{
  "annotation_id": "5620c54f-5620-4c14-a770-9c9a4daa89a0",
  "date_created": "2026-02-17T05:53:24.225000Z",
  "date_modified": "2026-02-17T05:53:24.225000Z",
  "file_hash": "4b5af759397a27aabd6e2b12810a23071de12674fab4bb4fa3eb0129e5ee9127",
  "private": false,
  "record": {
    "abstract": "We introduce \\emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distributions to the OT map, using only few-shot samples from each distribution as a prompt and \\emph{without} gradient updates at inference. We parameterize the solution operator and develop scaling-law theory in two regimes. In the \\emph{nonparametric} setting, when tasks concentrate on a low-intrinsic-dimension manifold of source--target pairs, we establish generalization bounds that quantify how in-context accuracy scales with prompt size, intrinsic task dimension, and model capacity. In the \\emph{parametric} setting (e.g., Gaussian families), we give an explicit architecture that recovers the exact OT map in context and provide finite-sample excess-risk bounds. Our numerical experiments on synthetic transports and generative-modeling benchmarks validate the framework.",
    "arxiv_id": "2601.09979",
    "authors": [
      "Frank Cole",
      "Dixi Wang",
      "Yineng Chen",
      "Yulong Lu",
      "Rongjie Lai"
    ],
    "categories": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "In-Context Operator Learning on the Space of Probability Measures",
    "url": "https://arxiv.org/abs/2601.09979",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a293f101-b33a-4a36-b84b-74a758067551",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}