| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.0, "p_not_A": 1.0}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.0, "not_A": 1.0}, "instance_id": "explicit_probability__seed_000042__repr_direct", "latent_instance_id": "explicit_probability__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "0", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 42, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.0, "p_not_A": 1.0}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.0, "p_not_A": 1.0}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.0, "not_A": 1.0}, "instance_id": "explicit_probability__seed_000042__repr_ratio", "latent_instance_id": "explicit_probability__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "0", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 42, "state": {"probability_ratio_A_to_not_A": "0:1", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.0, "p_not_A": 1.0}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.0, "not_A": 1.0}, "instance_id": "explicit_probability__seed_000042__repr_prose", "latent_instance_id": "explicit_probability__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "0", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of A is 0, and the remaining probability belongs to the other outcome. {'p_A': 0.0, 'p_not_A': 1.0}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.0, "p_not_A": 1.0}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.0, "not_A": 1.0}, "instance_id": "explicit_probability__seed_000042__repr_distractor", "latent_instance_id": "explicit_probability__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "0", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 42, "state": {"irrelevant": {"batch_code": "ZX-042", "container_temperature_c": 18.1, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.0, "p_not_A": 1.0}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.052631578947, "p_not_A": 0.947368421053}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.052631578947, "not_A": 0.947368421053}, "instance_id": "explicit_probability__seed_000043__repr_direct", "latent_instance_id": "explicit_probability__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "[0.01,0.10]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 43, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.052631578947, "p_not_A": 0.947368421053}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.052631578947, "p_not_A": 0.947368421053}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.052631578947, "not_A": 0.947368421053}, "instance_id": "explicit_probability__seed_000043__repr_ratio", "latent_instance_id": "explicit_probability__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "[0.01,0.10]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 43, "state": {"probability_ratio_A_to_not_A": "1:19", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.052631578947, "p_not_A": 0.947368421053}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.052631578947, "not_A": 0.947368421053}, "instance_id": "explicit_probability__seed_000043__repr_prose", "latent_instance_id": "explicit_probability__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "[0.01,0.10]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 43, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.052631578947, and the remaining probability belongs to the other outcome. {'p_A': 0.052631578947, 'p_not_A': 0.947368421053}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.052631578947, "p_not_A": 0.947368421053}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.052631578947, "not_A": 0.947368421053}, "instance_id": "explicit_probability__seed_000043__repr_distractor", "latent_instance_id": "explicit_probability__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "[0.01,0.10]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 43, "state": {"irrelevant": {"batch_code": "ZX-043", "container_temperature_c": 18.8, "operator_shift": "swing", "sensor_revision": "rev-4", "warehouse_lane": "B"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.052631578947, "p_not_A": 0.947368421053}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.105263157895, "p_not_A": 0.894736842105}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.105263157895, "not_A": 0.894736842105}, "instance_id": "explicit_probability__seed_000044__repr_direct", "latent_instance_id": "explicit_probability__seed_000044", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 44, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.105263157895, "p_not_A": 0.894736842105}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.105263157895, "p_not_A": 0.894736842105}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.105263157895, "not_A": 0.894736842105}, "instance_id": "explicit_probability__seed_000044__repr_ratio", "latent_instance_id": "explicit_probability__seed_000044", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 44, "state": {"probability_ratio_A_to_not_A": "11:89", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.105263157895, "p_not_A": 0.894736842105}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.105263157895, "not_A": 0.894736842105}, "instance_id": "explicit_probability__seed_000044__repr_prose", "latent_instance_id": "explicit_probability__seed_000044", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 44, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.105263157895, and the remaining probability belongs to the other outcome. {'p_A': 0.105263157895, 'p_not_A': 0.894736842105}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.105263157895, "p_not_A": 0.894736842105}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.105263157895, "not_A": 0.894736842105}, "instance_id": "explicit_probability__seed_000044__repr_distractor", "latent_instance_id": "explicit_probability__seed_000044", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 44, "state": {"irrelevant": {"batch_code": "ZX-044", "container_temperature_c": 19.5, "operator_shift": "night", "sensor_revision": "rev-5", "warehouse_lane": "C"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.105263157895, "p_not_A": 0.894736842105}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.157894736842, "p_not_A": 0.8421052631579999}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.157894736842, "not_A": 0.8421052631579999}, "instance_id": "explicit_probability__seed_000045__repr_direct", "latent_instance_id": "explicit_probability__seed_000045", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 45, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.157894736842, "p_not_A": 0.8421052631579999}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.157894736842, "p_not_A": 0.8421052631579999}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.157894736842, "not_A": 0.8421052631579999}, "instance_id": "explicit_probability__seed_000045__repr_ratio", "latent_instance_id": "explicit_probability__seed_000045", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 45, "state": {"probability_ratio_A_to_not_A": "4:21", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.157894736842, "p_not_A": 0.8421052631579999}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.157894736842, "not_A": 0.8421052631579999}, "instance_id": "explicit_probability__seed_000045__repr_prose", "latent_instance_id": "explicit_probability__seed_000045", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 45, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.157894736842, and the remaining probability belongs to the other outcome. {'p_A': 0.157894736842, 'p_not_A': 0.8421052631579999}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.157894736842, "p_not_A": 0.8421052631579999}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.157894736842, "not_A": 0.8421052631579999}, "instance_id": "explicit_probability__seed_000045__repr_distractor", "latent_instance_id": "explicit_probability__seed_000045", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 45, "state": {"irrelevant": {"batch_code": "ZX-045", "container_temperature_c": 20.2, "operator_shift": "morning", "sensor_revision": "rev-1", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.157894736842, "p_not_A": 0.8421052631579999}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.210526315789, "p_not_A": 0.789473684211}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.210526315789, "not_A": 0.789473684211}, "instance_id": "explicit_probability__seed_000046__repr_direct", "latent_instance_id": "explicit_probability__seed_000046", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 46, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.210526315789, "p_not_A": 0.789473684211}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.210526315789, "p_not_A": 0.789473684211}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.210526315789, "not_A": 0.789473684211}, "instance_id": "explicit_probability__seed_000046__repr_ratio", "latent_instance_id": "explicit_probability__seed_000046", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 46, "state": {"probability_ratio_A_to_not_A": "21:79", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.210526315789, "p_not_A": 0.789473684211}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.210526315789, "not_A": 0.789473684211}, "instance_id": "explicit_probability__seed_000046__repr_prose", "latent_instance_id": "explicit_probability__seed_000046", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 46, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.210526315789, and the remaining probability belongs to the other outcome. {'p_A': 0.210526315789, 'p_not_A': 0.789473684211}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.210526315789, "p_not_A": 0.789473684211}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.210526315789, "not_A": 0.789473684211}, "instance_id": "explicit_probability__seed_000046__repr_distractor", "latent_instance_id": "explicit_probability__seed_000046", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 46, "state": {"irrelevant": {"batch_code": "ZX-046", "container_temperature_c": 20.9, "operator_shift": "swing", "sensor_revision": "rev-2", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.210526315789, "p_not_A": 0.789473684211}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.263157894737, "p_not_A": 0.736842105263}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.263157894737, "not_A": 0.736842105263}, "instance_id": "explicit_probability__seed_000047__repr_direct", "latent_instance_id": "explicit_probability__seed_000047", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 47, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.263157894737, "p_not_A": 0.736842105263}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.263157894737, "p_not_A": 0.736842105263}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.263157894737, "not_A": 0.736842105263}, "instance_id": "explicit_probability__seed_000047__repr_ratio", "latent_instance_id": "explicit_probability__seed_000047", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 47, "state": {"probability_ratio_A_to_not_A": "13:37", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.263157894737, "p_not_A": 0.736842105263}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.263157894737, "not_A": 0.736842105263}, "instance_id": "explicit_probability__seed_000047__repr_prose", "latent_instance_id": "explicit_probability__seed_000047", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 47, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.263157894737, and the remaining probability belongs to the other outcome. {'p_A': 0.263157894737, 'p_not_A': 0.736842105263}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.263157894737, "p_not_A": 0.736842105263}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.263157894737, "not_A": 0.736842105263}, "instance_id": "explicit_probability__seed_000047__repr_distractor", "latent_instance_id": "explicit_probability__seed_000047", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 47, "state": {"irrelevant": {"batch_code": "ZX-047", "container_temperature_c": 21.6, "operator_shift": "night", "sensor_revision": "rev-3", "warehouse_lane": "F"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.263157894737, "p_not_A": 0.736842105263}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.315789473684, "p_not_A": 0.684210526316}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.315789473684, "not_A": 0.684210526316}, "instance_id": "explicit_probability__seed_000048__repr_direct", "latent_instance_id": "explicit_probability__seed_000048", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 48, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.315789473684, "p_not_A": 0.684210526316}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.315789473684, "p_not_A": 0.684210526316}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.315789473684, "not_A": 0.684210526316}, "instance_id": "explicit_probability__seed_000048__repr_ratio", "latent_instance_id": "explicit_probability__seed_000048", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 48, "state": {"probability_ratio_A_to_not_A": "8:17", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.315789473684, "p_not_A": 0.684210526316}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.315789473684, "not_A": 0.684210526316}, "instance_id": "explicit_probability__seed_000048__repr_prose", "latent_instance_id": "explicit_probability__seed_000048", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 48, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.315789473684, and the remaining probability belongs to the other outcome. {'p_A': 0.315789473684, 'p_not_A': 0.684210526316}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.315789473684, "p_not_A": 0.684210526316}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.315789473684, "not_A": 0.684210526316}, "instance_id": "explicit_probability__seed_000048__repr_distractor", "latent_instance_id": "explicit_probability__seed_000048", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 48, "state": {"irrelevant": {"batch_code": "ZX-048", "container_temperature_c": 22.3, "operator_shift": "morning", "sensor_revision": "rev-4", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.315789473684, "p_not_A": 0.684210526316}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.368421052632, "p_not_A": 0.631578947368}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.368421052632, "not_A": 0.631578947368}, "instance_id": "explicit_probability__seed_000049__repr_direct", "latent_instance_id": "explicit_probability__seed_000049", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 49, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.368421052632, "p_not_A": 0.631578947368}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.368421052632, "p_not_A": 0.631578947368}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.368421052632, "not_A": 0.631578947368}, "instance_id": "explicit_probability__seed_000049__repr_ratio", "latent_instance_id": "explicit_probability__seed_000049", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 49, "state": {"probability_ratio_A_to_not_A": "37:63", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.368421052632, "p_not_A": 0.631578947368}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.368421052632, "not_A": 0.631578947368}, "instance_id": "explicit_probability__seed_000049__repr_prose", "latent_instance_id": "explicit_probability__seed_000049", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 49, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.368421052632, and the remaining probability belongs to the other outcome. {'p_A': 0.368421052632, 'p_not_A': 0.631578947368}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.368421052632, "p_not_A": 0.631578947368}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.368421052632, "not_A": 0.631578947368}, "instance_id": "explicit_probability__seed_000049__repr_distractor", "latent_instance_id": "explicit_probability__seed_000049", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 49, "state": {"irrelevant": {"batch_code": "ZX-049", "container_temperature_c": 23.0, "operator_shift": "swing", "sensor_revision": "rev-5", "warehouse_lane": "B"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.368421052632, "p_not_A": 0.631578947368}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.421052631579, "p_not_A": 0.578947368421}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.421052631579, "not_A": 0.578947368421}, "instance_id": "explicit_probability__seed_000050__repr_direct", "latent_instance_id": "explicit_probability__seed_000050", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 50, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.421052631579, "p_not_A": 0.578947368421}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.421052631579, "p_not_A": 0.578947368421}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.421052631579, "not_A": 0.578947368421}, "instance_id": "explicit_probability__seed_000050__repr_ratio", "latent_instance_id": "explicit_probability__seed_000050", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 50, "state": {"probability_ratio_A_to_not_A": "21:29", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.421052631579, "p_not_A": 0.578947368421}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.421052631579, "not_A": 