logbook.json

{
  "schema_version": 1,
  "title": "Repro: Riemannian Stochastic Optimization for Sufficient Dimension Reduction",
  "emoji": "chart",
  "space_id": "snaykey/repro-foam",
  "paper": {
    "openreview_id": "aLnPza1dyT"
  },
  "tags": [
    "icml2026-repro",
    "paper-aLnPza1dyT"
  ],
  "updated_at": "2026-07-26T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Repro: Riemannian Stochastic Optimization for Sufficient Dimension Reduction",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-stiefel-reformulation-closed-form-gradient",
        "title": "SMAVE reformulates the MAVE objective as maximization of a smooth O(d)-invariant function on the Stiefel manifold St(p,d) and provides a closed-form Riemannian gradient for this objective (Proposition 2.7, Proposition 4.1, Section 4).",
        "file": "pages/claim-1-stiefel-reformulation-closed-form-gradient/page.md",
        "children": []
      },
      {
        "slug": "claim-2-almost-sure-convergence-rate",
        "title": "SMAVE is proven to converge almost surely to critical points under decaying step sizes and to achieve a non-asymptotic O(1/sqrt(T)) convergence rate matching optimal non-convex stochastic first-order methods (Propositions 4.3-4.4, Theorem 4.4, Section 4.3).",
        "file": "pages/claim-2-almost-sure-convergence-rate/page.md",
        "children": []
      },
      {
        "slug": "claim-3-synthetic-speedup-and-error",
        "title": "On synthetic benchmarks with n up to 5000 and p up to 200, SMAVE runs 34x to 64x faster than RMAVE while reducing estimation error (e.g., 0.25 vs 0.69 error at n=5000, p=200), requiring about 5.1 seconds versus RMAVE's 174 seconds at n=5000, p=200 (Table 2-3, Section 5.2).",
        "file": "pages/claim-3-synthetic-speedup-and-error/page.md",
        "children": []
      },
      {
        "slug": "claim-4-gas-sensor-real-data",
        "title": "On the Gas Sensor real-world regression dataset (p=128), SMAVE achieves lower MSE than RMAVE (0.018 vs 0.025, p=0.027) while running orders of magnitude faster, though on lower-dimensional datasets such as Wine Quality (p=11) and Pumadyn (p=32) RMAVE attains statistically better or comparable MSE (Tables 5-6, Section 5.3).",
        "file": "pages/claim-4-gas-sensor-real-data/page.md",
        "children": []
      },
      {
        "slug": "claim-5-per-iteration-cost-scaling",
        "title": "SMAVE's per-iteration computational cost is O(mkp^2) via sparse k-NN localization in the projected space with mini-batch size m, compared to the O(n^2 p^2) cost of OPG and RMAVE which use ambient-space or full pairwise weight-matrix computations (Section 4.1).",
        "file": "pages/claim-5-per-iteration-cost-scaling/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}