{
  "abstract": "Recursive feature machines (RFMs) learn representations of data by alternating between fitting a predictor to a dataset and updating features of that predictor using the average gradient outer product (AGOP). Connections between AGOPs and feature learning in neural networks motivate linear RFMs as a simple setting for analyzing how representations evolve during training. Here, we study the dynamics and statistics of linear RFM in noisy multi-output regression with isotropic sub-Gaussian input data and targets generated by a low-rank teacher matrix of dimension $d$. We extend the known connection between linear RFM and iteratively reweighted least squares from the interpolating setting to ridge-regularized multi-output regression with noise. We show that the learned feature matrix remains close to its infinite-data ideal counterpart at every iteration. Namely, for $n$ samples, we show the error in the feature matrix decays as $O(\\sqrt{d/n})$ with high probability. Experiments on real-world text and single-cell gene-expression data illustrate the features learned by this simple linear model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09196",
  "author_total": 4,
  "authors": [
    {
      "name": "Andrew Cheng"
    },
    {
      "name": "Bobak T. Kiani"
    },
    {
      "name": "Yue M. Lu"
    },
    {
      "name": "Adityanarayanan Radhakrishnan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0stdkcdd8fxt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09196",
  "fulltext_url": null,
  "id": "0stdkcdd8fxt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09196",
  "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": "W7220916747",
  "pdf_url": "https://arxiv.org/pdf/2610.09196",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0stdkcdd8fxt6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:48Z",
      "native_id": "2610.09196",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09196"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Exact Dynamics and Finite-Sample Trajectory Recovery of Linear Recursive Feature Machines",
  "title_text": "Exact Dynamics and Finite-Sample Trajectory Recovery of Linear Recursive Feature Machines",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:48Z",
  "url": "https://research.draconitic.com/paper/0stdkcdd8fxt6",
  "venue": "arXiv",
  "versions": []
}