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

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.

Large Reasoning Models produce Long Chains-of-Thought (LCoTs) which involve breaking down the problem into smaller reasoning steps before reaching the conclusion. However, these steps often contain contradictions, unsupported inferences, or irrelevant steps, even when the final answer is correct. We propose Long Chain-of-Thought Graph Verifier (LCoT-GV), a graph-based framework that represents LCoTs as reasoning graphs. Each node in the graph represents a reasoning step and the edges encode semantic and logical relations. A Graph Attention Network is then trained to predict chain-of-thought correctness from the reasoning graph. We construct a new graph-oriented verification dataset from multiple reasoning benchmarks for question answering in various domains. The results show that our method is competitive with the most similar approaches.

Large language models (LLMs) have become increasingly used for various tasks, often coupled with Chain-of-Thought (CoT) prompting to boost accuracy. Recent work has shown that high label-prediction accuracy does not guarantee correct intermediate reasoning, and the causes of reasoning flaws vary from sample to sample, yet existing remedies either focus on a single domain or assume that one flaw type applies uniformly across samples. A simple mitigation method is to provide the model with the correct answer, but we show that this yields no consistent improvement in reasoning quality. This indicates that the problem cannot be fixed by LLMs' awareness of answers, and must instead be addressed through the structure of reasoning. Motivated by this, we propose CRAFT (Consensus Reasoning knowledge graph Aggregation for Flaw-aware Trace synthesis), which aggregates the consensus components shared across multiple candidate reasoning traces to synthesize improved ones. CRAFT consistently improves label-prediction accuracy on both logical and mathematical reasoning benchmarks, outperforming most baselines, while its post-processed traces achieve higher quality under fine-grained benchmark evaluation.