{
 "schema_version": 1,
 "title": "Repro: Adaptive SAM with Polyak-type Step Size (SAM-SPS)",
 "emoji": "🎯",
 "space_id": "snaykey/repro-sam-sps",
 "paper": {
  "openreview_id": "On2B3By7PT"
 },
 "tags": [
  "icml2026-repro",
  "paper-On2B3By7PT"
 ],
 "updated_at": "2026-07-25T00:21:01+00:00",
 "root": {
  "slug": "index",
  "title": "Repro: Adaptive SAM with Polyak-type Step Size (SAM-SPS)",
  "file": "pages/index.md",
  "children": [
   {
    "slug": "claim-1",
    "title": "For strongly convex smooth objectives, the proposed Polyak-type scheduler for SAM yields linear convergence with rate (1 − μ(1−Lρ)²/4L)^t in the deterministic setting (Theorem 3.1).",
    "file": "pages/claim-1/page.md",
    "children": []
   },
   {
    "slug": "claim-2",
    "title": "For convex smooth objectives, the same scheduler achieves an O(1/T) sublinear convergence rate, f(x̄_T) − f* ≤ 2L‖x⁰−x*‖²/(T(1−Lρ)²), with convergence only up to a neighborhood in the stochastic setting due to gradient variance (Theorems 3.2, 3.5, 3.8).",
    "file": "pages/claim-2/page.md",
    "children": []
   },
   {
    "slug": "claim-3",
    "title": "The deterministic Polyak step size γ_t = [f(ê^t) − f* − ρ_t⟨∇f(ê^t),∇f(x^t)⟩]/‖∇f(ê^t)‖² is provably non-negative whenever ρ_t ≤ 1/L (Section 2.2, Proposition 2.1).",
    "file": "pages/claim-3/page.md",
    "children": []
   },
   {
    "slug": "claim-4",
    "title": "On CIFAR-100 with ResNet-32 using USAM, the Polyak scheduler reaches 92.23±0.22 test accuracy at ρ=0.2, outperforming constant learning rate (90.45±0.34) and cosine annealing (88.77±0.26) (Table 3).",
    "file": "pages/claim-4/page.md",
    "children": []
   },
   {
    "slug": "claim-5",
    "title": "On CIFAR-100 with ResNet-32 using standard SAM, the Polyak scheduler achieves a comparable improvement, reaching 92.24±0.07 accuracy at ρ=0.2, without manual learning-rate tuning (Table 4).",
    "file": "pages/claim-5/page.md",
    "children": []
   },
   {
    "slug": "claim-6",
    "title": "The Polyak scheduling approach extends to normalized SAM variants with comparable experimental gains over baseline schedules (Section 4.3).",
    "file": "pages/claim-6/page.md",
    "children": []
   },
   {
    "slug": "conclusion",
    "title": "Conclusion",
    "file": "pages/conclusion/page.md",
    "children": []
   }
  ]
 }
}