| { |
| "schema_version": 1, |
| "title": "Reproduction: Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function", |
| "emoji": "🎛️", |
| "space_id": "snaykey/repro-creator-causal-rep", |
| "paper": { |
| "openreview_id": "JnuwpwbZ8D" |
| }, |
| "tags": [ |
| "icml2026-repro", |
| "paper-JnuwpwbZ8D" |
| ], |
| "updated_at": "2026-07-30T18:00:00+00:00", |
| "root": { |
| "slug": "index", |
| "title": "Reproduction: Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function", |
| "file": "pages/index.md", |
| "children": [ |
| { |
| "slug": "claim-1-theorem-4-1", |
| "title": "Theorem 4.1 establishes a general first-order-logic framework giving pseudo-dimension bounds of O(p*prod(d_k+1)*log M + p^2*prod(d_k+1)*log Delta) for multi-dimensional hyperparameter tuning by connecting logical complexity to learning-theoretic complexity via quantifier elimination (Section 4).", |
| "file": "pages/claim-1-theorem-4-1/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-2-theorem-5-1", |
| "title": "Theorem 5.1 bounds the pseudo-dimension of piecewise-polynomial training-loss objectives (with training loss f equal to validation loss g) as O(p*d*log(M_f+T_f+d) + p^2*d*log Delta_f) for p-dimensional hyperparameters (Section 5).", |
| "file": "pages/claim-2-theorem-5-1/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-3-theorem-6-1", |
| "title": "Theorem 6.1 extends the framework to the bi-level validation-loss setting (f not equal to g), establishing Pdim(L) = O(p*d^2*log M_tot + p^2*d^2*log Delta_tot) without requiring identical training and validation objectives (Section 6).", |
| "file": "pages/claim-3-theorem-6-1/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-4-theorem-7-2", |
| "title": "Theorem 7.2 shows that when the optimal parameter path theta*(x, alpha) is piecewise rational, the pseudo-dimension bound simplifies to O(p*log(M_total*Delta_total)) by bypassing quantifier elimination (Section 7).", |
| "file": "pages/claim-4-theorem-7-2/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-5-theorem-8-1", |
| "title": "Theorem 8.1 provides the first learnability guarantee for weighted group LASSO regularization, a semi-algebraic (non-piecewise-polynomial) function class, with Pdim(L) = O(p^3*d + p^2*d^2), despite standard smoothness assumptions failing for this class (Section 8.1).", |
| "file": "pages/claim-5-theorem-8-1/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "claim-6-theorem-8-2", |
| "title": "Theorem 8.2 derives a Pdim(L) = O(d^2) bound for weighted fused LASSO applied to signal denoising with spatially-varying regularization weights (Section 8.2).", |
| "file": "pages/claim-6-theorem-8-2/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "executive-summary", |
| "title": "Executive summary", |
| "file": "pages/executive-summary/page.md", |
| "children": [] |
| }, |
| { |
| "slug": "conclusion", |
| "title": "Conclusion", |
| "file": "pages/conclusion/page.md", |
| "children": [] |
| } |
| ] |
| } |
| } |
