| { |
| "schema_version": 1, |
| "title": "Reproduction: A Fully First-Order Layer for Differentiable Optimization", |
| "emoji": "⚡", |
| "space_id": "ProCreations/repro-a-fully-first-order-layer-for-differentiable-optimization", |
| "paper": {"arxiv_id": "2512.02494"}, |
| "tags": ["icml2026-repro", "paper-jJur8Fq7IK"], |
| "updated_at": "2026-07-27T06:35:00+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": "FFOLayer native-scale reproduction", |
| "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: first-order oracle", "file": "pages/claim-1-first-order-rate/page.md", "children": []}, |
| {"slug": "claim-2-ghost-equivalence", "title": "Claim 2: ghost equivalence", "file": "pages/claim-2-ghost-equivalence/page.md", "children": []}, |
| {"slug": "claim-3-complexity", "title": "Claim 3: general-convex complexity", "file": "pages/claim-3-complexity/page.md", "children": []}, |
| {"slug": "claim-4-native-benchmarks", "title": "Claim 4: exact-solver benchmarks", "file": "pages/claim-4-native-benchmarks/page.md", "children": []}, |
| {"slug": "claim-5-objective-agnostic", "title": "Claim 5: objective-agnostic layer", "file": "pages/claim-5-objective-agnostic/page.md", "children": []}, |
| {"slug": "claim-6-lpgd-hessian", "title": "Claim 6: LPGD and Hessian cost", "file": "pages/claim-6-lpgd-hessian/page.md", "children": []}, |
| {"slug": "scope-and-integrity", "title": "Scope, controls and integrity", "file": "pages/scope-and-integrity/page.md", "children": []}, |
| {"slug": "conclusion", "title": "Conclusion", "file": "pages/conclusion/page.md", "children": []} |
| ] |
| }, |
| "agent_view_tokens": 6000, |
| "revision": "1785134100000000000" |
| } |
|
|
