{"ID":2835463,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.23083","arxiv_id":"2511.23083","title":"Spectral Concentration at the Edge of Stability: Information Geometry of Kernel Associative Memory","abstract":"High-capacity kernel Hopfield networks exhibit a \\textit{Ridge of Optimization} characterized by extreme stability. While previously linked to \\textit{Spectral Concentration}, its origin remains elusive. Here, we analyze the network dynamics on a statistical manifold, revealing that the Ridge corresponds to the Edge of Stability, a critical boundary where the Fisher Information Matrix becomes singular. We demonstrate that the apparent Euclidean force antagonism is a manifestation of \\textit{Dual Equilibrium} in the Riemannian space. This unifies learning dynamics and capacity via the Minimum Description Length principle, offering a geometric theory of self-organized criticality.","short_abstract":"High-capacity kernel Hopfield networks exhibit a \\textit{Ridge of Optimization} characterized by extreme stability. While previously linked to \\textit{Spectral Concentration}, its origin remains elusive. Here, we analyze the network dynamics on a statistical manifold, revealing that the Ridge corresponds to the Edge of...","url_abs":"https://arxiv.org/abs/2511.23083","url_pdf":"https://arxiv.org/pdf/2511.23083v5","authors":"[\"Akira Tamamori\"]","published":"2025-11-28T11:14:15Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.NE\",\"stat.ML\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}