{
  "schema_version": 1,
  "title": "Repro: Step-Size Stability in Stochastic Optimization: A Theoretical Perspective",
  "emoji": "chart",
  "space_id": "snaykey/repro-stepsize-stability",
  "paper": {
    "openreview_id": "yhvzMLgpdV"
  },
  "tags": [
    "icml2026-repro",
    "paper-yhvzMLgpdV"
  ],
  "updated_at": "2026-07-24T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Repro: Step-Size Stability in Stochastic Optimization: A Theoretical Perspective",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-stability-index-suboptimality-link",
        "title": "The paper introduces a stability index δ_t that quantifies how much a stochastic optimization step degrades progress as the step size grows, and links it directly to suboptimality bounds via average-iterate and last-iterate convergence theorems (Theorem 3, Theorem 4, Section 3).",
        "file": "pages/claim-1-stability-index-suboptimality-link/page.md",
        "children": []
      },
      {
        "slug": "claim-2-sgd-linear",
        "title": "For SGD, the stability index is derived as δ_t^SGD = (α_t/2)‖g_t‖^2, which scales linearly (unboundedly) with the step size α_t (Section 4).",
        "file": "pages/claim-2-sgd-linear/page.md",
        "children": []
      },
      {
        "slug": "claim-3-ngn-saturates",
        "title": "For NGN, the stability index δ_t^NGN = (γ_t/2)‖g_t‖^2 ≤ δ_t^SGD, and it saturates rather than growing unboundedly for large step sizes, unlike SGD (Section 4).",
        "file": "pages/claim-3-ngn-saturates/page.md",
        "children": []
      },
      {
        "slug": "claim-4-sps-sublinear",
        "title": "For SPS, the stability index is bounded as δ_t^SPS ≤ min{α_t‖g_t‖^2, f(x_t,s_t) - C_t}, scaling sub-linearly with step size, in contrast to SGD's linear scaling (Section 4).",
        "file": "pages/claim-4-sps-sublinear/page.md",
        "children": []
      },
      {
        "slug": "claim-5-robustness-ordering",
        "title": "Experiments on ResNet trained on CIFAR-10 and on linear/logistic regression tasks confirm that the theoretical stability-index bounds predict the empirically observed robustness ordering of SPS, NGN, and SPP over SGD across a range of step sizes (Section 5).",
        "file": "pages/claim-5-robustness-ordering/page.md",
        "children": []
      },
      {
        "slug": "protocol",
        "title": "Protocol & artifacts",
        "file": "pages/protocol/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}