{
  "article_slug": "positional-extrapolation-limits",
  "figures": [
    {
      "id": "rotation-compression",
      "title": "Range compression changes phase resolution",
      "kind": "analytical_curve",
      "x_label": "Token distance d",
      "y_label": "Cosine similarity",
      "x": {
        "name": "Token distance d",
        "values": [
          0,
          4,
          8,
          12,
          16,
          20,
          24,
          28,
          32,
          36,
          40,
          44,
          48,
          52,
          56,
          60,
          64,
          68,
          72,
          76,
          80,
          84,
          88,
          92,
          96,
          100,
          104,
          108,
          112,
          116,
          120,
          124,
          128
        ]
      },
      "series": [
        {
          "name": "Position scale 1",
          "values": [
            1.0,
            0.9210609940028851,
            0.6967067093471654,
            0.3623577544766734,
            -0.029199522301288815,
            -0.4161468365471424,
            -0.7373937155412458,
            -0.9422223406686583,
            -0.9982947757947531,
            -0.896758416334147,
            -0.6536436208636119,
            -0.30733286997841935,
            0.08749898343944727,
            0.4685166713003771,
            0.7755658785102502,
            0.960170286650366,
            0.9931849187581926,
            0.8693974903498248,
            0.6083513145322546,
            0.25125984258225487,
            -0.14550003380861354,
            -0.5192886541166856,
            -0.811093014061656,
            -0.974843621404164,
            -0.9846878557941267,
            -0.8390715290764524,
            -0.5609842574272288,
            -0.1943299064553348,
            0.20300486381875213,
            0.568289629767975,
            0.8438539587324921,
            0.9861923022788637,
            0.9728325656974354
          ]
        },
        {
          "name": "Position scale 2",
          "values": [
            1.0,
            0.9800665778412416,
            0.9210609940028851,
            0.8253356149096782,
            0.6967067093471654,
            0.5403023058681398,
            0.3623577544766734,
            0.16996714290024081,
            -0.029199522301288815,
            -0.2272020946930871,
            -0.4161468365471424,
            -0.5885011172553458,
            -0.7373937155412458,
            -0.8568887533689473,
            -0.9422223406686583,
            -0.9899924966004454,
            -0.9982947757947531,
            -0.9667981925794609,
            -0.896758416334147,
            -0.7909677119144165,
            -0.6536436208636119,
            -0.4902608213406994,
            -0.30733286997841935,
            -0.11215252693505398,
            0.08749898343944727,
            0.28366218546322625,
            0.4685166713003771,
            0.6346928759426347,
            0.7755658785102502,
            0.8855195169413194,
            0.960170286650366,
            0.9965420970232175,
            0.9931849187581926
          ]
        },
        {
          "name": "Position scale 4",
          "values": [
            1.0,
            0.9950041652780258,
            0.9800665778412416,
            0.955336489125606,
            0.9210609940028851,
            0.8775825618903728,
            0.8253356149096782,
            0.7648421872844884,
            0.6967067093471654,
            0.6216099682706644,
            0.5403023058681398,
            0.4535961214255773,
            0.3623577544766734,
            0.26749882862458735,
            0.16996714290024081,
            0.0707372016677029,
            -0.029199522301288815,
            -0.12884449429552486,
            -0.2272020946930871,
            -0.3232895668635036,
            -0.4161468365471424,
            -0.5048461045998576,
            -0.5885011172553458,
            -0.6662760212798244,
            -0.7373937155412458,
            -0.8011436155469337,
            -0.8568887533689473,
            -0.9040721420170612,
            -0.9422223406686583,
            -0.9709581651495907,
            -0.9899924966004454,
            -0.9991351502732795,
            -0.9982947757947531
          ]
        }
      ],
      "caption": "One-frequency author construction, omega=0.1 rad/position. Not a full RoPE spectrum or model retrieval accuracy."
    },
    {
      "id": "recency-horizon",
      "title": "Mass assigned to the latest 16 positions",
      "kind": "analytical_curve",
      "x_label": "Context length L (tokens)",
      "y_label": "Probability mass",
      "x": {
        "name": "Context length L (tokens)",
        "values": [
          16,
          32,
          64,
          128,
          256,
          512
        ]
      },
      "series": [
        {
          "name": "Slope 0",
          "values": [
            1.0,
            0.5,
            0.25,
            0.125,
            0.0625,
            0.03125
          ]
        },
        {
          "name": "Slope 0.01",
          "values": [
            1.0,
            0.5399148845555657,
            0.3127857867191315,
            0.20479757628282144,
            0.16024381777448893,
            0.1487451152480312
          ]
        },
        {
          "name": "Slope 0.05",
          "values": [
            1.0,
            0.6899744811276124,
            0.5740714535714135,
            0.5515875301553,
            0.5506725561644676,
            0.5506710358869756
          ]
        },
        {
          "name": "Slope 0.2",
          "values": [
            1.0,
            0.9608342772032358,
            0.9592404442663424,
            0.9592377960289451,
            0.9592377960216338,
            0.9592377960216338
          ]
        }
      ],
      "caption": "Content-neutral causal scores -m*d. All keys have equal content scores; learned content can offset the bias."
    }
  ]
}
