{"paper":{"title":"Neural Networks Efficiently Learn Low-Dimensional Representations with SGD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Alireza Mousavi-Hosseini, Ioannis Mitliagkas, Manuela Girotti, Murat A. Erdogdu, Sejun Park","submitted_at":"2022-09-29T15:29:10Z","abstract_excerpt":"We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\\boldsymbol{x}\\in \\mathbb{R}^d$ is Gaussian and the target $y \\in \\mathbb{R}$ follows a multiple-index model, i.e., $y=g(\\langle\\boldsymbol{u_1},\\boldsymbol{x}\\rangle,...,\\langle\\boldsymbol{u_k},\\boldsymbol{x}\\rangle)$ with a noisy link function $g$. We prove that the first-layer weights of the NN converge to the $k$-dimensional principal subspace spanned by the vectors $\\boldsymbol{u_1},...,\\boldsymbol{u_k}$ of the true model, when online SGD with weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.14863","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.14863/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"}