{"paper":{"title":"Learning Gaussian Multi-Index Models with Gradient Flow: Time Complexity and Directional Convergence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NE","math.AG"],"primary_cat":"cs.LG","authors_text":"Amire Bendjeddou, Berfin \\c{S}im\\c{s}ek, Daniel Hsu","submitted_at":"2024-11-13T17:25:25Z","abstract_excerpt":"This work focuses on the gradient flow dynamics of a neural network model that uses correlation loss to approximate a multi-index function on high-dimensional standard Gaussian data. Specifically, the multi-index function we consider is a sum of neurons $f^*(x) \\!=\\! \\sum_{j=1}^k \\! \\sigma^*(v_j^T x)$ where $v_1, \\dots, v_k$ are unit vectors, and $\\sigma^*$ lacks the first and second Hermite polynomials in its Hermite expansion. It is known that, for the single-index case ($k\\!=\\!1$), overcoming the search phase requires polynomial time complexity. We first generalize this result to multi-inde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.08798","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/2411.08798/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"}