0.578947368421}, "instance_id": "explicit_probability__seed_000050__repr_prose", "latent_instance_id": "explicit_probability__seed_000050", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 50, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.421052631579, and the remaining probability belongs to the other outcome. {'p_A': 0.421052631579, 'p_not_A': 0.578947368421}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.421052631579, "p_not_A": 0.578947368421}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.421052631579, "not_A": 0.578947368421}, "instance_id": "explicit_probability__seed_000050__repr_distractor", "latent_instance_id": "explicit_probability__seed_000050", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 50, "state": {"irrelevant": {"batch_code": "ZX-050", "container_temperature_c": 23.7, "operator_shift": "night", "sensor_revision": "rev-1", "warehouse_lane": "C"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.421052631579, "p_not_A": 0.578947368421}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.473684210526, "p_not_A": 0.526315789474}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.473684210526, "not_A": 0.526315789474}, "instance_id": "explicit_probability__seed_000051__repr_direct", "latent_instance_id": "explicit_probability__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 51, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.473684210526, "p_not_A": 0.526315789474}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.473684210526, "p_not_A": 0.526315789474}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.473684210526, "not_A": 0.526315789474}, "instance_id": "explicit_probability__seed_000051__repr_ratio", "latent_instance_id": "explicit_probability__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 51, "state": {"probability_ratio_A_to_not_A": "47:53", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.473684210526, "p_not_A": 0.526315789474}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.473684210526, "not_A": 0.526315789474}, "instance_id": "explicit_probability__seed_000051__repr_prose", "latent_instance_id": "explicit_probability__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 51, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.473684210526, and the remaining probability belongs to the other outcome. {'p_A': 0.473684210526, 'p_not_A': 0.526315789474}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.473684210526, "p_not_A": 0.526315789474}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.473684210526, "not_A": 0.526315789474}, "instance_id": "explicit_probability__seed_000051__repr_distractor", "latent_instance_id": "explicit_probability__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 51, "state": {"irrelevant": {"batch_code": "ZX-051", "container_temperature_c": 12.5, "operator_shift": "morning", "sensor_revision": "rev-2", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.473684210526, "p_not_A": 0.526315789474}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.526315789474, "p_not_A": 0.47368421052599996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.526315789474, "not_A": 0.47368421052599996}, "instance_id": "explicit_probability__seed_000052__repr_direct", "latent_instance_id": "explicit_probability__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 52, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.526315789474, "p_not_A": 0.47368421052599996}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.526315789474, "p_not_A": 0.47368421052599996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.526315789474, "not_A": 0.47368421052599996}, "instance_id": "explicit_probability__seed_000052__repr_ratio", "latent_instance_id": "explicit_probability__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 52, "state": {"probability_ratio_A_to_not_A": "53:47", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.526315789474, "p_not_A": 0.47368421052599996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.526315789474, "not_A": 0.47368421052599996}, "instance_id": "explicit_probability__seed_000052__repr_prose", "latent_instance_id": "explicit_probability__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 52, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.526315789474, and the remaining probability belongs to the other outcome. {'p_A': 0.526315789474, 'p_not_A': 0.47368421052599996}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.526315789474, "p_not_A": 0.47368421052599996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.526315789474, "not_A": 0.47368421052599996}, "instance_id": "explicit_probability__seed_000052__repr_distractor", "latent_instance_id": "explicit_probability__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 52, "state": {"irrelevant": {"batch_code": "ZX-052", "container_temperature_c": 13.2, "operator_shift": "swing", "sensor_revision": "rev-3", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.526315789474, "p_not_A": 0.47368421052599996}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.578947368421, "p_not_A": 0.42105263157899997}}, "gold_argmax": "A", "gold_distribution": {"A": 0.578947368421, "not_A": 0.42105263157899997}, "instance_id": "explicit_probability__seed_000053__repr_direct", "latent_instance_id": "explicit_probability__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 53, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.578947368421, "p_not_A": 0.42105263157899997}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.578947368421, "p_not_A": 0.42105263157899997}}, "gold_argmax": "A", "gold_distribution": {"A": 0.578947368421, "not_A": 0.42105263157899997}, "instance_id": "explicit_probability__seed_000053__repr_ratio", "latent_instance_id": "explicit_probability__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 53, "state": {"probability_ratio_A_to_not_A": "29:21", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.578947368421, "p_not_A": 0.42105263157899997}}, "gold_argmax": "A", "gold_distribution": {"A": 0.578947368421, "not_A": 0.42105263157899997}, "instance_id": "explicit_probability__seed_000053__repr_prose", "latent_instance_id": "explicit_probability__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 53, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.578947368421, and the remaining probability belongs to the other outcome. {'p_A': 0.578947368421, 'p_not_A': 0.42105263157899997}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.578947368421, "p_not_A": 0.42105263157899997}}, "gold_argmax": "A", "gold_distribution": {"A": 0.578947368421, "not_A": 0.42105263157899997}, "instance_id": "explicit_probability__seed_000053__repr_distractor", "latent_instance_id": "explicit_probability__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 53, "state": {"irrelevant": {"batch_code": "ZX-053", "container_temperature_c": 13.9, "operator_shift": "night", "sensor_revision": "rev-4", "warehouse_lane": "F"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.578947368421, "p_not_A": 0.42105263157899997}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.631578947368, "p_not_A": 0.368421052632}}, "gold_argmax": "A", "gold_distribution": {"A": 0.631578947368, "not_A": 0.368421052632}, "instance_id": "explicit_probability__seed_000054__repr_direct", "latent_instance_id": "explicit_probability__seed_000054", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 54, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.631578947368, "p_not_A": 0.368421052632}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.631578947368, "p_not_A": 0.368421052632}}, "gold_argmax": "A", "gold_distribution": {"A": 0.631578947368, "not_A": 0.368421052632}, "instance_id": "explicit_probability__seed_000054__repr_ratio", "latent_instance_id": "explicit_probability__seed_000054", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 54, "state": {"probability_ratio_A_to_not_A": "63:37", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.631578947368, "p_not_A": 0.368421052632}}, "gold_argmax": "A", "gold_distribution": {"A": 0.631578947368, "not_A": 0.368421052632}, "instance_id": "explicit_probability__seed_000054__repr_prose", "latent_instance_id": "explicit_probability__seed_000054", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 54, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.631578947368, and the remaining probability belongs to the other outcome. {'p_A': 0.631578947368, 'p_not_A': 0.368421052632}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.631578947368, "p_not_A": 0.368421052632}}, "gold_argmax": "A", "gold_distribution": {"A": 0.631578947368, "not_A": 0.368421052632}, "instance_id": "explicit_probability__seed_000054__repr_distractor", "latent_instance_id": "explicit_probability__seed_000054", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 54, "state": {"irrelevant": {"batch_code": "ZX-054", "container_temperature_c": 14.6, "operator_shift": "morning", "sensor_revision": "rev-5", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.631578947368, "p_not_A": 0.368421052632}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.684210526316, "p_not_A": 0.315789473684}}, "gold_argmax": "A", "gold_distribution": {"A": 0.684210526316, "not_A": 0.315789473684}, "instance_id": "explicit_probability__seed_000055__repr_direct", "latent_instance_id": "explicit_probability__seed_000055", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 55, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.684210526316, "p_not_A": 0.315789473684}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.684210526316, "p_not_A": 0.315789473684}}, "gold_argmax": "A", "gold_distribution": {"A": 0.684210526316, "not_A": 0.315789473684}, "instance_id": "explicit_probability__seed_000055__repr_ratio", "latent_instance_id": "explicit_probability__seed_000055", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 55, "state": {"probability_ratio_A_to_not_A": "17:8", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.684210526316, "p_not_A": 0.315789473684}}, "gold_argmax": "A", "gold_distribution": {"A": 0.684210526316, "not_A": 0.315789473684}, "instance_id": "explicit_probability__seed_000055__repr_prose", "latent_instance_id": "explicit_probability__seed_000055", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 55, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.684210526316, and the remaining probability belongs to the other outcome. {'p_A': 0.684210526316, 'p_not_A': 0.315789473684}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.684210526316, "p_not_A": 0.315789473684}}, "gold_argmax": "A", "gold_distribution": {"A": 0.684210526316, "not_A": 0.315789473684}, "instance_id": "explicit_probability__seed_000055__repr_distractor", "latent_instance_id": "explicit_probability__seed_000055", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 55, "state": {"irrelevant": {"batch_code": "ZX-055", "container_temperature_c": 15.3, "operator_shift": "swing", "sensor_revision": "rev-1", "warehouse_lane": "B"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.684210526316, "p_not_A": 0.315789473684}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}, "gold_argmax": "A", "gold_distribution": {"A": 0.736842105263, "not_A": 0.263157894737}, "instance_id": "explicit_probability__seed_000056__repr_direct", "latent_instance_id": "explicit_probability__seed_000056", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 56, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}, "gold_argmax": "A", "gold_distribution": {"A": 0.736842105263, "not_A": 0.263157894737}, "instance_id": "explicit_probability__seed_000056__repr_ratio", "latent_instance_id": "explicit_probability__seed_000056", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 56, "state": {"probability_ratio_A_to_not_A": "37:13", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}, "gold_argmax": "A", "gold_distribution": {"A": 0.736842105263, "not_A": 0.263157894737}, "instance_id": "explicit_probability__seed_000056__repr_prose", "latent_instance_id": "explicit_probability__seed_000056", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 56, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.736842105263, and the remaining probability belongs to the other outcome. {'p_A': 0.736842105263, 'p_not_A': 0.263157894737}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}, "gold_argmax": "A", "gold_distribution": {"A": 0.736842105263, "not_A": 0.263157894737}, "instance_id": "explicit_probability__seed_000056__repr_distractor", "latent_instance_id": "explicit_probability__seed_000056", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 56, "state": {"irrelevant": {"batch_code": "ZX-056", "container_temperature_c": 16.0, "operator_shift": "night", "sensor_revision": "rev-2", "warehouse_lane": "C"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.736842105263, "p_not_A": 0.263157894737}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}, "gold_argmax": "A", "gold_distribution": {"A": 0.789473684211, "not_A": 0.21052631578900005}, "instance_id": "explicit_probability__seed_000057__repr_direct", "latent_instance_id": "explicit_probability__seed_000057", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 57, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}, "gold_argmax": "A", "gold_distribution": {"A": 0.789473684211, "not_A": 0.21052631578900005}, "instance_id": "explicit_probability__seed_000057__repr_ratio", "latent_instance_id": "explicit_probability__seed_000057", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 57, "state": {"probability_ratio_A_to_not_A": "79:21", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}, "gold_argmax": "A", "gold_distribution": {"A": 0.789473684211, "not_A": 0.21052631578900005}, "instance_id": "explicit_probability__seed_000057__repr_prose", "latent_instance_id": "explicit_probability__seed_000057", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 57, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.789473684211, and the remaining probability belongs to the other outcome. {'p_A': 0.789473684211, 'p_not_A': 0.21052631578900005}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}, "gold_argmax": "A", "gold_distribution": {"A": 0.789473684211, "not_A": 0.21052631578900005}, "instance_id": "explicit_probability__seed_000057__repr_distractor", "latent_instance_id": "explicit_probability__seed_000057", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 57, "state": {"irrelevant": {"batch_code": "ZX-057", "container_temperature_c": 16.7, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.789473684211, "p_not_A": 0.21052631578900005}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}, "gold_argmax": "A", "gold_distribution": {"A": 0.842105263158, "not_A": 0.15789473684199995}, "instance_id": "explicit_probability__seed_000058__repr_direct", "latent_instance_id": "explicit_probability__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 58, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}, "gold_argmax": "A", "gold_distribution": {"A": 0.842105263158, "not_A": 0.15789473684199995}, "instance_id": "explicit_probability__seed_000058__repr_ratio", "latent_instance_id": "explicit_probability__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 58, "state": {"probability_ratio_A_to_not_A": "21:4", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}, "gold_argmax": "A", "gold_distribution": {"A": 0.842105263158, "not_A": 0.15789473684199995}, "instance_id": "explicit_probability__seed_000058__repr_prose", "latent_instance_id": "explicit_probability__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.842105263158, and the remaining probability belongs to the other outcome. {'p_A': 0.842105263158, 'p_not_A': 0.15789473684199995}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}, "gold_argmax": "A", "gold_distribution": {"A": 0.842105263158, "not_A": 0.15789473684199995}, "instance_id": "explicit_probability__seed_000058__repr_distractor", "latent_instance_id": "explicit_probability__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 58, "state": {"irrelevant": {"batch_code": "ZX-058", "container_temperature_c": 17.4, "operator_shift": "swing", "sensor_revision": "rev-4", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.842105263158, "p_not_A": 0.15789473684199995}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.894736842105, "not_A": 0.10526315789499996}, "instance_id": "explicit_probability__seed_000059__repr_direct", "latent_instance_id": "explicit_probability__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 59, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.894736842105, "not_A": 0.10526315789499996}, "instance_id": "explicit_probability__seed_000059__repr_ratio", "latent_instance_id": "explicit_probability__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 59, "state": {"probability_ratio_A_to_not_A": "89:11", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.894736842105, "not_A": 0.10526315789499996}, "instance_id": "explicit_probability__seed_000059__repr_prose", "latent_instance_id": "explicit_probability__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 59, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.894736842105, and the remaining probability belongs to the other outcome. {'p_A': 0.894736842105, 'p_not_A': 0.10526315789499996}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}, "gold_argmax": "A", "gold_distribution": {"A": 0.894736842105, "not_A": 0.10526315789499996}, "instance_id": "explicit_probability__seed_000059__repr_distractor", "latent_instance_id": "explicit_probability__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 