{"paper":{"title":"A Geometric Characterization of the Stationary Plateau for Two-Layer Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"cs.LG","authors_text":"Dawei Li, Ruoyu Sun, Tian Ding","submitted_at":"2026-06-03T01:03:34Z","abstract_excerpt":"We investigate the geometric structure of stationary plateaus that arise in the loss landscape of two-layer neural networks with smooth activation functions. We focus on the phenomenon of \"neuron splitting\" where duplicating a hidden neuron yields an affine set of stationary points in a wider network. We provide a comprehensive classification of all stationary points on these plateaus, determining under what conditions they constitute local minima or saddle points. Our characterization hinges on a per-neuron curvature object we term the \"inner Hessian\" matrix. Our analysis reveals that the def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04327","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04327/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}