Information-Theoretic Bound on Multi-Step LLM Reasoning

A recent study published on arXiv (2605.01704) reveals a critical weakness in multi-step reasoning within closed systems of large language models. When identical models engage in debate, they generate varied expressions of a singular viewpoint instead of authentic diverse opinions, which maintains accuracy but undermines the quality of reasoning. The researchers have termed this phenomenon the Debate Trap, with the overarching issue labeled as the Reasoning Trap. They introduce a theoretical framework for evidence-based reasoning failures consisting of three elements: (i) SFS (Supported Faithfulness Score), a metric that assesses atomic claims against evidence, achieving consistent rankings with Spearman rho=1.0; (ii) EGSR (Evidence-Grounded Socratic Reasoning), which shifts from adversarial debate to evidence-based questioning; and (iii) Theorem 1 (DPI Bound), demonstrating that standard multi-agent debate leads to Markov chains, thus constraining information transfer from evidence to outcomes. The study offers insights into the decline of closed-system reasoning and suggests metrics and strategies to address the problem.