59, "state": {"irrelevant": {"batch_code": "ZX-059", "container_temperature_c": 18.1, "operator_shift": "night", "sensor_revision": "rev-5", "warehouse_lane": "F"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.894736842105, "p_not_A": 0.10526315789499996}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}, "gold_argmax": "A", "gold_distribution": {"A": 0.947368421053, "not_A": 0.05263157894699999}, "instance_id": "explicit_probability__seed_000060__repr_direct", "latent_instance_id": "explicit_probability__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 60, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}, "gold_argmax": "A", "gold_distribution": {"A": 0.947368421053, "not_A": 0.05263157894699999}, "instance_id": "explicit_probability__seed_000060__repr_ratio", "latent_instance_id": "explicit_probability__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 60, "state": {"probability_ratio_A_to_not_A": "19:1", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}, "gold_argmax": "A", "gold_distribution": {"A": 0.947368421053, "not_A": 0.05263157894699999}, "instance_id": "explicit_probability__seed_000060__repr_prose", "latent_instance_id": "explicit_probability__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 60, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.947368421053, and the remaining probability belongs to the other outcome. {'p_A': 0.947368421053, 'p_not_A': 0.05263157894699999}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}, "gold_argmax": "A", "gold_distribution": {"A": 0.947368421053, "not_A": 0.05263157894699999}, "instance_id": "explicit_probability__seed_000060__repr_distractor", "latent_instance_id": "explicit_probability__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 60, "state": {"irrelevant": {"batch_code": "ZX-060", "container_temperature_c": 18.8, "operator_shift": "morning", "sensor_revision": "rev-1", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"p_A": 0.947368421053, "p_not_A": 0.05263157894699999}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_direct", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 61, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 1.0, "p_not_A": 0.0}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_ratio", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "ratio", "seed": 61, "state": {"probability_ratio_A_to_not_A": "1:0", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_prose", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 61, "state": {"description": "The state fully determines the target distribution. The probability of A is 1, and the remaining probability belongs to the other outcome. {'p_A': 1.0, 'p_not_A': 0.0}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 1, "family": "explicit_probability", "generator_metadata": {"parameters": {"p_A": 1.0, "p_not_A": 0.0}}, "gold_argmax": "A", "gold_distribution": {"A": 1.0, "not_A": 0.0}, "instance_id": "explicit_probability__seed_000061__repr_distractor", "latent_instance_id": "explicit_probability__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "1", "prompt": "Given the fully specified state, what is the probability that event A occurs? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 61, "state": {"irrelevant": {"batch_code": "ZX-061", "container_temperature_c": 19.5, "operator_shift": "swing", "sensor_revision": "rev-2", "warehouse_lane": "B"}, "representation": "distractor", "sufficient_statistics": {"p_A": 1.0, "p_not_A": 0.0}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_counts", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 42, "state": {"counts": {"nif": 200, "zor": 800}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_scaled_counts", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 42, "state": {"counts": {"nif": 20000, "zor": 80000}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_ratio", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 42, "state": {"probability_ratio_zor_to_nif": "4:1", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_table", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"counts": {"nif": 10, "zor": 40}, "sampling": "uniform"}, "table": [{"count": 40, "label": "zor"}, {"count": 10, "label": "nif"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_prose", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.8, and the remaining probability belongs to the other outcome. {'counts': {'zor': 40, 'nif': 10}, 'sampling': 'uniform'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 10, "zor": 40}, "reduced_counts": {"nif": 1, "zor": 4}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.2, "zor": 0.8}, "instance_id": "frequency__seed_000042__repr_distractor", "latent_instance_id": "frequency__seed_000042", "outcomes": ["zor", "nif"], "probability_band": "(0.70,0.90]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 42, "state": {"irrelevant": {"batch_code": "ZX-042", "container_temperature_c": 18.1, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 10, "zor": 40}, "sampling": "uniform"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_counts", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 46, "state": {"counts": {"nif": 350, "zor": 650}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_scaled_counts", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 46, "state": {"counts": {"nif": 35000, "zor": 65000}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_ratio", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 46, "state": {"probability_ratio_zor_to_nif": "13:7", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_table", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 46, "state": {"representation": "table", "state": {"counts": {"nif": 7, "zor": 13}, "sampling": "uniform"}, "table": [{"count": 13, "label": "zor"}, {"count": 7, "label": "nif"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_prose", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 46, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.65, and the remaining probability belongs to the other outcome. {'counts': {'zor': 13, 'nif': 7}, 'sampling': 'uniform'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 7, "zor": 13}, "reduced_counts": {"nif": 7, "zor": 13}}}, "gold_argmax": "zor", "gold_distribution": {"nif": 0.35, "zor": 0.65}, "instance_id": "frequency__seed_000046__repr_distractor", "latent_instance_id": "frequency__seed_000046", "outcomes": ["zor", "nif"], "probability_band": "(0.55,0.70]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 46, "state": {"irrelevant": {"batch_code": "ZX-046", "container_temperature_c": 20.9, "operator_shift": "swing", "sensor_revision": "rev-2", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 7, "zor": 13}, "sampling": "uniform"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_counts", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 50, "state": {"counts": {"nif": 710, "zor": 290}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_scaled_counts", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 50, "state": {"counts": {"nif": 71000, "zor": 29000}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_ratio", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 50, "state": {"probability_ratio_zor_to_nif": "29:71", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_table", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 50, "state": {"representation": "table", "state": {"counts": {"nif": 71, "zor": 29}, "sampling": "uniform"}, "table": [{"count": 29, "label": "zor"}, {"count": 71, "label": "nif"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_prose", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 50, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.29, and the remaining probability belongs to the other outcome. {'counts': {'zor': 29, 'nif': 71}, 'sampling': 'uniform'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 71, "zor": 29}, "reduced_counts": {"nif": 71, "zor": 29}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.71, "zor": 0.29}, "instance_id": "frequency__seed_000050__repr_distractor", "latent_instance_id": "frequency__seed_000050", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 50, "state": {"irrelevant": {"batch_code": "ZX-050", "container_temperature_c": 23.7, "operator_shift": "night", "sensor_revision": "rev-1", "warehouse_lane": "C"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 71, "zor": 29}, "sampling": "uniform"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_counts", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 54, "state": {"counts": {"nif": 800, "zor": 200}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_scaled_counts", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 54, "state": {"counts": {"nif": 80000, "zor": 20000}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_ratio", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 54, "state": {"probability_ratio_zor_to_nif": "1:4", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_table", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 54, "state": {"representation": "table", "state": {"counts": {"nif": 16, "zor": 4}, "sampling": "uniform"}, "table": [{"count": 4, "label": "zor"}, {"count": 16, "label": "nif"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_prose", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 54, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.2, and the remaining probability belongs to the other outcome. {'counts': {'zor': 4, 'nif': 16}, 'sampling': 'uniform'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 16, "zor": 4}, "reduced_counts": {"nif": 4, "zor": 1}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.8, "zor": 0.2}, "instance_id": "frequency__seed_000054__repr_distractor", "latent_instance_id": "frequency__seed_000054", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 54, "state": {"irrelevant": {"batch_code": "ZX-054", "container_temperature_c": 14.6, "operator_shift": "morning", "sensor_revision": "rev-5", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 16, "zor": 4}, "sampling": "uniform"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_counts", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "counts", "seed": 58, "state": {"counts": {"nif": 880, "zor": 120}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_scaled_counts", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "scaled_counts", "seed": 58, "state": {"counts": {"nif": 88000, "zor": 12000}, "representation": "counts", "sampling": "uniform"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_ratio", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "ratio", "seed": 58, "state": {"probability_ratio_zor_to_nif": "3:22", "representation": "ratio"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_table", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "table", "seed": 58, "state": {"representation": "table", "state": {"counts": {"nif": 44, "zor": 6}, "sampling": "uniform"}, "table": [{"count": 6, "label": "zor"}, {"count": 44, "label": "nif"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_prose", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of zor is 0.12, and the remaining probability belongs to the other outcome. {'counts': {'zor': 6, 'nif': 44}, 'sampling': 'uniform'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 2, "family": "frequency", "generator_metadata": {"parameters": {"counts": {"nif": 44, "zor": 6}, "reduced_counts": {"nif": 22, "zor": 3}}}, "gold_argmax": "nif", "gold_distribution": {"nif": 0.88, "zor": 0.12}, "instance_id": "frequency__seed_000058__repr_distractor", "latent_instance_id": "frequency__seed_000058", "outcomes": ["zor", "nif"], "probability_band": "(0.10,0.30]", "prompt": "An item is sampled uniformly from the collection. What is the probability distribution over item labels? Return a normalized probability for each of: zor, nif.", "representation": "distractor", "seed": 58, "state": {"irrelevant": {"batch_code": "ZX-058", "container_temperature_c": 17.4, "operator_shift": "swing", "sensor_revision": "rev-4", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"counts": {"nif": 44, "zor": 6}, "sampling": "uniform"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.07457999999999998, "target": 0.92542}, "instance_id": "compound__seed_000042__repr_direct", "latent_instance_id": "compound__seed_000042", "outcomes": ["target", "not_target"], "probability_band": "(0.90,0.99]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 42, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.07457999999999998, "target": 0.92542}, "instance_id": "compound__seed_000042__repr_table", "latent_instance_id": "compound__seed_000042", "outcomes": ["target", "not_target"], "probability_band": "(0.90,0.99]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}, "table": [{"field": "subtask", "value": "complement"}, {"field": "p_A", "value": 0.07458}, {"field": "query", "value": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.07458, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.07457999999999998, "target": 0.92542}, "instance_id": "compound__seed_000042__repr_prose", "latent_instance_id": "compound__seed_000042", "outcomes": ["target", "not_target"], "probability_band": "(0.90,0.99]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.92542, and the remaining probability belongs to the other outcome. {'subtask': 'complement', 'p_A': 0.07458, 'query': 'not_A'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.866202024277, "target": 0.133797975723}, "instance_id": "compound__seed_000043__repr_direct", "latent_instance_id": "compound__seed_000043", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 43, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.866202024277, "target": 0.133797975723}, "instance_id": "compound__seed_000043__repr_table", "latent_instance_id": "compound__seed_000043", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 43, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}, "table": [{"field": "subtask", "value": "intersection"}, {"field": "p_A", "value": 0.200973}, {"field": "p_B", "value": 0.665751}, {"field": "independent", "value": true}, {"field": "query", "value": "A_and_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.200973, "p_B": 0.665751, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.866202024277, "target": 0.133797975723}, "instance_id": "compound__seed_000043__repr_prose", "latent_instance_id": "compound__seed_000043", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 43, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.133797975723, and the remaining probability belongs to the other outcome. {'subtask': 'intersection', 'p_A': 0.200973, 'p_B': 0.665751, 'independent': True, 'query': 'A_and_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.0066510489960001085, "target": 0.9933489510039999}, "instance_id": "compound__seed_000044__repr_direct", "latent_instance_id": "compound__seed_000044", "outcomes": ["target", "not_target"], "probability_band": "(0.99,1)", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 44, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.0066510489960001085, "target": 0.9933489510039999}, "instance_id": "compound__seed_000044__repr_table", "latent_instance_id": "compound__seed_000044", "outcomes": ["target", "not_target"], "probability_band": "(0.99,1)", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 44, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}, "table": [{"field": "subtask", "value": "union"}, {"field": "p_A", "value": 0.387226}, {"field": "p_B", "value": 0.989146}, {"field": "independent", "value": true}, {"field": "query", "value": "A_or_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.387226, "p_B": 0.989146, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.0066510489960001085, "target": 0.9933489510039999}, "instance_id": "compound__seed_000044__repr_prose", "latent_instance_id": "compound__seed_000044", "outcomes": ["target", "not_target"], "probability_band": "(0.99,1)", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 44, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.993348951004, and the remaining probability belongs to the other outcome. {'subtask': 'union', 'p_A': 0.387226, 'p_B': 0.989146, 'independent': True, 'query': 'A_or_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7214935573757005, "target": 0.27850644262429947}, "instance_id": "compound__seed_000045__repr_direct", "latent_instance_id": "compound__seed_000045", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 45, "state": {"representation": "direct", "sufficient_statistics": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7214935573757005, "target": 0.27850644262429947}, "instance_id": "compound__seed_000045__repr_table", "latent_instance_id": "compound__seed_000045", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 45, "state": {"representation": "table", "state": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}, "table": [{"field": "subtask", "value": "repeated_exact"}, {"field": "n", "value": 7}, {"field": "k", "value": 3}, {"field": "success_probability", "value": 0.490136}, {"field": "query", "value": "exactly_k_successes"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.490136}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7214935573757005, "target": 0.27850644262429947}, "instance_id": "compound__seed_000045__repr_prose", "latent_instance_id": "compound__seed_000045", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 45, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.278506442624, and the remaining probability belongs to the other outcome. {'subtask': 'repeated_exact', 'n': 7, 'k': 3, 'success_probability': 0.490136, 'query': 'exactly_k_successes'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7182662538699691, "target": 0.28173374613003094}, "instance_id": "compound__seed_000046__repr_direct", "latent_instance_id": "compound__seed_000046", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 46, "state": {"representation": "direct", "sufficient_statistics": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7182662538699691, "target": 0.28173374613003094}, "instance_id": "compound__seed_000046__repr_table", "latent_instance_id": "compound__seed_000046", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 46, "state": {"representation": "table", "state": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}, "table": [{"field": "subtask", "value": "hypergeometric"}, {"field": "good", "value": 6}, {"field": "bad", "value": 14}, {"field": "draws_without_replacement", "value": 4}, {"field": "k_good", "value": 2}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 4, "good": 6, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7182662538699691, "target": 0.28173374613003094}, "instance_id": "compound__seed_000046__repr_prose", "latent_instance_id": "compound__seed_000046", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 46, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.28173374613, and the remaining probability belongs to the other outcome. {'subtask': 'hypergeometric', 'good': 6, 'bad': 14, 'draws_without_replacement': 4, 'k_good': 2}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.84647, "target": 0.15353000000000006}, "instance_id": "compound__seed_000047__repr_direct", "latent_instance_id": "compound__seed_000047", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 47, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.84647, "target": 0.15353000000000006}, "instance_id": "compound__seed_000047__repr_table", "latent_instance_id": "compound__seed_000047", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 47, "state": {"representation": "table", "state": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}, "table": [{"field": "subtask", "value": "complement"}, {"field": "p_A", "value": 0.84647}, {"field": "query", "value": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.84647, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.84647, "target": 0.15353000000000006}, "instance_id": "compound__seed_000047__repr_prose", "latent_instance_id": "compound__seed_000047", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 47, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.15353, and the remaining probability belongs to the other outcome. {'subtask': 'complement', 'p_A': 0.84647, 'query': 'not_A'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.622812018519, "target": 0.377187981481}, "instance_id": "compound__seed_000048__repr_direct", "latent_instance_id": "compound__seed_000048", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 48, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.622812018519, "target": 0.377187981481}, "instance_id": "compound__seed_000048__repr_table", "latent_instance_id": "compound__seed_000048", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 48, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}, "table": [{"field": "subtask", "value": "intersection"}, {"field": "p_A", "value": 0.933733}, {"field": "p_B", "value": 0.403957}, {"field": "independent", "value": true}, {"field": "query", "value": "A_and_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.933733, "p_B": 0.403957, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.622812018519, "target": 0.377187981481}, "instance_id": "compound__seed_000048__repr_prose", "latent_instance_id": "compound__seed_000048", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 48, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.377187981481, and the remaining probability belongs to the other outcome. {'subtask': 'intersection', 'p_A': 0.933733, 'p_B': 0.403957, 'independent': True, 'query': 'A_and_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.39837028522200013, "target": 0.6016297147779999}, "instance_id": "compound__seed_000049__repr_direct", "latent_instance_id": "compound__seed_000049", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 49, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.39837028522200013, "target": 0.6016297147779999}, "instance_id": "compound__seed_000049__repr_table", "latent_instance_id": "compound__seed_000049", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 49, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}, "table": [{"field": "subtask", "value": "union"}, {"field": "p_A", "value": 0.031994}, {"field": "p_B", "value": 0.588463}, {"field": "independent", "value": true}, {"field": "query", "value": "A_or_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.031994, "p_B": 0.588463, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.39837028522200013, "target": 0.6016297147779999}, "instance_id": "compound__seed_000049__repr_prose", "latent_instance_id": "compound__seed_000049", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 49, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.601629714778, and the remaining probability belongs to the other outcome. {'subtask': 'union', 'p_A': 0.031994, 'p_B': 0.588463, 'independent': True, 'query': 'A_or_B'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 4, "n": 9, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.2224}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.912362307039702, "target": 0.08763769296029794}, "instance_id": "compound__seed_000050__repr_prose", "latent_instance_id": "compound__seed_000050", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 50, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.0876376929603, and the remaining probability belongs to the other outcome. {'subtask': 'repeated_exact', 'n': 9, 'k': 4, 'success_probability': 0.2224, 'query': 'exactly_k_successes'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 1, "good": 19, "k_good": 1, "subtask": "hypergeometric"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.4242424242424242, "target": 0.5757575757575758}, "instance_id": "compound__seed_000051__repr_direct", "latent_instance_id": "compound__seed_000051", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 51, "state": {"representation": "direct", "sufficient_statistics": {"bad": 14, "draws_without_replacement": 1, "good": 19, "k_good": 1, "subtask": "hypergeometric"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 1, "good": 19, "k_good": 1, "subtask": "hypergeometric"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.4242424242424242, "target": 0.5757575757575758}, "instance_id": "compound__seed_000051__repr_table", "latent_instance_id": "compound__seed_000051", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 51, "state": {"representation": "table", "state": {"bad": 14, "draws_without_replacement": 1, "good": 19, "k_good": 1, "subtask": "hypergeometric"}, "table": [{"field": "subtask", "value": "hypergeometric"}, {"field": "good", "value": 19}, {"field": "bad", "value": 14}, {"field": "draws_without_replacement", "value": 1}, {"field": "k_good", "value": 1}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 14, "draws_without_replacement": 1, "good": 19, "k_good": 1, "subtask": "hypergeometric"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.4242424242424242, "target": 0.5757575757575758}, "instance_id": "compound__seed_000051__repr_prose", "latent_instance_id": "compound__seed_000051", "outcomes": ["target", "not_target"], "probability_band": "(0.55,0.70]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 51, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.575757575758, and the remaining probability belongs to the other outcome. {'subtask': 'hypergeometric', 'good': 19, 'bad': 14, 'draws_without_replacement': 1, 'k_good': 1}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.453999, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.45399900000000004, "target": 0.546001}, "instance_id": "compound__seed_000052__repr_direct", "latent_instance_id": "compound__seed_000052", "outcomes": ["target", "not_target"], "probability_band": "(0.45,0.55]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 52, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.453999, "query": "not_A", "subtask": "complement"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.453999, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.45399900000000004, "target": 0.546001}, "instance_id": "compound__seed_000052__repr_table", "latent_instance_id": "compound__seed_000052", "outcomes": ["target", "not_target"], "probability_band": "(0.45,0.55]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 52, "state": {"representation": "table", "state": {"p_A": 0.453999, "query": "not_A", "subtask": "complement"}, "table": [{"field": "subtask", "value": "complement"}, {"field": "p_A", "value": 0.453999}, {"field": "query", "value": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.453999, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.45399900000000004, "target": 0.546001}, "instance_id": "compound__seed_000052__repr_prose", "latent_instance_id": "compound__seed_000052", "outcomes": ["target", "not_target"], "probability_band": "(0.45,0.55]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 52, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.546001, and the remaining probability belongs to the other outcome. {'subtask': 'complement', 'p_A': 0.453999, 'query': 'not_A'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.619861, "p_B": 0.0114, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9929335846, "target": 0.0070664154000000005}, "instance_id": "compound__seed_000053__repr_direct", "latent_instance_id": "compound__seed_000053", "outcomes": ["target", "not_target"], "probability_band": "(0,0.01)", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 53, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.619861, "p_B": 0.0114, "query": "A_and_B", "subtask": "intersection"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.619861, "p_B": 0.0114, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9929335846, "target": 0.0070664154000000005}, "instance_id": "compound__seed_000053__repr_table", "latent_instance_id": "compound__seed_000053", "outcomes": ["target", "not_target"], "probability_band": "(0,0.01)", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 53, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.619861, "p_B": 0.0114, "query": "A_and_B", "subtask": "intersection"}, "table": [{"field": "subtask", "value": "intersection"}, {"field": "p_A", "value": 0.619861}, {"field": "p_B", "value": 0.0114}, {"field": "independent", "value": true}, {"field": "query", "value": "A_and_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.619861, "p_B": 0.0114, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9929335846, "target": 0.0070664154000000005}, "instance_id": "compound__seed_000053__repr_prose", "latent_instance_id": "compound__seed_000053", "outcomes": ["target", "not_target"], "probability_band": "(0,0.01)", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 53, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.0070664154, and the remaining probability belongs to the other outcome. {'subtask': 'intersection', 'p_A': 0.619861, 'p_B': 0.0114, 'independent': True, 'query': 'A_and_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.808057, "p_B": 0.435333, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.10838387798100002, "target": 0.891616122019}, "instance_id": "compound__seed_000054__repr_direct", "latent_instance_id": "compound__seed_000054", "outcomes": ["target", "not_target"], "probability_band": "(0.70,0.90]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 54, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.808057, "p_B": 0.435333, "query": "A_or_B", "subtask": "union"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.808057, "p_B": 0.435333, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.10838387798100002, "target": 0.891616122019}, "instance_id": "compound__seed_000054__repr_table", "latent_instance_id": "compound__seed_000054", "outcomes": ["target", "not_target"], "probability_band": "(0.70,0.90]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 54, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.808057, "p_B": 0.435333, "query": "A_or_B", "subtask": "union"}, "table": [{"field": "subtask", "value": "union"}, {"field": "p_A", "value": 0.808057}, {"field": "p_B", "value": 0.435333}, {"field": "independent", "value": true}, {"field": "query", "value": "A_or_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.808057, "p_B": 0.435333, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.10838387798100002, "target": 0.891616122019}, "instance_id": "compound__seed_000054__repr_prose", "latent_instance_id": "compound__seed_000054", "outcomes": ["target", "not_target"], "probability_band": "(0.70,0.90]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 54, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.891616122019, and the remaining probability belongs to the other outcome. {'subtask': 'union', 'p_A': 0.808057, 'p_B': 0.435333, 'independent': True, 'query': 'A_or_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.963857}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9999465186141359, "target": 5.348138586410087e-05}, "instance_id": "compound__seed_000055__repr_direct", "latent_instance_id": "compound__seed_000055", "outcomes": ["target", "not_target"], "probability_band": "(0,0.01)", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 55, "state": {"representation": "direct", "sufficient_statistics": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.963857}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.963857}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9999465186141359, "target": 5.348138586410087e-05}, "instance_id": "compound__seed_000055__repr_table", "latent_instance_id": "compound__seed_000055", "outcomes": ["target", "not_target"], "probability_band": "(0,0.01)", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 55, "state": {"representation": "table", "state": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.963857}, "table": [{"field": "subtask", "value": "repeated_exact"}, {"field": "n", "value": 7}, {"field": "k", "value": 3}, {"field": "success_probability", "value": 0.963857}, {"field": "query", "value": "exactly_k_successes"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 3, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.963857}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9999465186141359, "target": 5.348138586410087e-05}, "instance_id": "compound__seed_000055__repr_prose", "latent_instance_id": "compound__seed_000055", "outcomes": ["target", "not_target"], "probability_band": "(0,0.01)", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 55, "state": {"description": "The state fully determines the target distribution. The probability of target is 5.34813858641e-05, and the remaining probability belongs to the other outcome. {'subtask': 'repeated_exact', 'n': 7, 'k': 3, 'success_probability': 0.963857, 'query': 'exactly_k_successes'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 20, "draws_without_replacement": 2, "good": 17, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7957957957957957, "target": 0.2042042042042042}, "instance_id": "compound__seed_000056__repr_direct", "latent_instance_id": "compound__seed_000056", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 56, "state": {"representation": "direct", "sufficient_statistics": {"bad": 20, "draws_without_replacement": 2, "good": 17, "k_good": 2, "subtask": "hypergeometric"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 20, "draws_without_replacement": 2, "good": 17, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7957957957957957, "target": 0.2042042042042042}, "instance_id": "compound__seed_000056__repr_table", "latent_instance_id": "compound__seed_000056", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 56, "state": {"representation": "table", "state": {"bad": 20, "draws_without_replacement": 2, "good": 17, "k_good": 2, "subtask": "hypergeometric"}, "table": [{"field": "subtask", "value": "hypergeometric"}, {"field": "good", "value": 17}, {"field": "bad", "value": 20}, {"field": "draws_without_replacement", "value": 2}, {"field": "k_good", "value": 2}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 20, "draws_without_replacement": 2, "good": 17, "k_good": 2, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.7957957957957957, "target": 0.2042042042042042}, "instance_id": "compound__seed_000056__repr_prose", "latent_instance_id": "compound__seed_000056", "outcomes": ["target", "not_target"], "probability_band": "(0.10,0.30]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 56, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.204204204204, and the remaining probability belongs to the other outcome. {'subtask': 'hypergeometric', 'good': 17, 'bad': 20, 'draws_without_replacement': 2, 'k_good': 2}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.226962, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.226962, "target": 