{
  "task_id": "causal-circuits",
  "policy": "adaptive_classical",
  "policy_type": "classical, not an LLM",
  "estimator": "Regularized inverse-link regressions; approximate noise propagation",
  "public_spec": {
    "task_id": "causal-circuits",
    "version": "0.2.0",
    "budget": 8,
    "cost_semantics": "Every accepted experiment costs one credit; at most two repeats per action. Invalid requests cost nothing. The budget is a hard constraint; unused credits do not directly increase the score.",
    "measurement_noise": "Independent additive zero-mean Gaussian noise per output and replicate, with the listed fixed standard deviations. Readouts are not clipped. Each measurement has equal synthetic exposure/cost. Repeating observe_initial returns the same initial data, not new measurements.",
    "split_definition": "Train and test use independent parameter/noise draws from the same published distributions. No claim of out-of-family generalization.",
    "status": "Original synthetic prototype; no physical calibration or LLM training result.",
    "submission": "Submit one finite numeric matrix in the exact prediction_shape. Submission is terminal and cannot be retried after acceptance.",
    "scoring": {
      "name": "inverse_normalized_mse",
      "formula": "score = 1 / (1 + mean(((prediction - noiseless_hidden_target) / scale)^2))",
      "scale": [
        0.035,
        0.035
      ],
      "range": [
        0,
        1
      ],
      "meaning": "Higher is better. Exact latent-mean prediction scores 1. A normalized RMSE equal to one measurement-noise standard deviation scores 0.5. Measurement noise is not added to hidden targets."
    },
    "title": "Synthetic causal circuits",
    "outputs": [
      "x",
      "y"
    ],
    "noise_std": [
      0.035,
      0.035
    ],
    "instructions": "Infer a synthetic nonlinear causal circuit from noisy single-node interventions. Use up to eight experiments, then predict x and y under the listed combined interventions. The causal equations and prior are known; their coefficients are hidden. There is no score for identifying a unique graph.",
    "model": "x=tanh(bx+wu*u+wv*v), y=tanh(by+wx*x+yu*u+yv*v). Interventions replace the equation of the clamped node. Unclamped roots u=v=0.",
    "prior": "bx,by independently Uniform(-0.2,0.2); wu,wv,wx,yu,yv independently Uniform(-0.9,0.9).",
    "initial_queries": [
      {
        "u": 0.0,
        "v": 0.0
      }
    ],
    "prediction_queries": [
      {
        "u": -0.8,
        "v": -0.8
      },
      {
        "u": -0.8,
        "v": 0.8
      },
      {
        "u": 0.8,
        "v": -0.8
      },
      {
        "u": 0.8,
        "v": 0.8
      },
      {
        "u": -0.4,
        "v": 0.7
      },
      {
        "u": 0.6,
        "v": -0.3
      },
      {
        "u": -0.6,
        "x": 0.6
      },
      {
        "v": 0.6,
        "x": -0.6
      }
    ],
    "experiments": [
      {
        "id": "clamp-u-0",
        "label": "Clamp u to -1",
        "query": {
          "u": -1.0
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-u-1",
        "label": "Clamp u to -0.4",
        "query": {
          "u": -0.4
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-u-2",
        "label": "Clamp u to 0.4",
        "query": {
          "u": 0.4
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-u-3",
        "label": "Clamp u to 1",
        "query": {
          "u": 1.0
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-v-0",
        "label": "Clamp v to -1",
        "query": {
          "v": -1.0
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-v-1",
        "label": "Clamp v to -0.4",
        "query": {
          "v": -0.4
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-v-2",
        "label": "Clamp v to 0.4",
        "query": {
          "v": 0.4
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-v-3",
        "label": "Clamp v to 1",
        "query": {
          "v": 1.0
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-x-0",
        "label": "Clamp x to -1",
        "query": {
          "x": -1.0
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-x-1",
        "label": "Clamp x to -0.4",
        "query": {
          "x": -0.4
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-x-2",
        "label": "Clamp x to 0.4",
        "query": {
          "x": 0.4
        },
        "cost": 1,
        "max_replicates": 2
      },
      {
        "id": "clamp-x-3",
        "label": "Clamp x to 1",
        "query": {
          "x": 1.0
        },
        "cost": 1,
        "max_replicates": 2
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    "action_schema": {
      "type": "object",
      "properties": {
        "action_id": {
          "type": "string",
          "enum": [
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            "clamp-x-0",
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            "clamp-x-2",
            "clamp-x-3"
          ]
        }
      },
      "required": [
        "action_id"
      ],
      "additionalProperties": false
    },
    "prediction_shape": [
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      2
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  "initial": [
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    "normalized_mse": 0.45065716129929667,
    "rmse": 0.023495851178274824,
    "numeric_overflow": false,
    "experiments_used": 8,
    "budget_remaining": 0,
    "terminal": true
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  "transcript": {
    "task_id": "causal-circuits",
    "version": "0.2.0",
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  "selection_note": "Upper median score among all completed adaptive-classical runs, selected for illustration after evaluation; not an LLM rollout or a best run."
}