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

1 Introduction

• An incorrect intermediate claim can affect later reasoning, while SC’s final-answer vote leaves unresolved which claims cause disagreement or whether a minority trace contains a valid correction.Source: §1 · pp. 1–2
• DDRG builds source-grounded graphs from a frozen CoT bank, aligns local claims, and sends conflicts to an answer-blind verifier; a supported refutation on the majority answer’s path triggers one focused repair, otherwise SC is retained.This uses existing samples without expanding the CoT bank.Source: §1 · p. 2
• Native zero-shot DDRG, evaluated across five mathematical, logical, and medical reasoning cohorts, gains 8.65 and 15.83 percentage points in macro-average accuracy over direct answering for Qwen2.5-7B and Llama3.1-8B, respectively.It also achieves higher macro-average accuracy than CoT, the evaluated GoT and GoV adaptations, and SC.Source: §1 · p. 2

Reasoning diversity at test time

• Test-time methods explore alternative reasoning paths through sampled CoT traces, tree search, or adaptive computation; DDRG compares intermediate claims across existing traces without expanding the sampled bank.Source: §2 · p. 2

Graph-structured reasoning

• Graph-of-Thoughts combines and refines thoughts, Graph-of-Verification checks units in dependency order, and other methods aggregate graphs or model argument relations; DDRG aligns source-grounded claims across traces.Source: §2 · p. 2

Verification and correction

• Prior correction methods use feedback, verification questions, tools, retrieval, or learned multi-turn correction; DDRG derives verification targets from cross-trace disagreements and uses independently verified evidence for repair.Source: §2 · p. 2

3.1 Reasoning Graph Construction

• With K=3 frozen traces, DDRG parses answers and builds source-checked graphs whose quoted claim nodes retain provenance and support relations; failed graphs leave the SC vote unchanged.Source: §3.1 · p. 3

3.2 Disagreement Localization

• It aligns claims about the same local object into ordered disputes with quoted claims, context, and probes; final-answer nodes are excluded, and failed checks return the majority vote.Source: §3.2 · p. 3

3.3 Independent Verification

• An answer-blind verifier checks up to three disputes, derives local facts, and accepts only parsed, source-grounded directional refutations that pass fixed scoring checks.Source: §3.3 · p. 4

3.4 Answer-Path-Aware Correction

• The controller uses the earliest majority-answer trace and permits one regeneration only when accepted evidence refutes answer-path claims with independent derivation and alternative-answer provenance; otherwise it returns SC.A parseable regenerated answer is adopted without a second correctness check.Source: §3.4 · p. 4

4.1 Experimental Setup

• Evaluation covers five mathematical, logical, and medical benchmarks for Qwen2.5-7B and Llama3.1-8B, with accuracy macro-averaged equally across benchmarks.Baselines include direct answering, independent CoT, SC@3, and GoT and GoV question-answering adaptations; DDRG reuses the three SC responses.Source: §4.1 · pp. 4–5

4.2 Main Results

• 72.74% (Qwen) and 66.58% (Llama) are DDRG’s highest evaluated benchmark-macro accuracies; same-bank SC rises from 72.09% to 72.74% and 66.17% to 66.58%, respectively.The paired audit records beneficial and harmful changes, so accepted verification evidence does not guarantee a correct regeneration; the comparison supports the complete frozen-bank procedure, not a uniform graph-only advantage.Source: §4.2 · pp. 5–6
• Qwen’s largest net gain is MedQA (+21), while Llama’s are LogiQA2 (+12) and GSM8K (+11); Llama has one net harmful change on FOLIO.Qwen has positive net corrections on all five benchmarks, but the solvers’ largest gains occur in different domains.Source: §4.2 · p. 6
• Because benchmark sizes differ, pooled correction counts are not normalized accuracy gains; the reported macro results weight datasets equally.For example, Qwen’s 21 net additional MedQA answers correspond to +1.65 percentage points, while Llama’s 11 net GSM8K answers correspond to +0.83 points.Source: §4.2 · p. 6

4.3 Ablation and Evidence-use Controls

• 117 correct answers for graph-free and 119 for without-path compare with 118 for full DDRG; same-evidence replay selection trails actual regeneration.The control differences are small and do not establish either restriction’s necessity; actual regeneration reaches 72.74% Qwen macro accuracy versus 72.42% for selection, with three more correct answers overall and fewer harmful changes.Source: §4.3 · pp. 6–7

4.4 Source-grounded Case Study

• On GSM8K test:147, DDRG resolves the omitted-return dependency and regenerates 75 from the SC-selected 90.Aligned claims expose the earlier returns; independent verification and evidence on the answer’s support path trigger one regeneration.Source: §4.4 · p. 7, Figure 4 · p. 7
• FOLIO validation 79 shows a verifier error changing correct SC answer B to C, while a ReClor case retains B when no supporting-path refutation is found.The FOLIO chain is an author explanation of the saved failure; the selected cases do not estimate prevalence.Source: §4.4 · pp. 7–8

