{
  "abstract": "The theoretical understanding of multi-layer neural networks is largely confined to overparameterized settings, which obscure parameter identifiability and incur high sample complexity. Neural tangent kernel (NTK) provides a general theory for wide networks, but does not offer efficient sample-complexity guarantees. Recent feature-learning results go beyond kernel methods for single-neuron, multi-index, and hierarchical targets. However, the analysis is often restricted to shallow or specific architectures and to the overparameterized regime. We break this paradigm to achieve parameter-level recovery of deep target networks, albeit by using active data queries. Specifically, we study $L$-layer polynomial networks with even degree-$k$ monomial activations and nonnegative higher-layer weights. This structure makes the target network input-convex, while the optimization landscape remains highly nonconvex with respect to the parameters. Leveraging input convexity and active queries, we propose \\textbf{ASPIRE} (\\textbf{A}ctive \\textbf{S}am\\textbf{P}ling for \\textbf{I}terative \\textbf{R}ecovery via \\textbf{E}igendirections), a layerwise sampling-based diagonalization algorithm that recovers all network parameters to $δ$-accuracy with sample complexity $ \\widetilde O_{k,L}\\left(d^{L^2+O(L)}δ^{-2e}\\right) $ in polynomial time. To our knowledge, this is the \\emph{first} parameter-recovery guarantee for deep target networks whose exponent grows only polynomially with depth, as well as the \\emph{first} justification for the effectiveness of using high-quality data in neural network training, with a remarkably \\emph{exponential} separation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04999",
  "author_total": 4,
  "authors": [
    {
      "name": "Jinqi Tang"
    },
    {
      "name": "Qian Chen"
    },
    {
      "name": "Shihong Ding"
    },
    {
      "name": "Cong Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0b7sg6ff9v6bc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04999",
  "fulltext_url": null,
  "id": "0b7sg6ff9v6bc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04999",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7220658395",
  "pdf_url": "https://arxiv.org/pdf/2610.04999",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0b7sg6ff9v6bc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.04999",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04999"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond Overparameterization: Provable Learning of Input-Convex Multi-Layer Polynomial Networks with Active Queries",
  "title_text": "Beyond Overparameterization: Provable Learning of Input-Convex Multi-Layer Polynomial Networks with Active Queries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/0b7sg6ff9v6bc",
  "venue": "arXiv",
  "versions": []
}