{"slug": "thermodynamic-signatures-of-reasoning-free-energy-and-spectral-form-factor-for", "title": "Thermodynamic Signatures of Reasoning: Free-Energy and Spectral-Form-Factor Diagnostics for Hallucination Detection in Large Language Models", "summary": "Researchers introduced Free-Energy Signatures (Fes), a spectral descriptor for hallucination detection in large language models that treats attention Laplacians as Hamiltonians to extract thermodynamic potentials. The method achieved a +6.5 AUROC improvement over LapEig and +2.4 over GoR-4 across six models and benchmarks, with a training-free detector. A complementary random-matrix-theory analysis revealed that correct generations exhibit Wigner-Dyson spectral statistics while hallucinations show Poisson-like statistics.", "body_md": "arXiv:2606.19404v1 Announce Type: new\nAbstract: Hallucination detection in large language models (LLMs) is deployment-critical, and recent work shows that the spectrum of attention-derived graph Laplacians carries strong signal about reasoning quality. Prior spectral diagnostics, however, summarize the Laplacian spectrum by a handful of eigenvalues or hand-picked scalars, leaving most of its structure unused. We propose Free-Energy Signatures (Fes), a spectral descriptor that treats each layer's attention Laplacian as a Hamiltonian and extracts its thermodynamic potentials partition function, free energy, spectral entropy, heat capacity together with the random-matrix-theory (RMT) spectral form factor. We prove three results: (i)~Lipschitz stability of Fes under attention perturbation; (ii)~an expressiveness result showing that Fes enriches finite spectral summaries and approximates moment-derived spectral functionals under explicit regularity and grid-resolution assumptions; and (iii)~a finite-sample PAC bound on the AUROC of a training-free detector built from Fes. Empirically, across six open-weight LLMs and six benchmarks, a lightweight probe on Fes descriptors achieves the strongest aggregate AUROC among attention-spectral baselines, improving over LapEig by $+6.5$ AUROC points and over GoR-4 by $+2.4$ points on average, while requiring no update to the underlying LLM. In the fully unsupervised setting, an RMT-deviation score achieves mean AUROC $0.71$, providing a label-free but weaker detector. A complementary RMT analysis shows that correct generations exhibit more Wigner-Dyson like spectral statistics, whereas hallucinations exhibit more Poisson-like statistics. The anonymized code and config are provided in the supplementary material.", "url": "https://wpnews.pro/news/thermodynamic-signatures-of-reasoning-free-energy-and-spectral-form-factor-for", "canonical_source": "https://arxiv.org/abs/2606.19404", "published_at": "2026-06-19 04:00:00+00:00", "updated_at": "2026-06-19 04:09:21.826270+00:00", "lang": "en", "topics": ["large-language-models", "ai-safety", "ai-research"], "entities": ["Free-Energy Signatures", "LapEig", "GoR-4", "arXiv"], "alternates": {"html": "https://wpnews.pro/news/thermodynamic-signatures-of-reasoning-free-energy-and-spectral-form-factor-for", "markdown": "https://wpnews.pro/news/thermodynamic-signatures-of-reasoning-free-energy-and-spectral-form-factor-for.md", "text": "https://wpnews.pro/news/thermodynamic-signatures-of-reasoning-free-energy-and-spectral-form-factor-for.txt", "jsonld": "https://wpnews.pro/news/thermodynamic-signatures-of-reasoning-free-energy-and-spectral-form-factor-for.jsonld"}}