{"paper":{"title":"Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CV","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aarti Singh, Barnabas Poczos, Jason D. Lee, Simon S. Du, Yuandong Tian","submitted_at":"2017-12-03T15:00:35Z","abstract_excerpt":"We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i.e., $f(\\mathbf{Z}, \\mathbf{w}, \\mathbf{a}) = \\sum_j a_j\\sigma(\\mathbf{w}^T\\mathbf{Z}_j)$, in which both the convolutional weights $\\mathbf{w}$ and the output weights $\\mathbf{a}$ are parameters to be learned. When the labels are the outputs from a teacher network of the same architecture with fixed weights $(\\mathbf{w}^*, \\mathbf{a}^*)$, we prove that with Gaussian input $\\mathbf{Z}$, there is a spurious local minimizer. Surprisingly, in the presence of the spur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00779","kind":"arxiv","version":2},"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"}