GCL-MAD: Graph-guided Conflict Localization for LLM Multi-Agent Debate

Multi-agent debate (MAD) has emerged as a promising paradigm for improving the reasoning capabilities of large language models. However, final decisions in existing MAD may be influenced by arguments presented with greater fluency or confidence rather than the actual correctness of reasoning. Moreover, intermediate reasoning errors are often embedded within plausible complete reasoning trajectories, making it difficult to identify which specific steps are responsible for an incorrect conclusion. To address these limitations, we propose GCL-MAD, a structured multi-agent debate framework that shifts debate from exchanging complete reasoning trajectories to reasoning about verifiable epistemic components. Specifically, outputs from agents with complementary roles are organized into structured fields, such as an answer, assumptions, or skeptical points or boundary conditions, with each populated field represented as one epistemic component node. Based on these components,a graph-construction agent organizes potential relationships among these components into an Epistemic Conflict Graph, where conflict edges are associated with explicit rationales describing their underlying causes. Guided by this graph, GCL-MAD identifies conflict-related edges and their associated components, enabling targeted verification only within these regions rather than re-verifying complete reasoning trajectories. Experiments across six reasoning benchmarks and two backbone models show that GCL-MAD consistently improves reasoning performance and supports more reliable answer correction through localized verification.