https://neckpinch.com/authors/christophe-baehr/New arXiv papers by Christophe Baehr, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2503.19867/arxiv:2503.19867Tue, 25 Mar 2025 00:00:00 GMTMing Lei, Christophe Baehr — This paper establishes a unified framework integrating geometric flows with deep learning through three fundamental innovations. First, we propose a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to loss landscape topology, formally proved to preserve isometric knowledge embedding (Theorem ). Second, we derive explicit phase transition thresholds and critical learning rates (Theorem ) through curvature blowup analysis, enabling automated singularity resolution via geometric surgery (Lemma ). Third, we establish an AdS/CFT-type holographic duality (Theorem ) between neural networks and conformal field theories, providing entanglement entropy bounds for regularization design. Experiments demonstrate 2.1× convergence acceleration and 63% topological simplification while maintaining 𝓞(Nlog N) complexity, outperforming Riemannian baselines by 15.2% in few-shot accuracy. Theoretically, we prove exponential stability (Theorem ) through a new Lyapunov function combining Perelman entropy with Wasserstein gradient flows, fundamentally advancing geometric deep learning.Ricci flowSingularitiesSurgeryPerelman entropyStability & uniquenessDiscrete & graph Ricci