4.5 Compute and Reproducibility

• 239,681.91 GPU seconds cover 5,868 Qwen predictions, excluding loading and idle residency; historical baseline timings use a different accounting basis.The paper therefore makes no controlled efficiency comparison.Source: §4.5 · p. 8

5.1 Disagreement-conditioned Performance

• Qwen gains 23 correct answers among 1,258 majority banks and 11 among 190 ties; Llama gains 15 among 1,787 and 16 among 404.Observed point gains are larger on ties. The post-hoc groups include invalid answer strings, and gold labels are used only to score them.Source: §5.1 · p. 8

5.2 Intervention, Preservation, and Rescue

• Qwen preserved 99.19% of initially correct SC answers and rescued 4.82% of SC errors; Llama preserved 99.79% and rescued 2.47%.Qwen attempted regeneration on 173 questions and Llama on 117; directional verdicts alone do not trigger correction unless linked to the voted answer’s support path.Source: §5.2 · p. 8

5.3 Candidate Recovery and New Answers

• Most successful corrections recover bank-present answers: 60 of Qwen’s 63 rescues and 34 of Llama’s 38.Qwen corrected 60 of 442 SC errors when the bank contained a correct answer, versus three of 864 without one; Llama corrected 34 of 651 and four of 885, respectively. These are retrospective diagnostics, not controller-accessible oracle information.Source: §5.3 · pp. 8–9

• DDRG yields positive net correction over same-bank voting across two solvers, with saved outcomes including candidate recovery, new correct answers, and harmful changes.Source: §6 · p. 9

• Full-cohort results combine graph processing, a larger verifier, and regeneration, while matched-verifier controls do not establish a separate causal advantage for graph structure or answer-path restriction.Source: Limitations · p. 9
• Both solvers are evaluated on frozen executions, not repeated generation seeds or unseen task families.Source: Limitations · p. 9
• Quoted source spans establish provenance rather than truth; graph dependencies and local verdicts can be wrong, and silver development references are not independent gold verification data.Historical missing verifier records limit complete raw-stage attribution for part of the Llama run; different timing-accounting scopes prevent an efficiency claim.Source: Limitations · p. 9

• Medical-question benchmark accuracy does not measure clinical safety or effectiveness and does not support autonomous medical use.Source: Ethical Considerations · p. 9
• Local verification can introduce errors into answers that were initially correct.Source: Ethical Considerations · p. 9
• A source-grounded presentation can make mistaken reasoning appear credible; provenance and verdict scores do not guarantee factual correctness.Source: Ethical Considerations · p. 9

Appendix roadmap.

• The appendix roadmap assigns prompts to Appendix B, verification interfaces and gates to C, transition counts and statistical calculations to D, and case evidence to E.Appendix A covers model and cohort identities, per-benchmark SC accuracies and gains, and structural controls.Source: Appendix roadmap · p. 11

A.2 Models and Execution Identity

• The solver and verifier checkpoints are identified by model name and pinned revision, and the appendix records the DDRG source and release hash.The listed solvers are Qwen2.5-7B-Instruct and Llama-3.1-8B-Instruct; the verifier is Qwen3-30B-A3B-Instruct-2507.Source: §A.2 · p. 11

A.3 Decoding and Candidate Banks

• The evaluation uses frozen cohorts and candidate banks, specified decoding settings, and offline-only gold-label scoring; invalid outputs remain in the full denominator.The dataset-license declarations include an unresolved discrepancy for MedQA, and the project license is pending author confirmation; the source declarations do not establish complete rights clearance.Source: §A.3 · pp. 11–12

A.1 Same-bank SC and Paired Gains

• Table 3 reports same-bank SC accuracies and DDRG percentage-point gains by benchmark, with an equal-benchmark macro average; invalid predictions remain in the frozen denominators.The appendix says the table supplements the main comparison without repeating its accuracy rows; it provides no cell values here.Source: §A.1 · p. 11, Table 3 · p. 12

A.4 Evaluation Roles

• The zero-shot operating point was fixed on a registered calibration grid before full evaluation, while a silver-reference diagnostic is reported only as a reproducibility reference.The silver-reference diagnostic is marked QUALITY_BLOCKED_SILVER, with 22/29 agreement at 25.44% coverage.Source: §A.4 · p. 12

A.5 Native Llama Condition and Result Audit

• The Llama audit uses a pinned Llama3.1-8B-Instruct solver with the unadapted native Qwen3-30B verifier and reports accuracy for 4,868 labeled questions, not 1,000 hidden ReClor test questions.The full registered panel contains 5,868 unique predictions; four 100-question blocks use preregistered 32K solver-context recovery, while the verifier remains at 8K.Source: §A.5 · p. 12
• 66.58% benchmark-macro accuracy for native Llama DDRG compares with 66.17% for same-bank SC, yielding 31 net correct answers from 38 wrong-to-right and seven right-to-wrong transitions.The audit also records 117 regeneration attempts, 60 final-answer changes, and six invalid final predictions retained in denominators.Source: §A.5 · p. 12

