{
  "article_slug": "algorithmic-stability-training",
  "figures": [
    {
      "id": "time-sensitivity",
      "kind": "analytical_curve",
      "caption": "Author-constructed full-batch quadratic, n=20, lambda=1, eta=.1. Exact parameter bound and conservative loss bound; not measured SGD sensitivity.",
      "x": {
        "name": "Gradient steps T",
        "values": [
          0,
          1,
          2,
          5,
          10,
          20
        ]
      },
      "series": [
        {
          "name": "Parameter bound 2cT/n",
          "values": [
            0.0,
            0.009999999999999998,
            0.017999999999999995,
            0.03361599999999999,
            0.044631290879999994,
            0.049423539247696574
          ]
        },
        {
          "name": "Loss bound 4cT/n",
          "values": [
            0.0,
            0.019999999999999997,
            0.03599999999999999,
            0.06723199999999999,
            0.08926258175999999,
            0.09884707849539315
          ]
        }
      ]
    },
    {
      "id": "expected-gap",
      "kind": "analytical_curve",
      "caption": "Exact expected generalization gap cT/n in the author-constructed IID Rademacher quadratic problem, lambda=1, eta=.1, T=10. Not a neural training benchmark.",
      "x": {
        "name": "Sample size n",
        "values": [
          5,
          10,
          20,
          50,
          100
        ]
      },
      "series": [
        {
          "name": "Expected gap",
          "values": [
            0.08926258175999999,
            0.044631290879999994,
            0.022315645439999997,
            0.008926258175999999,
            0.004463129087999999
          ]
        }
      ]
    }
  ],
  "cover_prompt": "Premium scientific editorial cover, landscape3:2, no words. Two almost identical translucent jade training paths run across a warm ivory plane; a single amber seed replaces one pale seed near their origin, producing a small controlled separation between golden trajectories rather than chaos. Fine brass measuring arcs, quiet mathematical sculpture, restrained materials, generous negative space. Conceptual illustration of replace-one sensitivity, not measured data.",
  "numeric_data_provenance": "Computed and checked by the corresponding standalone standard-library script; constructed, not empirical."
}