0.773038}, "instance_id": "compound__seed_000057__repr_direct", "latent_instance_id": "compound__seed_000057", "outcomes": ["target", "not_target"], "probability_band": "(0.70,0.90]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 57, "state": {"representation": "direct", "sufficient_statistics": {"p_A": 0.226962, "query": "not_A", "subtask": "complement"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.226962, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.226962, "target": 0.773038}, "instance_id": "compound__seed_000057__repr_table", "latent_instance_id": "compound__seed_000057", "outcomes": ["target", "not_target"], "probability_band": "(0.70,0.90]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 57, "state": {"representation": "table", "state": {"p_A": 0.226962, "query": "not_A", "subtask": "complement"}, "table": [{"field": "subtask", "value": "complement"}, {"field": "p_A", "value": 0.226962}, {"field": "query", "value": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"p_A": 0.226962, "query": "not_A", "subtask": "complement"}}, "gold_argmax": "target", "gold_distribution": {"not_target": 0.226962, "target": 0.773038}, "instance_id": "compound__seed_000057__repr_prose", "latent_instance_id": "compound__seed_000057", "outcomes": ["target", "not_target"], "probability_band": "(0.70,0.90]", "prompt": "Event A has the supplied probability. What is the probability that A does not occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 57, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.773038, and the remaining probability belongs to the other outcome. {'subtask': 'complement', 'p_A': 0.226962, 'query': 'not_A'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.448231, "p_B": 0.751995, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.662932529155, "target": 0.337067470845}, "instance_id": "compound__seed_000058__repr_direct", "latent_instance_id": "compound__seed_000058", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 58, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.448231, "p_B": 0.751995, "query": "A_and_B", "subtask": "intersection"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.448231, "p_B": 0.751995, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.662932529155, "target": 0.337067470845}, "instance_id": "compound__seed_000058__repr_table", "latent_instance_id": "compound__seed_000058", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 58, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.448231, "p_B": 0.751995, "query": "A_and_B", "subtask": "intersection"}, "table": [{"field": "subtask", "value": "intersection"}, {"field": "p_A", "value": 0.448231}, {"field": "p_B", "value": 0.751995}, {"field": "independent", "value": true}, {"field": "query", "value": "A_and_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.448231, "p_B": 0.751995, "query": "A_and_B", "subtask": "intersection"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.662932529155, "target": 0.337067470845}, "instance_id": "compound__seed_000058__repr_prose", "latent_instance_id": "compound__seed_000058", "outcomes": ["target", "not_target"], "probability_band": "(0.30,0.45]", "prompt": "Events A and B are independent. What is the probability that both occur? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.337067470845, and the remaining probability belongs to the other outcome. {'subtask': 'intersection', 'p_A': 0.448231, 'p_B': 0.751995, 'independent': True, 'query': 'A_and_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.479732, "p_B": 0.030902, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.504190678264, "target": 0.495809321736}, "instance_id": "compound__seed_000059__repr_direct", "latent_instance_id": "compound__seed_000059", "outcomes": ["target", "not_target"], "probability_band": "(0.45,0.55]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 59, "state": {"representation": "direct", "sufficient_statistics": {"independent": true, "p_A": 0.479732, "p_B": 0.030902, "query": "A_or_B", "subtask": "union"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.479732, "p_B": 0.030902, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.504190678264, "target": 0.495809321736}, "instance_id": "compound__seed_000059__repr_table", "latent_instance_id": "compound__seed_000059", "outcomes": ["target", "not_target"], "probability_band": "(0.45,0.55]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 59, "state": {"representation": "table", "state": {"independent": true, "p_A": 0.479732, "p_B": 0.030902, "query": "A_or_B", "subtask": "union"}, "table": [{"field": "subtask", "value": "union"}, {"field": "p_A", "value": 0.479732}, {"field": "p_B", "value": 0.030902}, {"field": "independent", "value": true}, {"field": "query", "value": "A_or_B"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"independent": true, "p_A": 0.479732, "p_B": 0.030902, "query": "A_or_B", "subtask": "union"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.504190678264, "target": 0.495809321736}, "instance_id": "compound__seed_000059__repr_prose", "latent_instance_id": "compound__seed_000059", "outcomes": ["target", "not_target"], "probability_band": "(0.45,0.55]", "prompt": "Events A and B are independent. What is the probability that at least one occurs? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 59, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.495809321736, and the remaining probability belongs to the other outcome. {'subtask': 'union', 'p_A': 0.479732, 'p_B': 0.030902, 'independent': True, 'query': 'A_or_B'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 1, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.576366}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9766793181437634, "target": 0.023320681856236536}, "instance_id": "compound__seed_000060__repr_direct", "latent_instance_id": "compound__seed_000060", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 60, "state": {"representation": "direct", "sufficient_statistics": {"k": 1, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.576366}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 1, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.576366}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9766793181437634, "target": 0.023320681856236536}, "instance_id": "compound__seed_000060__repr_table", "latent_instance_id": "compound__seed_000060", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 60, "state": {"representation": "table", "state": {"k": 1, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.576366}, "table": [{"field": "subtask", "value": "repeated_exact"}, {"field": "n", "value": 7}, {"field": "k", "value": 1}, {"field": "success_probability", "value": 0.576366}, {"field": "query", "value": "exactly_k_successes"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"k": 1, "n": 7, "query": "exactly_k_successes", "subtask": "repeated_exact", "success_probability": 0.576366}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9766793181437634, "target": 0.023320681856236536}, "instance_id": "compound__seed_000060__repr_prose", "latent_instance_id": "compound__seed_000060", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "Independent Bernoulli trials use the supplied success probability. What is the probability of exactly k successes? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 60, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.0233206818562, and the remaining probability belongs to the other outcome. {'subtask': 'repeated_exact', 'n': 7, 'k': 1, 'success_probability': 0.576366, 'query': 'exactly_k_successes'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9521739130434783, "target": 0.04782608695652174}, "instance_id": "compound__seed_000061__repr_direct", "latent_instance_id": "compound__seed_000061", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "direct", "seed": 61, "state": {"representation": "direct", "sufficient_statistics": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9521739130434783, "target": 0.04782608695652174}, "instance_id": "compound__seed_000061__repr_table", "latent_instance_id": "compound__seed_000061", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "table", "seed": 61, "state": {"representation": "table", "state": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}, "table": [{"field": "subtask", "value": "hypergeometric"}, {"field": "good", "value": 13}, {"field": "bad", "value": 13}, {"field": "draws_without_replacement", "value": 4}, {"field": "k_good", "value": 4}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 3, "family": "compound", "generator_metadata": {"parameters": {"bad": 13, "draws_without_replacement": 4, "good": 13, "k_good": 4, "subtask": "hypergeometric"}}, "gold_argmax": "not_target", "gold_distribution": {"not_target": 0.9521739130434783, "target": 0.04782608695652174}, "instance_id": "compound__seed_000061__repr_prose", "latent_instance_id": "compound__seed_000061", "outcomes": ["target", "not_target"], "probability_band": "[0.01,0.10]", "prompt": "A sample is drawn without replacement. What is the probability of exactly k good items? Return a normalized probability for each of: target, not_target.", "representation": "prose", "seed": 61, "state": {"description": "The state fully determines the target distribution. The probability of target is 0.0478260869565, and the remaining probability belongs to the other outcome. {'subtask': 'hypergeometric', 'good': 13, 'bad': 13, 'draws_without_replacement': 4, 'k_good': 4}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.48366013071895425, "not_A": 0.5163398692810457}, "instance_id": "conditional__seed_000042__repr_table", "latent_instance_id": "conditional__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 74, "not_B": 48, "row": "A"}, {"B": 79, "not_B": 55, "row": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.48366013071895425, "not_A": 0.5163398692810457}, "instance_id": "conditional__seed_000042__repr_nested", "latent_instance_id": "conditional__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "nested", "seed": 42, "state": {"nested": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "representation": "nested_state"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.48366013071895425, "not_A": 0.5163398692810457}, "instance_id": "conditional__seed_000042__repr_direct", "latent_instance_id": "conditional__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 42, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.48366013071895425, "not_A": 0.5163398692810457}, "instance_id": "conditional__seed_000042__repr_prose", "latent_instance_id": "conditional__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.483660130719, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 74, 'not_B': 48}, 'not_A': {'B': 79, 'not_B': 55}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.48366013071895425, "not_A": 0.5163398692810457}, "instance_id": "conditional__seed_000042__repr_distractor", "latent_instance_id": "conditional__seed_000042", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 42, "state": {"irrelevant": {"batch_code": "ZX-042", "container_temperature_c": 18.1, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 74, "not_B": 48}, "not_A": {"B": 79, "not_B": 55}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 65, "not_B": 81}, "not_A": {"B": 48, "not_B": 34}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5752212389380531, "not_A": 0.4247787610619469}, "instance_id": "conditional__seed_000043__repr_table", "latent_instance_id": "conditional__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 43, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 65, "not_B": 81}, "not_A": {"B": 48, "not_B": 34}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 65, "not_B": 81, "row": "A"}, {"B": 48, "not_B": 34, "row": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 65, "not_B": 81}, "not_A": {"B": 48, "not_B": 34}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5752212389380531, "not_A": 0.4247787610619469}, "instance_id": "conditional__seed_000043__repr_nested", "latent_instance_id": "conditional__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "nested", "seed": 43, "state": {"nested": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 65, "not_B": 81}, "not_A": {"B": 48, "not_B": 34}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "representation": "nested_state"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 65, "not_B": 81}, "not_A": {"B": 48, "not_B": 34}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5752212389380531, "not_A": 0.4247787610619469}, "instance_id": "conditional__seed_000043__repr_prose", "latent_instance_id": "conditional__seed_000043", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 43, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.575221238938, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 65, 'not_B': 81}, 'not_A': {'B': 48, 'not_B': 34}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 40, "not_B": 42}, "not_A": {"B": 52, "not_B": 79}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.43478260869565216, "not_A": 0.5652173913043479}, "instance_id": "conditional__seed_000045__repr_direct", "latent_instance_id": "conditional__seed_000045", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 45, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 40, "not_B": 42}, "not_A": {"B": 52, "not_B": 79}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 40, "not_B": 42}, "not_A": {"B": 52, "not_B": 79}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.43478260869565216, "not_A": 0.5652173913043479}, "instance_id": "conditional__seed_000045__repr_prose", "latent_instance_id": "conditional__seed_000045", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 45, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.434782608696, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 40, 'not_B': 42}, 'not_A': {'B': 52, 'not_B': 79}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 48, "not_B": 44}, "not_A": {"B": 89, "not_B": 16}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.35036496350364965, "not_A": 0.6496350364963503}, "instance_id": "conditional__seed_000048__repr_direct", "latent_instance_id": "conditional__seed_000048", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 48, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 48, "not_B": 44}, "not_A": {"B": 89, "not_B": 16}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 48, "not_B": 44}, "not_A": {"B": 89, "not_B": 16}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.35036496350364965, "not_A": 0.6496350364963503}, "instance_id": "conditional__seed_000048__repr_prose", "latent_instance_id": "conditional__seed_000048", "outcomes": ["A", "not_A"], "probability_band": "(0.30,0.45]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 48, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.350364963504, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 48, 'not_B': 44}, 'not_A': {'B': 89, 'not_B': 16}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 67, "not_B": 52}, "not_A": {"B": 29, "not_B": 79}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.6979166666666666, "not_A": 0.30208333333333337}, "instance_id": "conditional__seed_000050__repr_direct", "latent_instance_id": "conditional__seed_000050", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 50, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 67, "not_B": 52}, "not_A": {"B": 29, "not_B": 79}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5853658536585366, "not_A": 0.41463414634146345}, "instance_id": "conditional__seed_000051__repr_table", "latent_instance_id": "conditional__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 51, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 72, "not_B": 78, "row": "A"}, {"B": 51, "not_B": 6, "row": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5853658536585366, "not_A": 0.41463414634146345}, "instance_id": "conditional__seed_000051__repr_nested", "latent_instance_id": "conditional__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "nested", "seed": 51, "state": {"nested": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "representation": "nested_state"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5853658536585366, "not_A": 0.41463414634146345}, "instance_id": "conditional__seed_000051__repr_direct", "latent_instance_id": "conditional__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 51, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5853658536585366, "not_A": 0.41463414634146345}, "instance_id": "conditional__seed_000051__repr_prose", "latent_instance_id": "conditional__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 51, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.585365853659, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 72, 'not_B': 78}, 'not_A': {'B': 51, 'not_B': 6}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5853658536585366, "not_A": 0.41463414634146345}, "instance_id": "conditional__seed_000051__repr_distractor", "latent_instance_id": "conditional__seed_000051", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 51, "state": {"irrelevant": {"batch_code": "ZX-051", "container_temperature_c": 12.5, "operator_shift": "morning", "sensor_revision": "rev-2", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 72, "not_B": 78}, "not_A": {"B": 51, "not_B": 6}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.2857142857142857, "not_A": 