The Reasoning Trap: An Information-Theoretic Bound on Closed-System Multi-Step LLM Reasoning
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2026
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| _version_ | 1866914533263540224 |
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| author | Shin, Kwan Soo |
| author_facet | Shin, Kwan Soo |
| contents | When copies of the same language model are prompted to debate, they produce diverse phrasings of one perspective rather than diverse perspectives. Multi-agent debate (MAD), and more broadly closed-system reasoning where agents iteratively transform each other's outputs, tends to preserve answer accuracy while degrading the reasoning behind those answers. We name the multi-agent case the Debate Trap and the broader phenomenon the Reasoning Trap, offering a programmatic theory of evidence-grounded reasoning failure.The framework has three parts: (i) SFS (Supported Faithfulness Score), a claim-level metric verifying decomposed atomic claims against provided evidence (decomposer-invariant rankings: Spearman rho=1.0); (ii) EGSR (Evidence-Grounded Socratic Reasoning), replacing adversarial argumentation with evidence-grounded inquiry; (iii) Theorem 1 (DPI Bound): under standard MAD, the chain E -> O^0 -> O^1 -> ... is Markov, and the Data Processing Inequality implies E[I(E;O^{t+1})] <= E[I(E;O^t)]. Three companion results -- open-system recovery (Theorem 2), EGSR accumulation (Lemma 2), and vote-aggregation floor (Proposition 1) -- partition multi-step LLM reasoning by its information-theoretic relationship to E. Across 16 conditions on SciFact (300 claims) and FEVER (1,000 claims), DebateCV (C13) preserves 88% of baseline accuracy while SFS drops 43%; majority-vote MAD (C15) reduces SFS to 1.7% of baseline (p < 10^{-6}, d = -0.96); EGSR recovers 98%. An R6 cohort study (Korean n=10x30 FEVER; English n=3x200 SciFact) finds inter-rater Fleiss kappa <= +0.018 with 0.8-1.4 Likert intra-rater shifts across language and domain -- the human agreement that faithfulness metrics have been calibrated against is not itself stable. We offer one falsifiable conjecture: any closed-system reasoning protocol preserving Theorem 1's Markov structure is, in expectation, subject to the same DPI bound. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_01704 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Reasoning Trap: An Information-Theoretic Bound on Closed-System Multi-Step LLM Reasoning Shin, Kwan Soo Computation and Language Artificial Intelligence Machine Learning When copies of the same language model are prompted to debate, they produce diverse phrasings of one perspective rather than diverse perspectives. Multi-agent debate (MAD), and more broadly closed-system reasoning where agents iteratively transform each other's outputs, tends to preserve answer accuracy while degrading the reasoning behind those answers. We name the multi-agent case the Debate Trap and the broader phenomenon the Reasoning Trap, offering a programmatic theory of evidence-grounded reasoning failure.The framework has three parts: (i) SFS (Supported Faithfulness Score), a claim-level metric verifying decomposed atomic claims against provided evidence (decomposer-invariant rankings: Spearman rho=1.0); (ii) EGSR (Evidence-Grounded Socratic Reasoning), replacing adversarial argumentation with evidence-grounded inquiry; (iii) Theorem 1 (DPI Bound): under standard MAD, the chain E -> O^0 -> O^1 -> ... is Markov, and the Data Processing Inequality implies E[I(E;O^{t+1})] <= E[I(E;O^t)]. Three companion results -- open-system recovery (Theorem 2), EGSR accumulation (Lemma 2), and vote-aggregation floor (Proposition 1) -- partition multi-step LLM reasoning by its information-theoretic relationship to E. Across 16 conditions on SciFact (300 claims) and FEVER (1,000 claims), DebateCV (C13) preserves 88% of baseline accuracy while SFS drops 43%; majority-vote MAD (C15) reduces SFS to 1.7% of baseline (p < 10^{-6}, d = -0.96); EGSR recovers 98%. An R6 cohort study (Korean n=10x30 FEVER; English n=3x200 SciFact) finds inter-rater Fleiss kappa <= +0.018 with 0.8-1.4 Likert intra-rater shifts across language and domain -- the human agreement that faithfulness metrics have been calibrated against is not itself stable. We offer one falsifiable conjecture: any closed-system reasoning protocol preserving Theorem 1's Markov structure is, in expectation, subject to the same DPI bound. |
| title | The Reasoning Trap: An Information-Theoretic Bound on Closed-System Multi-Step LLM Reasoning |
| topic | Computation and Language Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2605.01704 |