{"paper":{"title":"Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Denny Wu, Jason D. Lee, Kazusato Oko, Taiji Suzuki","submitted_at":"2024-06-03T17:56:58Z","abstract_excerpt":"We study the problem of gradient descent learning of a single-index target function $f_*(\\boldsymbol{x}) = \\textstyle\\sigma_*\\left(\\langle\\boldsymbol{x},\\boldsymbol{\\theta}\\rangle\\right)$ under isotropic Gaussian data in $\\mathbb{R}^d$, where the unknown link function $\\sigma_*:\\mathbb{R}\\to\\mathbb{R}$ has information exponent $p$ (defined as the lowest degree in the Hermite expansion). Prior works showed that gradient-based training of neural networks can learn this target with $n\\gtrsim d^{\\Theta(p)}$ samples, and such complexity is predicted to be necessary by the correlational statistical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01581","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/2406.01581/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"}