suffering attention dilution, or rely on expensive multi-sampling. We introduce Node-wise Consistency Verification (NCV), a training-free framework that recasts verification as lightweight binary consistency checks at the node level. By decomposing the chain of thought into interconnected verification nodes, NCV precisely localizes errors and avoids unnecessary long-form generation. Experiments demonstrate that our approach enhances interpretability and efficiency, presenting a scalable solution for reliable LLM reasoning verification. On public datasets, NCV achieves a 10\% to 25\% improvement in F1 scores over baselines while utilizing $6\times$~$58\times$ fewer tokens than traditional methods like CoT-based verifiers.

NCV: A Node-Wise Consistency Verification Approach for Low-Cost Structured Error Localization in LLM Reasoning

TL;DR

NCV tackles the challenge of verifying long multi-step reasoning by converting chain-of-thought into a structured set of atomic verification nodes, enabling lightweight binary judgments. It eliminates attention dilution and reduces token costs compared to end-to-end CoT-based verifiers, achieving 10-25% F1 gains across four ProcessBench datasets. The approach demonstrates strong error localization, outperforming baselines while using 6-58× fewer tokens, and provides a scalable, training-free verification framework. The results suggest NCV as a practical method for reliable reasoning verification in real-time or large-scale deployments.

Abstract

Verifying multi-step reasoning in large language models is difficult due to imprecise error localization and high token costs. Existing methods either assess entire reasoning chains, suffering attention dilution, or rely on expensive multi-sampling. We introduce Node-wise Consistency Verification (NCV), a training-free framework that recasts verification as lightweight binary consistency checks at the node level. By decomposing the chain of thought into interconnected verification nodes, NCV precisely localizes errors and avoids unnecessary long-form generation. Experiments demonstrate that our approach enhances interpretability and efficiency, presenting a scalable solution for reliable LLM reasoning verification. On public datasets, NCV achieves a 10\% to 25\% improvement in F1 scores over baselines while utilizing ~ fewer tokens than traditional methods like CoT-based verifiers.

Paper Structure

This paper contains 14 sections, 8 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Node-wise Consistency Verification
  3. Problem Formulation
  4. Structured Decomposition
  5. Sequential Node Verification
  6. Consistency Strategies for Binary Mode
  7. NCV Algorithm
  8. Computational Efficiency Analysis
  9. Experiments
  10. Experimental Setup
  11. Main Results
  12. Ablation Experiments
  13. Cost-Effectiveness Analysis
  14. Conclusion

Figures (1)

  • Figure 1: Comparison between End-to-End (E2E) verification and Node-wise Consistency Verification (NCV). (a) E2E approach processes the entire problem and solution simultaneously, consuming extensive tokens through Chain-of-Thought reasoning but failing to precisely localize errors. (b) NCV decomposes the reasoning into structured steps and nodes, enabling sequential verification with minimal token consumption and accurate error localization.