{"paper":{"title":"Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.PR","authors_text":"Elliot Paquette, Lucas Benigni","submitted_at":"2025-08-27T16:41:01Z","abstract_excerpt":"We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\\in\\mathbb{R}^{n\\times d}$ is an i.i.d random matrix, $W\\in\\mathbb{R}^{d\\times p}$ is an i.i.d $\\mathcal{N}(0,1)$ matrix and $D\\in\\mathbb{R}^{p\\times p}$ is a diagonal matrix with i.i.d bounded entries, we consider the matrix\n  \\[\n  \\mathrm{NTK}\n  =\n  \\frac{1}{d}XX^\\top\n  \\odot\n  \\frac{1}{p}\n  \\sigma'\\left(\n  \\frac{1}{\\sqrt{d}}XW\n  \\right)D^2\n  \\sigma'\\left(\n  \\frac{1}{\\sqrt{d}}XW\n  \\right)^\\top\n  \\]\n  where $\\sigma'$ is a pseudo-Lipsc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20036","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/2508.20036/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"}