{
  "annotation_id": "aee05b19-b35b-45d8-8fa3-5898db70ea4d",
  "date_created": "2026-02-17T05:53:04.962000Z",
  "date_modified": "2026-02-17T05:53:04.962000Z",
  "file_hash": "3e5e0286230d55b44940a6146d8714de84482dd8fce8238e464f1f70694f0452",
  "private": false,
  "record": {
    "abstract": "NVIDIA\u0027s CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.",
    "arxiv_id": "2601.05972",
    "authors": [
      "Jack Carlisle",
      "Jay Shah",
      "Reuben Stern",
      "Paul VanKoughnett"
    ],
    "categories": [
      "cs.PL",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Categorical Foundations for CuTe Layouts",
    "url": "https://arxiv.org/abs/2601.05972",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f304d896-a360-4643-a0f8-b2db1387795c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}