0.7142857142857143}, "instance_id": "conditional__seed_000052__repr_table", "latent_instance_id": "conditional__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 52, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 6, "not_B": 27, "row": "A"}, {"B": 15, "not_B": 59, "row": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.2857142857142857, "not_A": 0.7142857142857143}, "instance_id": "conditional__seed_000052__repr_nested", "latent_instance_id": "conditional__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "nested", "seed": 52, "state": {"nested": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "representation": "nested_state"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.2857142857142857, "not_A": 0.7142857142857143}, "instance_id": "conditional__seed_000052__repr_direct", "latent_instance_id": "conditional__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 52, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.2857142857142857, "not_A": 0.7142857142857143}, "instance_id": "conditional__seed_000052__repr_prose", "latent_instance_id": "conditional__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 52, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.285714285714, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 6, 'not_B': 27}, 'not_A': {'B': 15, 'not_B': 59}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.2857142857142857, "not_A": 0.7142857142857143}, "instance_id": "conditional__seed_000052__repr_distractor", "latent_instance_id": "conditional__seed_000052", "outcomes": ["A", "not_A"], "probability_band": "(0.10,0.30]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 52, "state": {"irrelevant": {"batch_code": "ZX-052", "container_temperature_c": 13.2, "operator_shift": "swing", "sensor_revision": "rev-3", "warehouse_lane": "E"}, "representation": "distractor", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 6, "not_B": 27}, "not_A": {"B": 15, "not_B": 59}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.967741935483871, "not_A": 0.032258064516129004}, "instance_id": "conditional__seed_000053__repr_table", "latent_instance_id": "conditional__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 53, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 60, "not_B": 90, "row": "A"}, {"B": 2, "not_B": 36, "row": "not_A"}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.967741935483871, "not_A": 0.032258064516129004}, "instance_id": "conditional__seed_000053__repr_nested", "latent_instance_id": "conditional__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "nested", "seed": 53, "state": {"nested": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "representation": "nested_state"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.967741935483871, "not_A": 0.032258064516129004}, "instance_id": "conditional__seed_000053__repr_direct", "latent_instance_id": "conditional__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 53, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.967741935483871, "not_A": 0.032258064516129004}, "instance_id": "conditional__seed_000053__repr_prose", "latent_instance_id": "conditional__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 53, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.967741935484, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 60, 'not_B': 90}, 'not_A': {'B': 2, 'not_B': 36}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.967741935483871, "not_A": 0.032258064516129004}, "instance_id": "conditional__seed_000053__repr_distractor", "latent_instance_id": "conditional__seed_000053", "outcomes": ["A", "not_A"], "probability_band": "(0.90,0.99]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 53, "state": {"irrelevant": {"batch_code": "ZX-053", "container_temperature_c": 13.9, "operator_shift": "night", "sensor_revision": "rev-4", "warehouse_lane": "F"}, "representation": "distractor", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 60, "not_B": 90}, "not_A": {"B": 2, "not_B": 36}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 70, "not_B": 25}, "not_A": {"B": 14, "not_B": 46}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.8333333333333334, "not_A": 0.16666666666666663}, "instance_id": "conditional__seed_000054__repr_table", "latent_instance_id": "conditional__seed_000054", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 54, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 70, "not_B": 25}, "not_A": {"B": 14, "not_B": 46}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 70, "not_B": 25, "row": "A"}, {"B": 14, "not_B": 46, "row": "not_A"}]}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 61, "not_B": 73}, "not_A": {"B": 28, "not_B": 83}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.6853932584269663, "not_A": 0.3146067415730337}, "instance_id": "conditional__seed_000056__repr_prose", "latent_instance_id": "conditional__seed_000056", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 56, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.685393258427, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 61, 'not_B': 73}, 'not_A': {'B': 28, 'not_B': 83}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 69, "not_B": 34}, "not_A": {"B": 12, "not_B": 42}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.8518518518518519, "not_A": 0.14814814814814814}, "instance_id": "conditional__seed_000058__repr_direct", "latent_instance_id": "conditional__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 58, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 69, "not_B": 34}, "not_A": {"B": 12, "not_B": 42}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 69, "not_B": 34}, "not_A": {"B": 12, "not_B": 42}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.8518518518518519, "not_A": 0.14814814814814814}, "instance_id": "conditional__seed_000058__repr_prose", "latent_instance_id": "conditional__seed_000058", "outcomes": ["A", "not_A"], "probability_band": "(0.70,0.90]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.851851851852, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 69, 'not_B': 34}, 'not_A': {'B': 12, 'not_B': 42}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 17}, "not_A": {"B": 30, "not_B": 88}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5652173913043478, "not_A": 0.4347826086956522}, "instance_id": "conditional__seed_000059__repr_table", "latent_instance_id": "conditional__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "table", "seed": 59, "state": {"representation": "table", "state": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 17}, "not_A": {"B": 30, "not_B": 88}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}, "table": [{"B": 39, "not_B": 17, "row": "A"}, {"B": 30, "not_B": 88, "row": "not_A"}]}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 17}, "not_A": {"B": 30, "not_B": 88}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5652173913043478, "not_A": 0.4347826086956522}, "instance_id": "conditional__seed_000059__repr_direct", "latent_instance_id": "conditional__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 59, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 17}, "not_A": {"B": 30, "not_B": 88}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 17}, "not_A": {"B": 30, "not_B": 88}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.5652173913043478, "not_A": 0.4347826086956522}, "instance_id": "conditional__seed_000059__repr_prose", "latent_instance_id": "conditional__seed_000059", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 59, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.565217391304, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 39, 'not_B': 17}, 'not_A': {'B': 30, 'not_B': 88}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 14}, "not_A": {"B": 23, "not_B": 57}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.6290322580645161, "not_A": 0.3709677419354839}, "instance_id": "conditional__seed_000060__repr_direct", "latent_instance_id": "conditional__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 60, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 14}, "not_A": {"B": 23, "not_B": 57}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 14}, "not_A": {"B": 23, "not_B": 57}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.6290322580645161, "not_A": 0.3709677419354839}, "instance_id": "conditional__seed_000060__repr_prose", "latent_instance_id": "conditional__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 60, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.629032258065, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 39, 'not_B': 14}, 'not_A': {'B': 23, 'not_B': 57}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 14}, "not_A": {"B": 23, "not_B": 57}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "A", "gold_distribution": {"A": 0.6290322580645161, "not_A": 0.3709677419354839}, "instance_id": "conditional__seed_000060__repr_distractor", "latent_instance_id": "conditional__seed_000060", "outcomes": ["A", "not_A"], "probability_band": "(0.55,0.70]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 60, "state": {"irrelevant": {"batch_code": "ZX-060", "container_temperature_c": 18.8, "operator_shift": "morning", "sensor_revision": "rev-1", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 39, "not_B": 14}, "not_A": {"B": 23, "not_B": 57}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
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| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 47, "not_B": 48}, "not_A": {"B": 55, "not_B": 80}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.46078431372549017, "not_A": 0.5392156862745099}, "instance_id": "conditional__seed_000061__repr_direct", "latent_instance_id": "conditional__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "direct", "seed": 61, "state": {"representation": "direct", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 47, "not_B": 48}, "not_A": {"B": 55, "not_B": 80}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 47, "not_B": 48}, "not_A": {"B": 55, "not_B": 80}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.46078431372549017, "not_A": 0.5392156862745099}, "instance_id": "conditional__seed_000061__repr_prose", "latent_instance_id": "conditional__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "prose", "seed": 61, "state": {"description": "The state fully determines the target distribution. The probability of A is 0.460784313725, and the remaining probability belongs to the other outcome. {'contingency': {'A': {'B': 47, 'not_B': 48}, 'not_A': {'B': 55, 'not_B': 80}}, 'query': 'P(A|B)', 'sampling': 'uniform among records satisfying B', 'temporal_filter': 'all records observed before cutoff T', 'boundary_rule': 'include records exactly at cutoff T'}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 4, "family": "conditional", "generator_metadata": {"parameters": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 47, "not_B": 48}, "not_A": {"B": 55, "not_B": 80}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}, "gold_argmax": "not_A", "gold_distribution": {"A": 0.46078431372549017, "not_A": 0.5392156862745099}, "instance_id": "conditional__seed_000061__repr_distractor", "latent_instance_id": "conditional__seed_000061", "outcomes": ["A", "not_A"], "probability_band": "(0.45,0.55]", "prompt": "Using the specified conditioning population B, what is the probability distribution over A versus not_A? Return a normalized probability for each of: A, not_A.", "representation": "distractor", "seed": 61, "state": {"irrelevant": {"batch_code": "ZX-061", "container_temperature_c": 19.5, "operator_shift": "swing", "sensor_revision": "rev-2", "warehouse_lane": "B"}, "representation": "distractor", "sufficient_statistics": {"boundary_rule": "include records exactly at cutoff T", "contingency": {"A": {"B": 47, "not_B": 48}, "not_A": {"B": 55, "not_B": 80}}, "query": "P(A|B)", "sampling": "uniform among records satisfying B", "temporal_filter": "all records observed before cutoff T"}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.04367480789658851, "not_H": 0.9563251921034115}, "instance_id": "bayes__seed_000042__repr_direct", "latent_instance_id": "bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 42, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.04367480789658851, "not_H": 0.9563251921034115}, "instance_id": "bayes__seed_000042__repr_counts", "latent_instance_id": "bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 42, "state": {"event_counts_by_hypothesis": {"H": 33, "not_H": 717}, "observed_event": true, "prior_counts": {"H": 75, "not_H": 925}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.04367480789658851, "not_H": 0.9563251921034115}, "instance_id": "bayes__seed_000042__repr_table", "latent_instance_id": "bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}, "table": [{"P(E|hypothesis)": 0.439104, "hypothesis": "H", "prior": 0.07458}, {"P(E|hypothesis)": 0.774864, "hypothesis": "not_H", "prior": 0.92542}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.04367480789658851, "not_H": 0.9563251921034115}, "instance_id": "bayes__seed_000042__repr_prose", "latent_instance_id": "bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.0436748078966, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.07458, 'not_H': 0.92542}, 'likelihood_event': {'H': 0.439104, 'not_H': 0.774864}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.04367480789658851, "not_H": 0.9563251921034115}, "instance_id": "bayes__seed_000042__repr_distractor", "latent_instance_id": "bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 42, "state": {"irrelevant": {"batch_code": "ZX-042", "container_temperature_c": 18.1, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.439104, "not_H": 0.774864}, "observed_event": true, "priors": {"H": 0.07458, "not_H": 0.92542}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8768016590833436, "not_H": 0.12319834091665638}, "instance_id": "bayes__seed_000045__repr_direct", "latent_instance_id": "bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 45, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8768016590833436, "not_H": 0.12319834091665638}, "instance_id": "bayes__seed_000045__repr_counts", "latent_instance_id": "bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 45, "state": {"event_counts_by_hypothesis": {"H": 375, "not_H": 53}, "observed_event": true, "prior_counts": {"H": 480, "not_H": 520}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8768016590833436, "not_H": 0.12319834091665638}, "instance_id": "bayes__seed_000045__repr_table", "latent_instance_id": "bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 45, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}, "table": [{"P(E|hypothesis)": 0.780272, "hypothesis": "H", "prior": 0.480479}, {"P(E|hypothesis)": 0.101396, "hypothesis": "not_H", "prior": 0.519521}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8768016590833436, "not_H": 0.12319834091665638}, "instance_id": "bayes__seed_000045__repr_prose", "latent_instance_id": "bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 45, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.876801659083, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.480479, 'not_H': 0.519521}, 'likelihood_event': {'H': 0.780272, 'not_H': 0.101396}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8768016590833436, "not_H": 0.12319834091665638}, "instance_id": "bayes__seed_000045__repr_distractor", "latent_instance_id": "bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 45, "state": {"irrelevant": {"batch_code": "ZX-045", "container_temperature_c": 20.2, "operator_shift": "morning", "sensor_revision": "rev-1", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.780272, "not_H": 0.101396}, "observed_event": true, "priors": {"H": 0.480479, "not_H": 0.519521}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8313821568498233, "not_H": 0.1686178431501767}, "instance_id": "bayes__seed_000048__repr_direct", "latent_instance_id": "bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 48, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8313821568498233, "not_H": 0.1686178431501767}, "instance_id": "bayes__seed_000048__repr_counts", "latent_instance_id": "bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 48, "state": {"event_counts_by_hypothesis": {"H": 223, "not_H": 45}, "observed_event": true, "prior_counts": {"H": 934, "not_H": 66}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8313821568498233, "not_H": 0.1686178431501767}, "instance_id": "bayes__seed_000048__repr_table", "latent_instance_id": "bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 48, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}, "table": [{"P(E|hypothesis)": 0.23861, "hypothesis": "H", "prior": 0.933733}, {"P(E|hypothesis)": 0.681894, "hypothesis": "not_H", "prior": 0.06626699999999996}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8313821568498233, "not_H": 0.1686178431501767}, "instance_id": "bayes__seed_000048__repr_prose", "latent_instance_id": "bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 48, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.83138215685, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.933733, 'not_H': 0.06626699999999996}, 'likelihood_event': {'H': 0.23861, 'not_H': 0.681894}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8313821568498233, "not_H": 0.1686178431501767}, "instance_id": "bayes__seed_000048__repr_distractor", "latent_instance_id": "bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 