# Beyond Answer Voting: Fine-Grained Correction of LLM Reasoning through Graph Alignment across Sampled Traces

arXiv: https://arxiv.org/abs/2610.18606 · HTML: https://mlsanity.com/paper/2610.18606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 11 of 11)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [Reasoning Consensus: Structural Ensembling of LLM Reasoning via Weighted DAG Aggregation](https://mlsanity.com/paper/2607.27783/) (2026)

## Abstract (arXiv)

Large language models increasingly tackle tasks that require multi-step reasoning, where errors in intermediate claims can affect the final answer. Self-consistency (SC) improves reasoning by voting over sampled final answers, but its vote leaves intermediate disagreements unresolved. To address this problem, we introduce DDRG (Disagreement-Driven Verification Guided by Reasoning Graphs), a framework for selective correction from a frozen bank of reasoning traces. Our insight is that graph alignment can expose claim-level disagreements and provide correction evidence without expanding the sampled trace bank. DDRG builds source-grounded claim graphs and sends localized conflicts to an answer-blind verifier. A verifier-supported refutation that reaches the majority answer's supporting path triggers one focused repair; otherwise, DDRG returns the exact SC vote. Experimental results across five benchmarks show that native zero-shot DDRG improves macro-average accuracy over direct answering by 8.65 and 15.83 percentage points for Qwen2.5-7B and Llama3.1-8B. It also exceeds CoT, the evaluated GoT and GoV question-answering adaptations, and SC on this macro metric. DDRG links local verification to selective correction without enlarging the initial candidate bank.