{"paper":{"title":"Hessian-information geometric formulation of a class of deterministic neural network models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.PS"],"primary_cat":"math-ph","authors_text":"Shin-itiro Goto","submitted_at":"2019-04-29T14:21:35Z","abstract_excerpt":"In this paper a class of dynamical systems describing deterministic neural network models are formulated from a viewpoint of differential geometry. This class includes the Hopfield model and gradient systems, and is such that the so-called activation functions induce information and Hessian geometries. In this formulation, it is shown that the phase space compressibility of a dynamical system belonging to this class is written in terms of the Laplace operator defined on Hessian manifolds, where phase space compressibility is associated with a volume-form of a manifold, and expresses how such a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12734","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}