48, "state": {"irrelevant": {"batch_code": "ZX-048", "container_temperature_c": 22.3, "operator_shift": "morning", "sensor_revision": "rev-4", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.23861, "not_H": 0.681894}, "observed_event": true, "priors": {"H": 0.933733, "not_H": 0.06626699999999996}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.9696712044107276, "not_H": 0.030328795589272373}, "instance_id": "bayes__seed_000051__repr_direct", "latent_instance_id": "bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 51, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.9696712044107276, "not_H": 0.030328795589272373}, "instance_id": "bayes__seed_000051__repr_counts", "latent_instance_id": "bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 51, "state": {"event_counts_by_hypothesis": {"H": 264, "not_H": 8}, "observed_event": true, "prior_counts": {"H": 411, "not_H": 589}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.9696712044107276, "not_H": 0.030328795589272373}, "instance_id": "bayes__seed_000051__repr_table", "latent_instance_id": "bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 51, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}, "table": [{"P(E|hypothesis)": 0.64129, "hypothesis": "H", "prior": 0.410511}, {"P(E|hypothesis)": 0.013968, "hypothesis": "not_H", "prior": 0.5894889999999999}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.9696712044107276, "not_H": 0.030328795589272373}, "instance_id": "bayes__seed_000051__repr_prose", "latent_instance_id": "bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 51, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.969671204411, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.410511, 'not_H': 0.5894889999999999}, 'likelihood_event': {'H': 0.64129, 'not_H': 0.013968}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.9696712044107276, "not_H": 0.030328795589272373}, "instance_id": "bayes__seed_000051__repr_distractor", "latent_instance_id": "bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 51, "state": {"irrelevant": {"batch_code": "ZX-051", "container_temperature_c": 12.5, "operator_shift": "morning", "sensor_revision": "rev-2", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.64129, "not_H": 0.013968}, "observed_event": true, "priors": {"H": 0.410511, "not_H": 0.5894889999999999}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.4137933255962194, "not_H": 0.5862066744037806}, "instance_id": "bayes__seed_000054__repr_direct", "latent_instance_id": "bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 54, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.4137933255962194, "not_H": 0.5862066744037806}, "instance_id": "bayes__seed_000054__repr_counts", "latent_instance_id": "bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 54, "state": {"event_counts_by_hypothesis": {"H": 74, "not_H": 104}, "observed_event": true, "prior_counts": {"H": 808, "not_H": 192}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.4137933255962194, "not_H": 0.5862066744037806}, "instance_id": "bayes__seed_000054__repr_table", "latent_instance_id": "bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 54, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}, "table": [{"P(E|hypothesis)": 0.0912, "hypothesis": "H", "prior": 0.808057}, {"P(E|hypothesis)": 0.543916, "hypothesis": "not_H", "prior": 0.19194299999999997}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.4137933255962194, "not_H": 0.5862066744037806}, "instance_id": "bayes__seed_000054__repr_prose", "latent_instance_id": "bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 54, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.413793325596, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.808057, 'not_H': 0.19194299999999997}, 'likelihood_event': {'H': 0.0912, 'not_H': 0.543916}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.4137933255962194, "not_H": 0.5862066744037806}, "instance_id": "bayes__seed_000054__repr_distractor", "latent_instance_id": "bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 54, "state": {"irrelevant": {"batch_code": "ZX-054", "container_temperature_c": 14.6, "operator_shift": "morning", "sensor_revision": "rev-5", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.0912, "not_H": 0.543916}, "observed_event": true, "priors": {"H": 0.808057, "not_H": 0.19194299999999997}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.12523423738446504, "not_H": 0.874765762615535}, "instance_id": "bayes__seed_000057__repr_direct", "latent_instance_id": "bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 57, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.12523423738446504, "not_H": 0.874765762615535}, "instance_id": "bayes__seed_000057__repr_counts", "latent_instance_id": "bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 57, "state": {"event_counts_by_hypothesis": {"H": 104, "not_H": 725}, "observed_event": true, "prior_counts": {"H": 227, "not_H": 773}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.12523423738446504, "not_H": 0.874765762615535}, "instance_id": "bayes__seed_000057__repr_table", "latent_instance_id": "bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 57, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}, "table": [{"P(E|hypothesis)": 0.457145, "hypothesis": "H", "prior": 0.226962}, {"P(E|hypothesis)": 0.937508, "hypothesis": "not_H", "prior": 0.773038}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.12523423738446504, "not_H": 0.874765762615535}, "instance_id": "bayes__seed_000057__repr_prose", "latent_instance_id": "bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 57, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.125234237384, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.226962, 'not_H': 0.773038}, 'likelihood_event': {'H': 0.457145, 'not_H': 0.937508}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.12523423738446504, "not_H": 0.874765762615535}, "instance_id": "bayes__seed_000057__repr_distractor", "latent_instance_id": "bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 57, "state": {"irrelevant": {"batch_code": "ZX-057", "container_temperature_c": 16.7, "operator_shift": "morning", "sensor_revision": "rev-3", "warehouse_lane": "D"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.457145, "not_H": 0.937508}, "observed_event": true, "priors": {"H": 0.226962, "not_H": 0.773038}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8130236350735895, "not_H": 0.18697636492641045}, "instance_id": "bayes__seed_000060__repr_direct", "latent_instance_id": "bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 60, "state": {"representation": "direct", "sufficient_statistics": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8130236350735895, "not_H": 0.18697636492641045}, "instance_id": "bayes__seed_000060__repr_counts", "latent_instance_id": "bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "counts", "seed": 60, "state": {"event_counts_by_hypothesis": {"H": 546, "not_H": 125}, "observed_event": true, "prior_counts": {"H": 596, "not_H": 404}, "representation": "bayes_counts"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8130236350735895, "not_H": 0.18697636492641045}, "instance_id": "bayes__seed_000060__repr_table", "latent_instance_id": "bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 60, "state": {"representation": "table", "state": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}, "table": [{"P(E|hypothesis)": 0.915819, "hypothesis": "H", "prior": 0.59555}, {"P(E|hypothesis)": 0.310132, "hypothesis": "not_H", "prior": 0.40445}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8130236350735895, "not_H": 0.18697636492641045}, "instance_id": "bayes__seed_000060__repr_prose", "latent_instance_id": "bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 60, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.813023635074, and the remaining probability belongs to the other outcome. {'priors': {'H': 0.59555, 'not_H': 0.40445}, 'likelihood_event': {'H': 0.915819, 'not_H': 0.310132}, 'observed_event': True}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 5, "family": "bayes", "generator_metadata": {"parameters": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}, "gold_argmax": "H", "gold_distribution": {"H": 0.8130236350735895, "not_H": 0.18697636492641045}, "instance_id": "bayes__seed_000060__repr_distractor", "latent_instance_id": "bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "Given the prior probabilities and likelihoods, what is the posterior distribution after observing the event? Return a normalized probability for each of: H, not_H.", "representation": "distractor", "seed": 60, "state": {"irrelevant": {"batch_code": "ZX-060", "container_temperature_c": 18.8, "operator_shift": "morning", "sensor_revision": "rev-1", "warehouse_lane": "A"}, "representation": "distractor", "sufficient_statistics": {"likelihood_event": {"H": 0.915819, "not_H": 0.310132}, "observed_event": true, "priors": {"H": 0.59555, "not_H": 0.40445}}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.445825, "E_given_not_H": 0.083719}, {"E_given_H": 0.524281, "E_given_not_H": 0.252322}, {"E_given_H": 0.578817, "E_given_not_H": 0.410508}, {"E_given_H": 0.730384, "E_given_not_H": 0.499973}, {"E_given_H": 0.989777, "E_given_not_H": 0.565735}], "observed_prefix_length": 5, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239], "prior_H": 0.07458}, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239]}, "gold_argmax": "H", "gold_distribution": {"H": 0.7626689672812239, "not_H": 0.2373310327187761}, "instance_id": "sequential_bayes__seed_000042__repr_direct", "latent_instance_id": "sequential_bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 42, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.445825, "E_given_not_H": 0.083719}, {"E_given_H": 0.524281, "E_given_not_H": 0.252322}, {"E_given_H": 0.578817, "E_given_not_H": 0.410508}, {"E_given_H": 0.730384, "E_given_not_H": 0.499973}, {"E_given_H": 0.989777, "E_given_not_H": 0.565735}], "observed_prefix_length": 5, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239], "prior_H": 0.07458}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.445825, "E_given_not_H": 0.083719}, {"E_given_H": 0.524281, "E_given_not_H": 0.252322}, {"E_given_H": 0.578817, "E_given_not_H": 0.410508}, {"E_given_H": 0.730384, "E_given_not_H": 0.499973}, {"E_given_H": 0.989777, "E_given_not_H": 0.565735}], "observed_prefix_length": 5, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239], "prior_H": 0.07458}, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239]}, "gold_argmax": "H", "gold_distribution": {"H": 0.7626689672812239, "not_H": 0.2373310327187761}, "instance_id": "sequential_bayes__seed_000042__repr_table", "latent_instance_id": "sequential_bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 42, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.445825, "E_given_not_H": 0.083719}, {"E_given_H": 0.524281, "E_given_not_H": 0.252322}, {"E_given_H": 0.578817, "E_given_not_H": 0.410508}, {"E_given_H": 0.730384, "E_given_not_H": 0.499973}, {"E_given_H": 0.989777, "E_given_not_H": 0.565735}], "observed_prefix_length": 5, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239], "prior_H": 0.07458}, "table": [{"E_given_H": 0.445825, "E_given_not_H": 0.083719, "step": 1}, {"E_given_H": 0.524281, "E_given_not_H": 0.252322, "step": 2}, {"E_given_H": 0.578817, "E_given_not_H": 0.410508, "step": 3}, {"E_given_H": 0.730384, "E_given_not_H": 0.499973, "step": 4}, {"E_given_H": 0.989777, "E_given_not_H": 0.565735, "step": 5}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.445825, "E_given_not_H": 0.083719}, {"E_given_H": 0.524281, "E_given_not_H": 0.252322}, {"E_given_H": 0.578817, "E_given_not_H": 0.410508}, {"E_given_H": 0.730384, "E_given_not_H": 0.499973}, {"E_given_H": 0.989777, "E_given_not_H": 0.565735}], "observed_prefix_length": 5, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239], "prior_H": 0.07458}, "posterior_trajectory": [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239]}, "gold_argmax": "H", "gold_distribution": {"H": 0.7626689672812239, "not_H": 0.2373310327187761}, "instance_id": "sequential_bayes__seed_000042__repr_prose", "latent_instance_id": "sequential_bayes__seed_000042", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 42, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.762668967281, and the remaining probability belongs to the other outcome. {'prior_H': 0.07458, 'evidence_sequence': [{'E_given_H': 0.445825, 'E_given_not_H': 0.083719}, {'E_given_H': 0.524281, 'E_given_not_H': 0.252322}, {'E_given_H': 0.578817, 'E_given_not_H': 0.410508}, {'E_given_H': 0.730384, 'E_given_not_H': 0.499973}, {'E_given_H': 0.989777, 'E_given_not_H': 0.565735}], 'observed_prefix_length': 5, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.07458, 0.3002905296462592, 0.4713830541128846, 0.5570006071483515, 0.6474876942325162, 0.7626689672812239]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.476461, "E_given_not_H": 0.180556}, {"E_given_H": 0.672021, "E_given_not_H": 0.311353}, {"E_given_H": 0.713418, "E_given_not_H": 0.48903}, {"E_given_H": 0.936492, "E_given_not_H": 0.572474}, {"E_given_H": 0.01825, "E_given_not_H": 0.740022}], "observed_prefix_length": 5, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055], "prior_H": 0.200973}, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.077757405790055, "not_H": 0.922242594209945}, "instance_id": "sequential_bayes__seed_000043__repr_direct", "latent_instance_id": "sequential_bayes__seed_000043", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 43, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.476461, "E_given_not_H": 0.180556}, {"E_given_H": 0.672021, "E_given_not_H": 0.311353}, {"E_given_H": 0.713418, "E_given_not_H": 0.48903}, {"E_given_H": 0.936492, "E_given_not_H": 0.572474}, {"E_given_H": 0.01825, "E_given_not_H": 0.740022}], "observed_prefix_length": 5, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055], "prior_H": 0.200973}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.476461, "E_given_not_H": 0.180556}, {"E_given_H": 0.672021, "E_given_not_H": 0.311353}, {"E_given_H": 0.713418, "E_given_not_H": 0.48903}, {"E_given_H": 0.936492, "E_given_not_H": 0.572474}, {"E_given_H": 0.01825, "E_given_not_H": 0.740022}], "observed_prefix_length": 5, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055], "prior_H": 0.200973}, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.077757405790055, "not_H": 0.922242594209945}, "instance_id": "sequential_bayes__seed_000043__repr_table", "latent_instance_id": "sequential_bayes__seed_000043", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 43, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.476461, "E_given_not_H": 0.180556}, {"E_given_H": 0.672021, "E_given_not_H": 0.311353}, {"E_given_H": 0.713418, "E_given_not_H": 0.48903}, {"E_given_H": 0.936492, "E_given_not_H": 0.572474}, {"E_given_H": 0.01825, "E_given_not_H": 0.740022}], "observed_prefix_length": 5, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055], "prior_H": 0.200973}, "table": [{"E_given_H": 0.476461, "E_given_not_H": 0.180556, "step": 1}, {"E_given_H": 0.672021, "E_given_not_H": 0.311353, "step": 2}, {"E_given_H": 0.713418, "E_given_not_H": 0.48903, "step": 3}, {"E_given_H": 0.936492, "E_given_not_H": 0.572474, "step": 4}, {"E_given_H": 0.01825, "E_given_not_H": 0.740022, "step": 5}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.476461, "E_given_not_H": 0.180556}, {"E_given_H": 0.672021, "E_given_not_H": 0.311353}, {"E_given_H": 0.713418, "E_given_not_H": 0.48903}, {"E_given_H": 0.936492, "E_given_not_H": 0.572474}, {"E_given_H": 0.01825, "E_given_not_H": 0.740022}], "observed_prefix_length": 5, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055], "prior_H": 0.200973}, "posterior_trajectory": [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.077757405790055, "not_H": 0.922242594209945}, "instance_id": "sequential_bayes__seed_000043__repr_prose", "latent_instance_id": "sequential_bayes__seed_000043", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 43, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.0777574057901, and the remaining probability belongs to the other outcome. {'prior_H': 0.200973, 'evidence_sequence': [{'E_given_H': 0.476461, 'E_given_not_H': 0.180556}, {'E_given_H': 0.672021, 'E_given_not_H': 0.311353}, {'E_given_H': 0.713418, 'E_given_not_H': 0.48903}, {'E_given_H': 0.936492, 'E_given_not_H': 0.572474}, {'E_given_H': 0.01825, 'E_given_not_H': 0.740022}], 'observed_prefix_length': 5, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.200973, 0.3989410696285355, 0.5889152773068229, 0.6763672181802326, 0.7736960916675097, 0.077757405790055]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.590045, "E_given_not_H": 0.386229}, {"E_given_H": 0.856858, "E_given_not_H": 0.497218}, {"E_given_H": 0.961472, "E_given_not_H": 0.652775}, {"E_given_H": 0.038642, "E_given_not_H": 0.745681}], "observed_prefix_length": 4, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272], "prior_H": 0.387226}, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.11267528685894272, "not_H": 0.8873247131410573}, "instance_id": "sequential_bayes__seed_000044__repr_direct", "latent_instance_id": "sequential_bayes__seed_000044", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 44, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.590045, "E_given_not_H": 0.386229}, {"E_given_H": 0.856858, "E_given_not_H": 