{"paper":{"title":"A mean-field limit for certain deep neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel Yukimura, Dyego Ara\\'ujo, Roberto I. Oliveira","submitted_at":"2019-06-01T09:51:35Z","abstract_excerpt":"Understanding deep neural networks (DNNs) is a key challenge in the theory of machine learning, with potential applications to the many fields where DNNs have been successfully used. This article presents a scaling limit for a DNN being trained by stochastic gradient descent. Our networks have a fixed (but arbitrary) number $L\\geq 2$ of inner layers; $N\\gg 1$ neurons per layer; full connections between layers; and fixed weights (or \"random features\" that are not trained) near the input and output. Our results describe the evolution of the DNN during training in the limit when $N\\to +\\infty$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00193","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"}