A.6 Fixed-subset Matched-verifier Structural Controls

• The fixed-subset controls use the same ordered Qwen bank, matched official verifier, at most three probes, and at most one regeneration; the subset is fixed independently of prediction outcomes.Among 49 non-unanimous banks, SC is correct on 24 and full DDRG on 26, but these observations are not a full-cohort gain estimate.Source: §A.6 · p. 13
• On the fixed 160-question subset, correct counts were 116 for SC, 118 for full DDRG, 117 for graph-free, and 119 for without-path.The graph-free control removes inferred edges, answer-node routing, and graph-ancestor eligibility; without-path removes the majority support-path restriction, with both retaining the same maximum inference budgets.Source: §A.6 · p. 13

B Full Prompts for All Methods

• DDRG’s repair prompt directs the solver to use local evidence without candidate answers or labels, recompute the refuted step and affected suffix, and preserve retained context as unrefuted rather than guaranteed.It instructs the solver to treat disputed claims as assertions to assess, not additional facts, and to derive the answer from the question and local evidence.Source: B Full Prompts for All Methods · p. 15
• Verifier instructions require a concrete independently derived error for a decisive verdict and reject differences in detail, scope, or relevance as sufficient evidence of contradiction.UNKNOWN covers insufficient evidence or non-comparable claims; neither permits repair.Source: B Full Prompts for All Methods · pp. 16–17

C.1 Five-verdict Interface and Scoring

• The five-verdict scorer requires valid parsing and claim grounding, a normalized score of at least 0.5, and agreement between the generated and highest-scored verdict.Verdict scores sum conditional token log probabilities without length normalization and are not calibrated probabilities of factual correctness; only left/right correctness supplies decisive correction evidence. Malformed or truncated responses are nondecisive, and UNKNOWN never permits repair.Source: §C.1 · p. 17

C.2 Grounding, Eligibility, and Abstention

• Correction requires eligible evidence to refute a nonterminal ancestor on the majority answer’s support path, with one supported candidate-answer provenance value.Any decisive support for the majority suppresses correction. Eligible evidence and retained context feed one solver regeneration; graph abstention, failed gates, incompatible alternatives, absent evidence, or regeneration parse failure return SC, while every parseable regeneration is adopted.Source: §C.2 · p. 17

D Supplementary Results

• The supplementary funnel records 200 pre-regeneration fallbacks, 173 labeled regeneration attempts, and one unparseable regenerated response that returns to SC.Graph, probe, verifier, and question counts are stored separately because they refer to different pipeline stages.Source: D Supplementary Results · p. 18

D.1 Inference Allocation Accounting

• The source-bound Qwen audit covers all 5,868 registered predictions and records 239,681.909356 GPU seconds of inference allocation, reported for reproducibility rather than as an efficiency comparison.The allocation includes 202,591.770123 GPU seconds for labeled questions and 37,090.139233 GPU seconds for hidden ReClor predictions.Source: §D.1 · p. 18

D.2 Retrospective Candidate-selection Control

• The retrospective selection control yields 31 net additional correct answers and 72.42% Qwen macro accuracy, compared with 34 net improvements and 72.74% from fresh regeneration.The control replays recorded evidence and triggers without new model calls; it returns SC when evidence is ineligible.Source: §D.2 · p. 18

D.3 Post-hoc Statistical Calculation

• The Qwen paired bootstrap interval is [0.1447, 1.1504] percentage points, but these retrospective diagnostics are conditional on one frozen bank and decoding seed and do not establish graph causality or multi-seed stability.The bootstrap uses 20,000 replicates; hidden-label ReClor questions are excluded from scoring and uncertainty.Source: §D.3 · p. 18

E Case Evidence and Source Excerpts

• The selected cases illustrate successful and harmful correction rather than estimating how often either outcome occurs.The figures abbreviate claims and compress answer-support paths rather than reproducing full raw graph topology.Source: E Case Evidence and Source Excerpts · p. 18

E.1 Successful Correction: GSM8K Test 147

• The saved GSM8K regeneration returns the gold answer 75, correcting SC’s answer of 90.Table 4 records endpoint comparisons for the successful and harmful cases, not full intermediate traces for every baseline.Source: §E.1 · p. 19, Table 4 · p. 19
• Subtracting the 15 bees already returned from the initial 30, then adding 60 new departures, yields 75 bees still to return.The recorded bank is [90, 15, 75]; the error in the SC answer is including bees that had already returned, not incorrect addition.Source: §E.1 · p. 19

E.2 Harmful Correction: FOLIO Validation 79

• The verifier accepts the FOLIO refutation and regeneration changes the correct answer from B to C (Uncertain).The accepted verdict has normalized conditional score 0.651367.Source: §E.2 · p. 19
• The repair misses that the premises make the product conclusion contradictory: bakery implies hotpot or spicy, and either implies spicy.The premises also say products of Baked by Melissa are cupcakes, and cupcakes are bakeries that are not spicy.Source: §E.2 · p. 19