annotations/case_3.json

{
  "task": {
    "id": "case_3",
    "name": "frac_prevs",
    "summary": "Returns the fraction of 'x' in the input up to the i-th position for all i.",
    "examples": [
      {
        "input": [
          "BOS",
          "c",
          "x",
          "a",
          "c"
        ],
        "output": [
          "BOS",
          0.0,
          0.5,
          0.3333333333333333,
          0.25
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "b",
          "c",
          "c"
        ],
        "output": [
          "BOS",
          0.0,
          0.0,
          0.0,
          0.0
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "c",
          "x",
          "a"
        ],
        "output": [
          "BOS",
          0.0,
          0.0,
          0.3333333333333333,
          0.25
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "x",
          "a",
          "a"
        ],
        "output": [
          "BOS",
          0.0,
          0.5,
          0.3333333333333333,
          0.25
        ]
      },
      {
        "input": [
          "BOS",
          "x",
          "x",
          "x",
          "c"
        ],
        "output": [
          "BOS",
          1.0,
          1.0,
          1.0,
          0.75
        ]
      }
    ],
    "is_categorical": false
  },
  "program": "is_x = (rasp.tokens == \"x\").named(\"is_x\"); bools = rasp.numerical(is_x); prevs = rasp.Select(rasp.indices, rasp.indices, rasp.Comparison.LEQ); return rasp.numerical(rasp.Aggregate(prevs, bools, default=0)).named(\"frac_prevs\")",
  "components": [
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "INDICATOR",
        "note": "Computes per-position feature indicating whether the token at that position is 'x' or not."
      },
      "rasp_vars": [
        "is_x"
      ],
      "labels": [
        "is_x_3"
      ]
    },
    {
      "id": "L1H2_ATTN",
      "hook": "blocks.1.attn.hook_result[2]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Aggregates prefix fraction by attending over previous positions."
      },
      "rasp_vars": [
        "prevs",
        "frac_prevs"
      ],
      "labels": [
        "frac_prevs_1"
      ]
    }
  ]
}