{
  "article_slug": "unlearning-verification-boundaries",
  "figures": [
    {
      "id": "unlearning-verification-boundaries-1",
      "kind": "line_chart",
      "title": "Deletion must update curvature as well as cross-products",
      "x_label": "Removed record index",
      "y_label": "Scalar coefficient",
      "series": [
        {
          "name": "Exact retained-data optimum",
          "x": [
            1,
            2,
            3,
            4
          ],
          "y": [
            1.0,
            1.0,
            1.1363636363636365,
            0.7333333333333333
          ]
        },
        {
          "name": "Naive unchanged denominator",
          "x": [
            1,
            2,
            3,
            4
          ],
          "y": [
            0.967741935483871,
            0.8709677419354839,
            0.8064516129032258,
            0.3548387096774194
          ]
        }
      ],
      "caption": "Constructed data x=(1,2,3,4), y=(1,2,2,5), summed squared loss and lambda=1. Naive update is an author-created negative control, not a named published method."
    },
    {
      "id": "unlearning-verification-boundaries-2",
      "kind": "line_chart",
      "title": "Finite probe agreement does not imply functional equality",
      "x_label": "Input x",
      "y_label": "Prediction",
      "series": [
        {
          "name": "a=-4",
          "x": [
            0.0,
            0.025,
            0.05,
            0.075,
            0.1,
            0.125,
            0.15,
            0.175,
            0.2,
            0.225,
            0.25,
            0.275,
            0.3,
            0.325,
            0.35,
            0.375,
            0.4,
            0.425,
            0.45,
            0.475,
            0.5,
            0.525,
            0.55,
            0.575,
            0.6,
            0.625,
            0.65,
            0.675,
            0.7,
            0.725,
            0.75,
            0.775,
            0.8,
            0.825,
            0.85,
            0.875,
            0.9,
            0.925,
            0.95,
            0.975,
            1.0
          ],
          "y": [
            0.0,
            0.0975,
            0.19,
            0.2775,
            0.36000000000000004,
            0.4375,
            0.51,
            0.5774999999999999,
            0.6400000000000001,
            0.6975,
            0.75,
            0.7975,
            0.84,
            0.8775000000000001,
            0.9099999999999999,
            0.9375,
            0.96,
            0.9774999999999999,
            0.9900000000000001,
            0.9974999999999999,
            1.0,
            0.9974999999999999,
            0.99,
            0.9775,
            0.96,
            0.9375,
            0.9099999999999999,
            0.8775,
            0.8400000000000001,
            0.7975,
            0.75,
            0.6974999999999999,
            0.6399999999999999,
            0.5775000000000001,
            0.51,
            0.4375,
            0.35999999999999993,
            0.27749999999999986,
            0.19000000000000017,
            0.09750000000000009,
            -0.0
          ]
        },
        {
          "name": "a=0",
          "x": [
            0.0,
            0.025,
            0.05,
            0.075,
            0.1,
            0.125,
            0.15,
            0.175,
            0.2,
            0.225,
            0.25,
            0.275,
            0.3,
            0.325,
            0.35,
            0.375,
            0.4,
            0.425,
            0.45,
            0.475,
            0.5,
            0.525,
            0.55,
            0.575,
            0.6,
            0.625,
            0.65,
            0.675,
            0.7,
            0.725,
            0.75,
            0.775,
            0.8,
            0.825,
            0.85,
            0.875,
            0.9,
            0.925,
            0.95,
            0.975,
            1.0
          ],
          "y": [
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            -0.0,
            0.0
          ]
        },
        {
          "name": "a=4",
          "x": [
            0.0,
            0.025,
            0.05,
            0.075,
            0.1,
            0.125,
            0.15,
            0.175,
            0.2,
            0.225,
            0.25,
            0.275,
            0.3,
            0.325,
            0.35,
            0.375,
            0.4,
            0.425,
            0.45,
            0.475,
            0.5,
            0.525,
            0.55,
            0.575,
            0.6,
            0.625,
            0.65,
            0.675,
            0.7,
            0.725,
            0.75,
            0.775,
            0.8,
            0.825,
            0.85,
            0.875,
            0.9,
            0.925,
            0.95,
            0.975,
            1.0
          ],
          "y": [
            -0.0,
            -0.0975,
            -0.19,
            -0.2775,
            -0.36000000000000004,
            -0.4375,
            -0.51,
            -0.5774999999999999,
            -0.6400000000000001,
            -0.6975,
            -0.75,
            -0.7975,
            -0.84,
            -0.8775000000000001,
            -0.9099999999999999,
            -0.9375,
            -0.96,
            -0.9774999999999999,
            -0.9900000000000001,
            -0.9974999999999999,
            -1.0,
            -0.9974999999999999,
            -0.99,
            -0.9775,
            -0.96,
            -0.9375,
            -0.9099999999999999,
            -0.8775,
            -0.8400000000000001,
            -0.7975,
            -0.75,
            -0.6974999999999999,
            -0.6399999999999999,
            -0.5775000000000001,
            -0.51,
            -0.4375,
            -0.35999999999999993,
            -0.27749999999999986,
            -0.19000000000000017,
            -0.09750000000000009,
            0.0
          ]
        }
      ],
      "caption": "Constructed family f_a(x)=a*x*(x-1), reference f_0=0. All agree at tested endpoints 0 and 1, but nonzero a disagrees inside."
    }
  ]
}