{
  "article_slug": "neural-tangent-feature-learning",
  "figures": [
    {
      "id": "balanced-vs-frozen",
      "kind": "analytical_curve",
      "caption": "Author-constructed scalar model w0=.01: exact balanced gradient flow versus matched-initialization frozen tangent. Dimensionless; no empirical benchmark.",
      "x": {
        "name": "Dimensionless time",
        "values": [
          0,
          1,
          2,
          3,
          4,
          5
        ]
      },
      "series": [
        {
          "name": "Factorized dynamics",
          "values": [
            0.01,
            0.06945315965638048,
            0.3554609871366469,
            0.8029571527702831,
            0.9678567044042412,
            0.9955255179295147
          ]
        },
        {
          "name": "Frozen tangent",
          "values": [
            0.010000000000000009,
            0.029603313426312283,
            0.04881845523920003,
            0.06765311175159383,
            0.08611481707723057,
            0.10421095614440012
          ]
        }
      ]
    },
    {
      "id": "spectral-residual",
      "kind": "analytical_curve",
      "caption": "Author-constructed fixed-kernel residual modes with eigenvalues 1 and .01, both initialized at one. No trained-network measurement.",
      "x": {
        "name": "Dimensionless time",
        "values": [
          0,
          1,
          2,
          5,
          10
        ]
      },
      "series": [
        {
          "name": "Eigenvalue 1",
          "values": [
            1.0,
            0.36787944117144233,
            0.1353352832366127,
            0.006737946999085467,
            4.5399929762484854e-05
          ]
        },
        {
          "name": "Eigenvalue .01",
          "values": [
            1.0,
            0.9900498337491681,
            0.9801986733067553,
            0.951229424500714,
            0.9048374180359595
          ]
        }
      ]
    }
  ],
  "cover_prompt": "High-end scientific editorial cover, landscape3:2, no text or numerical labels. A golden tangent plane touches a curved dark-green translucent manifold; beyond the contact point, fine luminous threads depart from the plane into new curved pathways while an ivory geometric grid remains visible beneath. Restrained brass, deep teal and warm paper palette, sculptural realism, generous negative space, clear singular composition. Conceptual learning-regime illustration, not data.",
  "numeric_data_provenance": "Computed and checked by the corresponding standalone standard-library script; constructed, not empirical."
}