{
  "schema_version": 1,
  "title": "Reproduction: A Fully First-Order Layer for Differentiable Optimization",
  "emoji": "📊",
  "space_id": "snaykey/repro-first-order-diffopt",
  "paper": {
    "openreview_id": "jJur8Fq7IK"
  },
  "tags": [
    "icml2026-repro",
    "paper-jJur8Fq7IK"
  ],
  "updated_at": "2026-08-01T00:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: A Fully First-Order Layer for Differentiable Optimization",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-sec42-alg1-firstorder-oracle",
        "title": "FFOLayer computes an ε-approximate hypergradient using an active-set Lagrangian oracle that requires no Hessian evaluations, achieving Õ(1) first-order oracle calls per hypergradient estimate (Section 4.2, Algorithm 1).",
        "file": "pages/claim-1-sec42-alg1-firstorder-oracle/page.md",
        "children": []
      },
      {
        "slug": "claim-2-thm41-ghost-reformulation-preserves-hypergradient",
        "title": "Theorem 4.1 proves that the 'ghost bilevel optimization' reformulation, which treats active constraints as equalities, preserves the accuracy of the hypergradient computed at the original constrained-optimization solution (Section 4.1, Theorem 4.1).",
        "file": "pages/claim-2-thm41-ghost-reformulation-preserves-hypergradient/page.md",
        "children": []
      },
      {
        "slug": "claim-3-sec4-oracle-complexity",
        "title": "For constrained bilevel optimization, the method achieves an oracle complexity of Õ(δ⁻¹ε⁻³), matching best-known rates for non-smooth non-convex optimization, while extending prior guarantees from linear to general convex constraints (Section 4, complexity analysis).",
        "file": "pages/claim-3-sec4-oracle-complexity/page.md",
        "children": []
      },
      {
        "slug": "claim-4-dfl-qp-sudoku-convergence-faster-backward",
        "title": "On synthetic decision-focused-learning QP tasks and 9×9 Sudoku constraint-learning tasks formulated as linear programs, FFOLayer matches the convergence of exact differentiable-optimization solvers CvxpyLayer and qpth while using a substantially faster backward pass (Experiments section, synthetic QP and Sudoku benchmarks).",
        "file": "pages/claim-4-dfl-qp-sudoku-convergence-faster-backward/page.md",
        "children": []
      },
      {
        "slug": "claim-5-objective-agnostic-detach-coefficient",
        "title": "FFOLayer's PyTorch implementation is objective-agnostic, exposing task-loss influence via a single detached gradient coefficient c := detach(dF/dy*), allowing users to substitute it for CvxpyLayer with minimal code changes (Section on practical implementation).",
        "file": "pages/claim-5-objective-agnostic-detach-coefficient/page.md",
        "children": []
      },
      {
        "slug": "claim-6-outperforms-lpgd-no-hessian-inversion",
        "title": "FFOLayer outperforms the gradient-unrolling baseline LPGD in the reported experiments while eliminating the cubic-complexity Hessian inversion required by standard implicit differentiation (Experiments section, comparison with LPGD).",
        "file": "pages/claim-6-outperforms-lpgd-no-hessian-inversion/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}