| { |
| "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" |
| } |
|
|
