{
  "task": {
    "id": "case_26",
    "name": "token_cascade",
    "summary": "Creates a cascading effect by repeating each token in sequence incrementally.",
    "examples": [
      {
        "input": [
          "BOS",
          "b",
          "b",
          "a",
          "a",
          "b",
          "b",
          "a",
          "a",
          "a"
        ],
        "output": [
          "BOS",
          "b",
          "bb",
          "aaa",
          "aaaa",
          "bbbbb",
          "bbbbbb",
          "aaaaaaa",
          "aaaaaaaa",
          "aaaaaaaaa"
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "c",
          "a",
          "c",
          "a",
          "c",
          "c",
          "a",
          "a"
        ],
        "output": [
          "BOS",
          "c",
          "cc",
          "aaa",
          "cccc",
          "aaaaa",
          "cccccc",
          "ccccccc",
          "aaaaaaaa",
          "aaaaaaaaa"
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "a",
          "c",
          "c",
          "a",
          "a",
          "c",
          "b",
          "c"
        ],
        "output": [
          "BOS",
          "c",
          "aa",
          "ccc",
          "cccc",
          "aaaaa",
          "aaaaaa",
          "ccccccc",
          "bbbbbbbb",
          "ccccccccc"
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "c",
          "c",
          "b",
          "c",
          "b",
          "b",
          "c",
          "b"
        ],
        "output": [
          "BOS",
          "c",
          "cc",
          "ccc",
          "bbbb",
          "ccccc",
          "bbbbbb",
          "bbbbbbb",
          "cccccccc",
          "bbbbbbbbb"
        ]
      },
      {
        "input": [
          "BOS",
          "c",
          "c",
          "c",
          "a",
          "c",
          "b",
          "a",
          "b",
          "b"
        ],
        "output": [
          "BOS",
          "c",
          "cc",
          "ccc",
          "aaaa",
          "ccccc",
          "bbbbbb",
          "aaaaaaa",
          "bbbbbbbb",
          "bbbbbbbbb"
        ]
      }
    ],
    "is_categorical": true
  },
  "program": "cascade_sop = rasp.SequenceMap(lambda x, i: x * (i + 1), sop, rasp.indices)\nreturn cascade_sop",
  "components": [
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Combines each token with its position index to repeat the token an increasing number of times across the sequence."
      },
      "rasp_vars": [
        "cascade_sop"
      ],
      "labels": [
        "sequence_map_1"
      ]
    }
  ]
}