logbook.json

{
  "schema_version": 1,
  "title": "Reproduction: Gradient Flow Through Diagram Expansions: Learning Regimes and Explicit Solutions",
  "emoji": "🧭",
  "space_id": "snaykey/repro-scent",
  "paper": {
    "openreview_id": "BXE3Z0EHCs"
  },
  "tags": [
    "icml2026-repro",
    "paper-BXE3Z0EHCs"
  ],
  "updated_at": "2026-07-31T00:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Gradient Flow Through Diagram Expansions: Learning Regimes and Explicit Solutions",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-thm31-loss-coefficients-polynomial",
        "title": "Theorem 3.1 shows that for targets expressible as polynomials in parameters and Kronecker deltas, the coefficients of the formal power series expansion of the loss's time derivatives are themselves polynomials in the width H, the parameterization exponent p, and the initialization variance sigma^2 (Theorem 3.1).",
        "file": "pages/claim-1-thm31-loss-coefficients-polynomial/page.md",
        "children": []
      },
      {
        "slug": "claim-2-thm41-pareto-polygon",
        "title": "Theorem 4.1 characterizes the leading and Pareto-optimal terms of the loss expansion for identity-tensor targets, organizing gradient-flow learning regimes into a polygon structure defined by scaling conditions on H, p, and sigma^2 (Section 4, Theorem 4.1).",
        "file": "pages/claim-2-thm41-pareto-polygon/page.md",
        "children": []
      },
      {
        "slug": "claim-3-prop82-ntk-regime",
        "title": "An NTK-like regime, in which features do not evolve during training, appears only at points/edges B-C of the Pareto polygon in the asymmetric parameterization case, while Proposition 8.2 proves the NTK kernel stays static throughout training in the symmetric matrix case (nu=2), explaining the absence of an NTK limit there (Section 4, Proposition 8.2).",
        "file": "pages/claim-3-prop82-ntk-regime/page.md",
        "children": []
      },
      {
        "slug": "claim-4-meanfield-scaling-conditions",
        "title": "Mean-field, feature-evolving regimes require the initialization variance to scale as sigma^2 proportional to 1/H (symmetric case) or sigma^2 proportional to 1/H^(2/nu) (asymmetric case), corresponding to edges B-E and C-D of the Pareto polygon respectively (Section 4).",
        "file": "pages/claim-4-meanfield-scaling-conditions/page.md",
        "children": []
      },
      {
        "slug": "claim-5-sec9-closed-form-sym-nu2",
        "title": "For the canonical polyadic (symmetric, nu=2) identity-tensor target, Section 9 derives a complete closed-form solution to the gradient flow (Equations 19-20), valid across all parameter scalings.",
        "file": "pages/claim-5-sec9-closed-form-sym-nu2/page.md",
        "children": []
      },
      {
        "slug": "claim-6-sec10-nu4-ascent-threshold",
        "title": "For the nu=4 symmetric case, Section 10 derives a gradient-ascent solution identifying convergent low-noise and divergent high-noise regimes separated by an explicit threshold given in Equation 23.",
        "file": "pages/claim-6-sec10-nu4-ascent-threshold/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}