logbook.json

{
 "schema_version": 1,
 "title": "Reproduction: Stability beyond Bounded Differences: Sharp Generalization Bounds under Finite Lp Moments",
 "emoji": "📈",
 "space_id": "snaykey/repro-stability-bounded-diff",
 "paper": {
  "arxiv_id": "2606.06855",
  "openreview_id": "SGTLVjx3MN"
 },
 "tags": [
  "icml2026-repro",
  "paper-SGTLVjx3MN"
 ],
 "updated_at": "2026-07-28T11:55:39.585709+00:00",
 "root": {
  "slug": "index",
  "title": "Reproduction: Stability beyond Bounded Differences: Sharp Generalization Bounds under Finite Lp Moments",
  "children": [
   {
    "slug": "executive-summary",
    "title": "Executive summary",
    "children": []
   },
   {
    "slug": "claim-1-theorem-2-2-two-regime-concentration",
    "title": "Theorem 2.2 establishes a concentration inequality for functions of independent random variables under finite Lp moment conditions exhibiting a two-regime bound combining polynomial and sub-Gaussian terms (Section 2.2).",
    "children": []
   },
   {
    "slug": "claim-2-theorem-2-6-heavy-tailed-regime",
    "title": "Theorem 2.6 extends the concentration results to the heavy-tailed regime p ∈ (1,2), yielding bounds unavailable to prior uniform-boundedness-based approaches (Section 2.2).",
    "children": []
   },
   {
    "slug": "claim-3-assumption-3-1-lp-lipschitz-stability",
    "title": "Assumption 3.1 defines (Lp,β)-Lipschitz stability, requiring only that the replace-one stability increment have finite p-th moments for some p≥2, replacing deterministic uniform stability (Section 3.1).",
    "children": []
   },
   {
    "slug": "claim-4-theorem-3-4-erm-generalization",
    "title": "Theorem 3.4 provides a high-probability generalization bound for empirical risk minimization under (Lp,β)-Lipschitz stability (Section 3.1).",
    "children": []
   },
   {
    "slug": "claim-5-theorems-3-9-3-10-transductive",
    "title": "Theorems 3.9 and 3.10 extend the concentration framework to sampling without replacement and derive generalization bounds R(h)−R̂(h) for transductive regression under (Lp,β)-Lipschitz stability (Section 3.2).",
    "children": []
   },
   {
    "slug": "claim-6-theorem-3-14-meta-learning",
    "title": "Theorem 3.14 establishes high-probability generalization bounds for meta-learning algorithms under Assumption 3.12, which decomposes stability into meta-stability across tasks, within-task stability, and test-sample stability (Section 3.3).",
    "children": []
   },
   {
    "slug": "conclusion",
    "title": "Conclusion",
    "children": []
   }
  ]
 },
 "revision": 1
}