{
  "annotation_id": "d0dd66ab-708f-43e8-9d1a-e43a2ff40458",
  "date_created": "2026-02-17T05:53:12.436000Z",
  "date_modified": "2026-02-17T05:53:12.436000Z",
  "file_hash": "83d423eee2715a61c0ed8569764806375da7973ed27e2ceefbefcb58306880c4",
  "private": false,
  "record": {
    "abstract": "This paper studies the AdamW-style Shampoo optimizer, an effective implementation of classical Shampoo that notably won the external tuning track of the AlgoPerf neural network training algorithm competition. Our analysis unifies one-sided and two-sided preconditioning and establishes the convergence rate $\\frac{1}{K}\\sum_{k=1}^K E\\left[\\|\\nabla f(X_k)\\|_*\\right]\\leq O(\\frac{\\sqrt{m+n}C}{K^{1/4}})$ measured by nuclear norm, where $K$ represents the iteration number, $(m,n)$ denotes the size of matrix parameters, and $C$ matches the constant in the optimal convergence rate of SGD. Theoretically, we have $\\|\\nabla f(X)\\|_F\\leq \\|\\nabla f(X)\\|_*\\leq \\sqrt{m+n}\\|\\nabla f(X)\\|_F$, supporting that our convergence rate can be considered to be analogous to the optimal $\\frac{1}{K}\\sum_{k=1}^KE\\left[\\|\\nabla f(X_k)\\|_F\\right]\\leq O(\\frac{C}{K^{1/4}})$ convergence rate of SGD in the ideal case of $\\|\\nabla f(X)\\|_*= \\Theta(\\sqrt{m+n})\\|\\nabla f(X)\\|_F$.",
    "arxiv_id": "2601.07326",
    "authors": [
      "Huan Li",
      "Yiming Dong",
      "Zhouchen Lin"
    ],
    "categories": [
      "math.OC",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Convergence Rate Analysis of the AdamW-Style Shampoo: Unifying One-sided and Two-Sided Preconditioning",
    "url": "https://arxiv.org/abs/2601.07326",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e7fd5b3c-9bf2-4af3-923d-e2d8b609d24b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}