{
  "schema_version": 1,
  "title": "Reproduction: Momentum Further Constrains Sharpness at the Edge of Stochastic Stability",
  "emoji": "🎯",
  "space_id": "snaykey/repro-momentum-sharpness-eos",
  "paper": {
    "openreview_id": "mL4i6z7Miy"
  },
  "tags": [
    "icml2026-repro",
    "paper-mL4i6z7Miy"
  ],
  "updated_at": "2026-07-31T00:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Momentum Further Constrains Sharpness at the Edge of Stochastic Stability",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-eoss-batch-dependent",
        "title": "SGD with momentum (SGDM) exhibits an Edge of Stochastic Stability regime whose batch-size-dependent behavior cannot be explained by a single stability threshold, unlike vanilla SGD (Section 3).",
        "file": "pages/claim-1-eoss-batch-dependent/page.md",
        "children": []
      },
      {
        "slug": "claim-2-theorem-4-1",
        "title": "In the noise-dominated (small-batch) regime, SGDM's mean-square stability condition reduces to a spectral-radius condition rho(I - eta_eff K + eta_eff^2 G) < 1 with effective learning rate eta_eff = eta/(1-beta) (Theorem 4.1).",
        "file": "pages/claim-2-theorem-4-1/page.md",
        "children": []
      },
      {
        "slug": "claim-3-small-batch-plateau",
        "title": "Batch Sharpness converges to a plateau of approximately 2(1-beta)/eta at small batch sizes, indicating momentum drives SGD toward flatter regions than vanilla SGD in this regime (Section 4).",
        "file": "pages/claim-3-small-batch-plateau/page.md",
        "children": []
      },
      {
        "slug": "claim-4-large-batch-plateau",
        "title": "Batch Sharpness converges to a plateau of approximately 2(1+beta)/eta for SGDM at large batch sizes, consistent with full-batch gradient descent dynamics and sharper minima (Section 4).",
        "file": "pages/claim-4-large-batch-plateau/page.md",
        "children": []
      },
      {
        "slug": "claim-5-figure3-mlp-cnn",
        "title": "Figure 3 empirically shows batch-size-dependent Batch Sharpness plateaus for MLP and CNN architectures on CIFAR-10, with SGD with Nesterov momentum (SGDN) reaching the deterministic plateau at smaller batch sizes than SGDM (Figure 3).",
        "file": "pages/claim-5-figure3-mlp-cnn/page.md",
        "children": []
      },
      {
        "slug": "claim-6-figure6-catapults",
        "title": "Figure 6 shows intervention experiments in which increasing learning rate or momentum, or decreasing batch size, triggers sharp loss 'catapults' once Batch Sharpness exceeds its operating plateau (Figure 6).",
        "file": "pages/claim-6-figure6-catapults/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}