{
  "annotation_id": "6d127bbb-aceb-4ebc-93a8-b08edfe4b16e",
  "date_created": "2026-02-17T05:53:08.894000Z",
  "date_modified": "2026-02-17T05:53:08.894000Z",
  "file_hash": "46a57bacb3e9b43a570e55687628543d894ad7201cef95d3e37876c0864cc140",
  "private": false,
  "record": {
    "abstract": "We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near each point $x$, to the subspace that captures the local variability of the function $f$. We pose this task as kernel adaptation along a manifold with noise, and introduce Local EGOP learning, a recursive algorithm that utilizes the Expected Gradient Outer Product (EGOP) quadratic form as both a metric and inverse-covariance of our target distribution. We prove that Local EGOP learning adapts to the regularity of the function of interest, showing that under a supervised noisy manifold hypothesis, intrinsic dimensional learning rates are achieved for arbitrarily high-dimensional noise. Empirically, we compare our algorithm to the feature learning capabilities of deep learning. Additionally, we demonstrate improved regression quality compared to two-layer neural networks in the continuous single-index setting.",
    "arxiv_id": "2601.07061",
    "authors": [
      "Alex Kokot",
      "Anand Hemmady",
      "Vydhourie Thiyageswaran",
      "Marina Meila"
    ],
    "categories": [
      "stat.ML",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Local EGOP for Continuous Index Learning",
    "url": "https://arxiv.org/abs/2601.07061",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f7e74cdf-f2bd-4041-aa77-23b5ad56b093",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}