{
  "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": []
      }
    ]
  }
}