{
  "abstract": "Fine-tuning pre-trained models on specialized tasks with scarce data is central to modern deep learning. Despite its empirical success, theoretical understanding of fine-tuning remains limited. We introduce a Gaussian multi-index setting to study fine-tuning from pre-trained weights, where the teacher network has $m+1$ features, $m$ of which are learned during pre-training and one of which must be learned during fine-tuning. For two-layer ReLU networks, we show that two-timescale training, i.e., updating the outer weights infinitely faster than the hidden ones, learns the new task-specific feature while preserving the pre-trained ones in the model representation. Moreover, only $\\mathcal{O}(d)$ fine-tuning samples are required for this recovery, independently of the number of pre-trained features. In contrast, with random initialization, the same number of samples is insufficient to recover the target parameters. Our results therefore demonstrate that pre-training can induce an implicit bias with a clear statistical advantage over random initialization, enabling feature learning from scarce fine-tuning data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34667",
  "author_total": 2,
  "authors": [
    {
      "name": "Etienne Boursier"
    },
    {
      "name": "Nicolas Flammarion"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f5nxwcspvhf9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34667",
  "fulltext_url": null,
  "id": "f5nxwcspvhf9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34667",
  "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|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7214707192",
  "pdf_url": "https://arxiv.org/pdf/2609.34667",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f5nxwcspvhf9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.34667",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34667"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Two-Timescale Fine-tuning Provably Learns New Features for Two-Layer ReLU Networks",
  "title_text": "Two-Timescale Fine-tuning Provably Learns New Features for Two-Layer ReLU Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/f5nxwcspvhf9g",
  "venue": "arXiv",
  "versions": []
}