{
  "abstract": "Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/λ$ in the weight decay. We show that on a structured feature map the same delay does not appear. For a band-limited Fourier feature map over $\\mathbb{Z}_p^2$ carrying a single-character target that lies inside the expressible class, enlarging the band at fixed positive weight decay drives peak held-out accuracy monotonically from $1.00$ to $0.07$, with no memorize-then-generalize regime anywhere along the sweep. The degradation is not an interpolation effect. It sets in at capacity ratio $q/n = 0.638$, far below the interpolation threshold, on separate grounds from the exact null space that appears above it. What does have a sharp boundary is the active support. Holding the nominal dimension fixed and masking the band back to $1089$ active modes restores held-out accuracy of $1.000$ with zero variance across seeds, while the full $4225$-mode band collapses to $0.185$. The number of active modes acts through the teacher-weighted spectrum of the empirical Gram matrix and not through the capacity ratio, which makes this a statement about feature geometry and not a restatement of double descent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15047",
  "author_total": 3,
  "authors": [
    {
      "name": "Chon-Fai Kam"
    },
    {
      "name": "Miloud Bessafi"
    },
    {
      "name": "Frederic Cadet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dt0053n3fs9re.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15047",
  "fulltext_url": null,
  "id": "dt0053n3fs9re",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15047",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213361183",
  "pdf_url": "https://arxiv.org/pdf/2609.15047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dt0053n3fs9re.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2609.15047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Structured Features Overfit Where Random Features Grok",
  "title_text": "Structured Features Overfit Where Random Features Grok",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/dt0053n3fs9re",
  "venue": "arXiv",
  "versions": []
}