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We establish the Shannon-Topological Bottleneck Theorem, proving that when a target boundary's geometric complexity exce","title":"Informational Frustration in Neural Manifolds: Shannon Bottlenecks and the Limits of Learnability","url":"https://arxiv.org/abs/2606.30512","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.30512v1 Announce Type: cross \nAbstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory. Classical frameworks like VC dimension and Rademacher complexity predict catastrophic overfitting in modern models, leaving a massive theoretical gap between theory and reality. In this paper, we bridge this divide by introducing a unified framework that links information theory, topology, and statistical mechanics to map the hard limits of deep learning. 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