{
  "schema_version": 1,
  "title": "Repro: A Theoretical Framework for Modular Learning of Robust Generative Models",
  "emoji": "jigsaw",
  "space_id": "snaykey/repro-modular-robust-gen",
  "paper": {
    "openreview_id": "ToCArdndt6"
  },
  "tags": [
    "icml2026-repro",
    "paper-ToCArdndt6"
  ],
  "updated_at": "2026-07-26T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Repro: A Theoretical Framework for Modular Learning of Robust Generative Models",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-robust-gate",
        "title": "The robust gate existence result is proven via a saddle point of a linearized minimax game over the normalized gate space G_1 and the mixture simplex, established using Kakutani's Fixed Point Theorem (Theorem 3, Section 4.2).",
        "file": "pages/claim-1-robust-gate/page.md",
        "children": []
      },
      {
        "slug": "claim-2-kl-bound",
        "title": "Theorem 3 bounds the KL divergence of the robust gated model to any mixture by log-sum-exp of the per-expert guarantees epsilon_k minus an overlap term (target-weighted conditional entropy) minus a diversity term equal to the Jensen-Shannon Divergence, so the modular approach can outperform aggregate retraining by a gap characterized by JSD (Section 4.2).",
        "file": "pages/claim-2-kl-bound/page.md",
        "children": []
      },
      {
        "slug": "claim-3-static-capacity",
        "title": "Any static (non-adaptive) mixture-weight gate is shown to be fundamentally capacity-limited, with a capacity lower bound of log(sum_k e^{epsilon_k}) for disjoint domains, motivating the need for an input-dependent gate (Theorem 16, Appendix B).",
        "file": "pages/claim-3-static-capacity/page.md",
        "children": []
      },
      {
        "slug": "claim-4-algorithm-distillation",
        "title": "The paper introduces a Stochastic Primal-Dual algorithm to solve the constrained minimax game at scale and a Structural Distillation method that maps the non-causal gate to a causal router for efficient autoregressive inference (Sections 5 and 7).",
        "file": "pages/claim-4-algorithm-distillation/page.md",
        "children": []
      },
      {
        "slug": "claim-5-empirical",
        "title": "Empirical results on synthetic benchmarks and real-world datasets (Wikipedia, Code, FineWeb) show the modular gated architecture mitigates gradient conflict and outperforms monolithic baselines in high-interference regimes (Section 8, Section 8.1).",
        "file": "pages/claim-5-empirical/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}