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

Haotian Liu; Yingjian Chen; Xiaohang Xu; Lang Huang; Yusuke Iwasawa; Yutaka Matsuo; Irene Li

cs.AIOct 13, 2026

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

Authors: Haotian Liu, Yingjian Chen, Xiaohang Xu, Lang Huang, Yusuke Iwasawa, Yutaka Matsuo, Irene Li

Organizations: School of Informatics, Xiamen University · The University of Tokyo · National Institute of Informatics (NII)

Abstract

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.

Figures & tables

Figure 1: Comparison of CoT, self-consistency (SC), and DDRG. CoT uses one trace; SC votes over final answers. DDRG verifies aligned local disagreements and uses answer-relevant evidence for one regeneration, retaining SC when correction is unwarranted.

Figure 2: DDRG overview. SC and DDRG share a frozen bank. The verifier assesses local claims; the controller tests answer-path relevance and permits one regeneration. Ineligible evidence or an unparseable response returns SC.

Method	MedQA	GSM8K	ReClor	LogiQA2	FOLIO	Macro Avg.
Qwen2.5-7B
Direct	60.88	70.36	70.00	63.80	55.39	64.09
CoT ( Wei et al., 2022 )	62.77	89.01	72.00	65.39	68.63	71.56
GoT (QA) ( Besta et al., 2024 )	63.16	90.90	70.40	64.89	59.31	69.73
GoV (QA) ( Fang et al., 2026 )	60.64	90.22	73.40	63.42	58.33	69.20
DDRG	64.02	92.27	74.40	67.30	65.69	72.74

Table 1: Full-cohort accuracy (%). Macro averages equally weight the five benchmarks. Bold marks the best result among the five displayed methods within each solver. GoT and GoV are QA adaptations (Section 4.1 ); SC and same-bank gains are reported separately in Appendix A.1 .

Panel of Figure 3 — Figure 3: Net corrections over same-bank SC. In each pair, the upper bar is Qwen and the lower bar is Llama. Net counts subtract harmful from beneficial changes; totals are $+34$ and $+31$ . Dataset sizes differ.

Figure 4: DDRG corrects GSM8K test:147 from SC’s 90 to 75. Aligned claim fragments expose the omitted earlier returns; independent verification and answer-path evidence trigger one regeneration. The illustrated local dependencies are condensed (Appendix E ).

Figure 5: Saved harmful correction on FOLIO validation 79. The abbreviated logical chain explains why B is correct; the verifier misses the contradiction and DDRG changes B to C.

Solver	Pattern	$N_{D}$	SC	DDRG	$\Delta$ pp
Qwen	2:1	1258	51.27	53.10	+1.83
	1:1:1	190	30.53	36.32	+5.79
Llama	2:1	1787	54.34	55.18	+0.84
	1:1:1	404	28.71	32.67	+3.96

Table 2: Post-hoc pooled accuracy by stored-answer pattern.

N_{D}

includes every question in the group, including failed and retained outputs. Gains are not full-cohort macro gains.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Qwen2.5-7B
Metric	MedQA	GSM8K	ReClor	LogiQA2	FOLIO	Overall
SC@3 accuracy (%)	62.37	91.89	74.00	66.98	65.20	72.09
DDRG $-$ SC (pp)	+1.65	+0.38	+0.40	+0.32	+0.49	+0.65
Llama3.1-8B
SC@3 accuracy (%)	69.52	87.64	63.60	54.71	55.39	66.17
DDRG $-$ SC (pp)	+0.55	+0.83	+0.40	+0.76	$-0.49$	+0.41

Appendix

Table 3: Same-bank SC baseline and DDRG gains. Overall is the equal-benchmark macro average for the accuracy and gain rows. Gains use exact correct/

N

; rounding may cause a 0.01-point difference from displayed accuracies in Table 1 .

Method	GSM8K 147	FOLIO 79
Direct	90	A
CoT	90	B
SC@3	90	B
GoT (QA)	45	B
GoV (QA)	90	B
DDRG	75	C

Appendix

Table 4: Recorded final answers for the successful and harmful cases. The table shows endpoint comparisons, not full intermediate traces for every baseline.

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Denoising Iterative Self-Correction: Structured Verification Loops for Reliable LLM Reasoning

Shen Yin, David Ken, Joel Stremmel

Thomson Reuters Labs

LLM Self-Correction LLM Self-Refinement LLM Answer Verification LLM Reliability

Open paper AskPDF arXiv

Large language models produce fluent but often incorrect multi-step reasoning, and naive correction methods risk degrading already-correct answers. We introduce Denoising Iterative Self-Correction (DISC), a test-time procedure that treats verification question outputs as noisy measurements of where a solution may be corrupted. Using these signals, DISC progressively reduces errors across multiple verify-judge-correct passes, analogous to traditional iterative denoising. A binary judgment gate controls correction precision by blocking rewrites that would damage already-correct answers while the verifier and corrector together repair errors. We evaluate this trade-off using two paired diagnostics: an improvement-to-degradation ratio (precision) and a repair rate (recall). Across three benchmarks (BIG-Bench Mistake, HotpotQA, GPQA Diamond) and four models, DISC dominates Chain-of-Verification and Self-Refine on the precision-recall trade-off, reaching 81.6% accuracy with 13x more improvements per degradation than Chain-of-Verification and 5x more than Self-Refine on BIG-Bench Mistake (Sonnet~4.5). On GPQA Diamond, we identify a capability floor below which judges acknowledge contradictions in evidence but cannot translate that recognition into a correction. We further show that cross-model role allocation -- assigning verification and judgment to a model different from the generator -- mitigates self-confirmation bias.

Abstract

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