{"paper":{"title":"High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Denny Wu, Greg Yang, Jimmy Ba, Murat A. Erdogdu, Taiji Suzuki, Zhichao Wang","submitted_at":"2022-05-03T12:09:59Z","abstract_excerpt":"We study the first gradient descent step on the first-layer parameters $\\boldsymbol{W}$ in a two-layer neural network: $f(\\boldsymbol{x}) = \\frac{1}{\\sqrt{N}}\\boldsymbol{a}^\\top\\sigma(\\boldsymbol{W}^\\top\\boldsymbol{x})$, where $\\boldsymbol{W}\\in\\mathbb{R}^{d\\times N}, \\boldsymbol{a}\\in\\mathbb{R}^{N}$ are randomly initialized, and the training objective is the empirical MSE loss: $\\frac{1}{n}\\sum_{i=1}^n (f(\\boldsymbol{x}_i)-y_i)^2$. In the proportional asymptotic limit where $n,d,N\\to\\infty$ at the same rate, and an idealized student-teacher setting, we show that the first gradient update cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01445","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/2205.01445/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"}