{
  "schema_version": 1,
  "title": "Reproduction: Thinned Mean Field Langevin Dynamics",
  "emoji": "🌀",
  "space_id": "snaykey/repro-thinned-mfld",
  "paper": {
    "openreview_id": "tt4UrPSGTo"
  },
  "tags": [
    "icml2026-repro",
    "paper-tt4UrPSGTo"
  ],
  "updated_at": "2026-08-02T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Thinned Mean Field Langevin Dynamics",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-kt-mfld-complexity",
        "title": "KT-MFLD (Kernel-Thinned Mean Field Langevin Dynamics) reduces per-iteration computational complexity from O(N^2) to O(N^{3/2}) by applying kernel thinning (kt-split-Compress) to reduce N particles to a coreset of size M=O(sqrt(N)) at each step (Section 3).",
        "file": "pages/claim-1-kt-mfld-complexity/page.md",
        "children": []
      },
      {
        "slug": "claim-2-thm33-error",
        "title": "Theorem 3.3 shows that for sufficiently large N and T with an appropriate step size, KT-MFLD's finite-particle approximation error scales as O(N^{-1}(log N)^3), matching standard MFLD up to logarithmic factors (Theorem 3.3).",
        "file": "pages/claim-2-thm33-error/page.md",
        "children": []
      },
      {
        "slug": "claim-3-assumptions",
        "title": "Assumptions 3.1 and 3.2 require boundedness, Lipschitzness, and convexity of q1, q2, R1, plus membership of q1 and the gradient of q2 in a reproducing kernel Hilbert space, and the paper verifies these hold for mean-field neural networks, MMD quantization, and predictively-oriented (PrO) posteriors (Section 3, Section 4).",
        "file": "pages/claim-3-assumptions/page.md",
        "children": []
      },
      {
        "slug": "claim-4-experiments",
        "title": "Experiments on student-teacher networks, MMD quantization, and PrO posteriors show KT-MFLD consistently outperforms random subsampling and random-batch baselines under equal computational budgets (Section 4).",
        "file": "pages/claim-4-experiments/page.md",
        "children": []
      },
      {
        "slug": "claim-5-curse-of-dimensionality",
        "title": "The authors note the thinning-induced error term suffers a curse of dimensionality, since the constant term can be exponentially small in dimension d, worsening particle-complexity dependence in high dimensions (Section on limitations).",
        "file": "pages/claim-5-curse-of-dimensionality/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": []
      }
    ]
  }
}