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"schema_version": 1,
"title": "Reproduction: A Fully First-Order Layer for Differentiable Optimization",
"emoji": "⚡",
"space_id": "SabaPivot/repro-a-fully-first-order-layer-for-differentiable-optimization",
"paper": {
"title": "A Fully First-Order Layer for Differentiable Optimization",
"openreview_id": "jJur8Fq7IK",
"openreview_url": "https://openreview.net/forum?id=jJur8Fq7IK",
"arxiv_url": "https://arxiv.org/abs/2512.02494"
},
"tags": [
"icml2026-repro",
"paper-jJur8Fq7IK"
],
"updated_at": "2026-07-31T01:14:09.659639+00:00",
"claims": [
"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).",
"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).",
"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).",
"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).",
"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).",
"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)."
],
"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-first-order-rate",
"title": "Claim 1 — ε-accurate, first-order and logarithmic",
"file": "pages/claim-1-first-order-rate/page.md",
"children": []
},
{
"slug": "claim-2-ghost-equivalence",
"title": "Claim 2 — ghost active-set equivalence",
"file": "pages/claim-2-ghost-equivalence/page.md",
"children": []
},
{
"slug": "claim-3-complexity",
"title": "Claim 3 — general-convex oracle complexity",
"file": "pages/claim-3-complexity/page.md",
"children": []
},
{
"slug": "claim-4-native-benchmarks",
"title": "Claim 4 — exact-solver convergence and backward timing",
"file": "pages/claim-4-native-benchmarks/page.md",
"children": []
},
{
"slug": "claim-5-objective-agnostic",
"title": "Claim 5 — objective-agnostic PyTorch layer",
"file": "pages/claim-5-objective-agnostic/page.md",
"children": []
},
{
"slug": "claim-6-lpgd-hessian",
"title": "Claim 6 — LPGD comparison and Hessian elimination",
"file": "pages/claim-6-lpgd-hessian/page.md",
"children": []
},
{
"slug": "claim-7-scope-and-integrity",
"title": "Scope, controls and integrity",
"file": "pages/claim-7-scope-and-integrity/page.md",
"children": []
},
{
"slug": "conclusion",
"title": "Conclusion",
"file": "pages/conclusion/page.md",
"children": []
}
]
},
"agent_view_tokens": 6000,
"revision": "1785134100000000000"
}
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