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{
  "schema_version": 1,
  "title": "Reproduction: Gradient Flow Sampler-based Distributionally Robust Optimization",
  "emoji": "🌊",
  "space_id": "ProCreations/repro-gradient-flow-sampler-based-distributionally-robust-optimization",
  "paper": {
    "arxiv_id": "2510.25956"
  },
  "tags": [
    "icml2026-repro",
    "paper-QRtzkKrbJi"
  ],
  "updated_at": "2026-07-23T15:58:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Gradient Flow Sampler-based Distributionally Robust Optimization",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-six-algorithms",
        "title": "Claim 1: The paper introduces a unified PDE gradient flow framework for distributionally robust optimization (DRO) with six concrete algorithms, including Wasserstein Gradient Flow (Algorithm 3) and Wasserstein Fisher-Rao flow (Algorithm 4) variants for entropy-regularized Wasserstein DRO (Section 4, Algorithms 3-4).",
        "file": "pages/claim-1-six-algorithms/page.md",
        "children": []
      },
      {
        "slug": "claim-2-flow-time",
        "title": "Claim 2: Proposition 1 shows the Wasserstein gradient flow sampler must run for time at least on the order of O((1/λ) log(L/√(λε))) to produce an ε-accurate gradient estimate (Section 4, Proposition 1).",
        "file": "pages/claim-2-flow-time/page.md",
        "children": []
      },
      {
        "slug": "claim-3-outer-loop",
        "title": "Claim 3: Theorem 1 proves the outer loop of the gradient-flow-sampler-based DRO algorithm requires O(1/ε²_opt) iterations to reach an ε-stationary point (Section 5, Theorem 1).",
        "file": "pages/claim-3-outer-loop/page.md",
        "children": []
      },
      {
        "slug": "claim-4-total-complexity",
        "title": "Claim 4: Theorem 2 bounds the total computational complexity of the WGF-based DRO algorithm (Algorithm 3) as Õ(L_Φ L²_U L²_f d² / (λ³_U ε⁴_opt)) (Section 5, Theorem 2).",
        "file": "pages/claim-4-total-complexity/page.md",
        "children": []
      },
      {
        "slug": "claim-5-cifar-robustness",
        "title": "Claim 5: On CIFAR-10 adversarial training under PGD attacks, the WFR- and WGF-based DRO methods achieve consistently higher robust accuracy across all perturbation settings compared to baseline DRO methods (Section 6.3).",
        "file": "pages/claim-5-cifar-robustness/page.md",
        "children": []
      },
      {
        "slug": "claim-6-half-bridge",
        "title": "Claim 6: Lemma 1 establishes that the entropy-regularized DRO problem is equivalent to a Schrödinger half-bridge problem, enabling sampling from the conditional worst-case distribution (Section 3.1, Lemma 1).",
        "file": "pages/claim-6-half-bridge/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 4096
}