0.497218}, {"E_given_H": 0.961472, "E_given_not_H": 0.652775}, {"E_given_H": 0.038642, "E_given_not_H": 0.745681}], "observed_prefix_length": 4, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272], "prior_H": 0.387226}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.590045, "E_given_not_H": 0.386229}, {"E_given_H": 0.856858, "E_given_not_H": 0.497218}, {"E_given_H": 0.961472, "E_given_not_H": 0.652775}, {"E_given_H": 0.038642, "E_given_not_H": 0.745681}], "observed_prefix_length": 4, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272], "prior_H": 0.387226}, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.11267528685894272, "not_H": 0.8873247131410573}, "instance_id": "sequential_bayes__seed_000044__repr_table", "latent_instance_id": "sequential_bayes__seed_000044", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 44, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.590045, "E_given_not_H": 0.386229}, {"E_given_H": 0.856858, "E_given_not_H": 0.497218}, {"E_given_H": 0.961472, "E_given_not_H": 0.652775}, {"E_given_H": 0.038642, "E_given_not_H": 0.745681}], "observed_prefix_length": 4, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272], "prior_H": 0.387226}, "table": [{"E_given_H": 0.590045, "E_given_not_H": 0.386229, "step": 1}, {"E_given_H": 0.856858, "E_given_not_H": 0.497218, "step": 2}, {"E_given_H": 0.961472, "E_given_not_H": 0.652775, "step": 3}, {"E_given_H": 0.038642, "E_given_not_H": 0.745681, "step": 4}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.590045, "E_given_not_H": 0.386229}, {"E_given_H": 0.856858, "E_given_not_H": 0.497218}, {"E_given_H": 0.961472, "E_given_not_H": 0.652775}, {"E_given_H": 0.038642, "E_given_not_H": 0.745681}], "observed_prefix_length": 4, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272], "prior_H": 0.387226}, "posterior_trajectory": [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.11267528685894272, "not_H": 0.8873247131410573}, "instance_id": "sequential_bayes__seed_000044__repr_prose", "latent_instance_id": "sequential_bayes__seed_000044", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 44, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.112675286859, and the remaining probability belongs to the other outcome. {'prior_H': 0.387226, 'evidence_sequence': [{'E_given_H': 0.590045, 'E_given_not_H': 0.386229}, {'E_given_H': 0.856858, 'E_given_not_H': 0.497218}, {'E_given_H': 0.961472, 'E_given_not_H': 0.652775}, {'E_given_H': 0.038642, 'E_given_not_H': 0.745681}], 'observed_prefix_length': 4, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.387226, 0.4911960750040619, 0.6245777218432159, 0.7101797586719204, 0.11267528685894272]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.822143, "E_given_not_H": 0.542897}, {"E_given_H": 0.936169, "E_given_not_H": 0.667027}, {"E_given_H": 0.053243, "E_given_not_H": 0.834742}, {"E_given_H": 0.152645, "E_given_not_H": 0.939538}, {"E_given_H": 0.44549, "E_given_not_H": 0.030503}, {"E_given_H": 0.533199, "E_given_not_H": 0.293377}], "observed_prefix_length": 6, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842], "prior_H": 0.480479}, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.3509406267523842, "not_H": 0.6490593732476158}, "instance_id": "sequential_bayes__seed_000045__repr_direct", "latent_instance_id": "sequential_bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 45, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.822143, "E_given_not_H": 0.542897}, {"E_given_H": 0.936169, "E_given_not_H": 0.667027}, {"E_given_H": 0.053243, "E_given_not_H": 0.834742}, {"E_given_H": 0.152645, "E_given_not_H": 0.939538}, {"E_given_H": 0.44549, "E_given_not_H": 0.030503}, {"E_given_H": 0.533199, "E_given_not_H": 0.293377}], "observed_prefix_length": 6, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842], "prior_H": 0.480479}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.822143, "E_given_not_H": 0.542897}, {"E_given_H": 0.936169, "E_given_not_H": 0.667027}, {"E_given_H": 0.053243, "E_given_not_H": 0.834742}, {"E_given_H": 0.152645, "E_given_not_H": 0.939538}, {"E_given_H": 0.44549, "E_given_not_H": 0.030503}, {"E_given_H": 0.533199, "E_given_not_H": 0.293377}], "observed_prefix_length": 6, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842], "prior_H": 0.480479}, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.3509406267523842, "not_H": 0.6490593732476158}, "instance_id": "sequential_bayes__seed_000045__repr_table", "latent_instance_id": "sequential_bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 45, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.822143, "E_given_not_H": 0.542897}, {"E_given_H": 0.936169, "E_given_not_H": 0.667027}, {"E_given_H": 0.053243, "E_given_not_H": 0.834742}, {"E_given_H": 0.152645, "E_given_not_H": 0.939538}, {"E_given_H": 0.44549, "E_given_not_H": 0.030503}, {"E_given_H": 0.533199, "E_given_not_H": 0.293377}], "observed_prefix_length": 6, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842], "prior_H": 0.480479}, "table": [{"E_given_H": 0.822143, "E_given_not_H": 0.542897, "step": 1}, {"E_given_H": 0.936169, "E_given_not_H": 0.667027, "step": 2}, {"E_given_H": 0.053243, "E_given_not_H": 0.834742, "step": 3}, {"E_given_H": 0.152645, "E_given_not_H": 0.939538, "step": 4}, {"E_given_H": 0.44549, "E_given_not_H": 0.030503, "step": 5}, {"E_given_H": 0.533199, "E_given_not_H": 0.293377, "step": 6}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.822143, "E_given_not_H": 0.542897}, {"E_given_H": 0.936169, "E_given_not_H": 0.667027}, {"E_given_H": 0.053243, "E_given_not_H": 0.834742}, {"E_given_H": 0.152645, "E_given_not_H": 0.939538}, {"E_given_H": 0.44549, "E_given_not_H": 0.030503}, {"E_given_H": 0.533199, "E_given_not_H": 0.293377}], "observed_prefix_length": 6, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842], "prior_H": 0.480479}, "posterior_trajectory": [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.3509406267523842, "not_H": 0.6490593732476158}, "instance_id": "sequential_bayes__seed_000045__repr_prose", "latent_instance_id": "sequential_bayes__seed_000045", "outcomes": ["H", "not_H"], "probability_band": "(0.30,0.45]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 45, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.350940626752, and the remaining probability belongs to the other outcome. {'prior_H': 0.480479, 'evidence_sequence': [{'E_given_H': 0.822143, 'E_given_not_H': 0.542897}, {'E_given_H': 0.936169, 'E_given_not_H': 0.667027}, {'E_given_H': 0.053243, 'E_given_not_H': 0.834742}, {'E_given_H': 0.152645, 'E_given_not_H': 0.939538}, {'E_given_H': 0.44549, 'E_given_not_H': 0.030503}, {'E_given_H': 0.533199, 'E_given_not_H': 0.293377}], 'observed_prefix_length': 6, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.480479, 0.5834302567775527, 0.6628088173304468, 0.11140990136733081, 0.01996332519820646, 0.22928667888620186, 0.3509406267523842]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.937407, "E_given_not_H": 0.652731}, {"E_given_H": 0.011657, "E_given_not_H": 0.818627}, {"E_given_H": 0.135231, "E_given_not_H": 0.970667}, {"E_given_H": 0.378969, "E_given_not_H": 0.026991}, {"E_given_H": 0.512249, "E_given_not_H": 0.239057}, {"E_given_H": 0.612355, "E_given_not_H": 0.332607}], "observed_prefix_length": 6, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519], "prior_H": 0.64222}, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.2207423923319519, "not_H": 0.7792576076680481}, "instance_id": "sequential_bayes__seed_000046__repr_direct", "latent_instance_id": "sequential_bayes__seed_000046", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 46, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.937407, "E_given_not_H": 0.652731}, {"E_given_H": 0.011657, "E_given_not_H": 0.818627}, {"E_given_H": 0.135231, "E_given_not_H": 0.970667}, {"E_given_H": 0.378969, "E_given_not_H": 0.026991}, {"E_given_H": 0.512249, "E_given_not_H": 0.239057}, {"E_given_H": 0.612355, "E_given_not_H": 0.332607}], "observed_prefix_length": 6, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519], "prior_H": 0.64222}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.937407, "E_given_not_H": 0.652731}, {"E_given_H": 0.011657, "E_given_not_H": 0.818627}, {"E_given_H": 0.135231, "E_given_not_H": 0.970667}, {"E_given_H": 0.378969, "E_given_not_H": 0.026991}, {"E_given_H": 0.512249, "E_given_not_H": 0.239057}, {"E_given_H": 0.612355, "E_given_not_H": 0.332607}], "observed_prefix_length": 6, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519], "prior_H": 0.64222}, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.2207423923319519, "not_H": 0.7792576076680481}, "instance_id": "sequential_bayes__seed_000046__repr_table", "latent_instance_id": "sequential_bayes__seed_000046", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 46, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.937407, "E_given_not_H": 0.652731}, {"E_given_H": 0.011657, "E_given_not_H": 0.818627}, {"E_given_H": 0.135231, "E_given_not_H": 0.970667}, {"E_given_H": 0.378969, "E_given_not_H": 0.026991}, {"E_given_H": 0.512249, "E_given_not_H": 0.239057}, {"E_given_H": 0.612355, "E_given_not_H": 0.332607}], "observed_prefix_length": 6, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519], "prior_H": 0.64222}, "table": [{"E_given_H": 0.937407, "E_given_not_H": 0.652731, "step": 1}, {"E_given_H": 0.011657, "E_given_not_H": 0.818627, "step": 2}, {"E_given_H": 0.135231, "E_given_not_H": 0.970667, "step": 3}, {"E_given_H": 0.378969, "E_given_not_H": 0.026991, "step": 4}, {"E_given_H": 0.512249, "E_given_not_H": 0.239057, "step": 5}, {"E_given_H": 0.612355, "E_given_not_H": 0.332607, "step": 6}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.937407, "E_given_not_H": 0.652731}, {"E_given_H": 0.011657, "E_given_not_H": 0.818627}, {"E_given_H": 0.135231, "E_given_not_H": 0.970667}, {"E_given_H": 0.378969, "E_given_not_H": 0.026991}, {"E_given_H": 0.512249, "E_given_not_H": 0.239057}, {"E_given_H": 0.612355, "E_given_not_H": 0.332607}], "observed_prefix_length": 6, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519], "prior_H": 0.64222}, "posterior_trajectory": [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.2207423923319519, "not_H": 0.7792576076680481}, "instance_id": "sequential_bayes__seed_000046__repr_prose", "latent_instance_id": "sequential_bayes__seed_000046", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 46, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.220742392332, and the remaining probability belongs to the other outcome. {'prior_H': 0.64222, 'evidence_sequence': [{'E_given_H': 0.937407, 'E_given_not_H': 0.652731}, {'E_given_H': 0.011657, 'E_given_not_H': 0.818627}, {'E_given_H': 0.135231, 'E_given_not_H': 0.970667}, {'E_given_H': 0.378969, 'E_given_not_H': 0.026991}, {'E_given_H': 0.512249, 'E_given_not_H': 0.239057}, {'E_given_H': 0.612355, 'E_given_not_H': 0.332607}], 'observed_prefix_length': 6, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.64222, 0.7205044267684261, 0.035408370477487204, 0.00508807008357708, 0.0669942424371729, 0.13334561791105332, 0.2207423923319519]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.052817, "E_given_not_H": 0.710634}, {"E_given_H": 0.26792, "E_given_not_H": 0.959866}, {"E_given_H": 0.439598, "E_given_not_H": 0.013463}], "observed_prefix_length": 3, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144], "prior_H": 0.84647}, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144]}, "gold_argmax": "H", "gold_distribution": {"H": 0.7887928911656144, "not_H": 0.21120710883438565}, "instance_id": "sequential_bayes__seed_000047__repr_direct", "latent_instance_id": "sequential_bayes__seed_000047", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 47, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.052817, "E_given_not_H": 0.710634}, {"E_given_H": 0.26792, "E_given_not_H": 0.959866}, {"E_given_H": 0.439598, "E_given_not_H": 0.013463}], "observed_prefix_length": 3, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144], "prior_H": 0.84647}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.052817, "E_given_not_H": 0.710634}, {"E_given_H": 0.26792, "E_given_not_H": 0.959866}, {"E_given_H": 0.439598, "E_given_not_H": 0.013463}], "observed_prefix_length": 3, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144], "prior_H": 0.84647}, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144]}, "gold_argmax": "H", "gold_distribution": {"H": 0.7887928911656144, "not_H": 0.21120710883438565}, "instance_id": "sequential_bayes__seed_000047__repr_table", "latent_instance_id": "sequential_bayes__seed_000047", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 47, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.052817, "E_given_not_H": 0.710634}, {"E_given_H": 0.26792, "E_given_not_H": 0.959866}, {"E_given_H": 0.439598, "E_given_not_H": 0.013463}], "observed_prefix_length": 3, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144], "prior_H": 0.84647}, "table": [{"E_given_H": 0.052817, "E_given_not_H": 0.710634, "step": 1}, {"E_given_H": 0.26792, "E_given_not_H": 0.959866, "step": 2}, {"E_given_H": 0.439598, "E_given_not_H": 0.013463, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.052817, "E_given_not_H": 0.710634}, {"E_given_H": 0.26792, "E_given_not_H": 0.959866}, {"E_given_H": 0.439598, "E_given_not_H": 0.013463}], "observed_prefix_length": 3, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144], "prior_H": 0.84647}, "posterior_trajectory": [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144]}, "gold_argmax": "H", "gold_distribution": {"H": 0.7887928911656144, "not_H": 0.21120710883438565}, "instance_id": "sequential_bayes__seed_000047__repr_prose", "latent_instance_id": "sequential_bayes__seed_000047", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 47, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.788792891166, and the remaining probability belongs to the other outcome. {'prior_H': 0.84647, 'evidence_sequence': [{'E_given_H': 0.052817, 'E_given_not_H': 0.710634}, {'E_given_H': 0.26792, 'E_given_not_H': 0.959866}, {'E_given_H': 0.439598, 'E_given_not_H': 0.013463}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.84647, 0.29066723964730085, 0.10263801870994302, 0.7887928911656144]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.275859, "E_given_not_H": 0.956606}, {"E_given_H": 0.380795, "E_given_not_H": 0.089245}, {"E_given_H": 0.504762, "E_given_not_H": 0.222895}], "observed_prefix_length": 3, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509], "prior_H": 0.933733}, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509]}, "gold_argmax": "H", "gold_distribution": {"H": 0.9751627237748509, "not_H": 0.024837276225149085}, "instance_id": "sequential_bayes__seed_000048__repr_direct", "latent_instance_id": "sequential_bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 48, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.275859, "E_given_not_H": 0.956606}, {"E_given_H": 0.380795, "E_given_not_H": 0.089245}, {"E_given_H": 0.504762, "E_given_not_H": 0.222895}], "observed_prefix_length": 3, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509], "prior_H": 0.933733}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.275859, "E_given_not_H": 0.956606}, {"E_given_H": 0.380795, "E_given_not_H": 0.089245}, {"E_given_H": 0.504762, "E_given_not_H": 0.222895}], "observed_prefix_length": 3, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509], "prior_H": 0.933733}, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509]}, "gold_argmax": "H", "gold_distribution": {"H": 0.9751627237748509, "not_H": 0.024837276225149085}, "instance_id": "sequential_bayes__seed_000048__repr_table", "latent_instance_id": "sequential_bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 48, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.275859, "E_given_not_H": 0.956606}, {"E_given_H": 0.380795, "E_given_not_H": 0.089245}, {"E_given_H": 0.504762, "E_given_not_H": 0.222895}], "observed_prefix_length": 3, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509], "prior_H": 0.933733}, "table": [{"E_given_H": 0.275859, "E_given_not_H": 0.956606, "step": 1}, {"E_given_H": 0.380795, "E_given_not_H": 0.089245, "step": 2}, {"E_given_H": 0.504762, "E_given_not_H": 0.222895, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.275859, "E_given_not_H": 0.956606}, {"E_given_H": 0.380795, "E_given_not_H": 0.089245}, {"E_given_H": 0.504762, "E_given_not_H": 0.222895}], "observed_prefix_length": 3, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509], "prior_H": 0.933733}, "posterior_trajectory": [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509]}, "gold_argmax": "H", "gold_distribution": {"H": 0.9751627237748509, "not_H": 0.024837276225149085}, "instance_id": "sequential_bayes__seed_000048__repr_prose", "latent_instance_id": "sequential_bayes__seed_000048", "outcomes": ["H", "not_H"], "probability_band": "(0.90,0.99]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 48, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.975162723775, and the remaining probability belongs to the other outcome. {'prior_H': 0.933733, 'evidence_sequence': [{'E_given_H': 0.275859, 'E_given_not_H': 0.956606}, {'E_given_H': 0.380795, 'E_given_not_H': 0.089245}, {'E_given_H': 0.504762, 'E_given_not_H': 0.222895}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.933733, 0.8025005524944498, 0.9454669778379197, 0.9751627237748509]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.346234, "E_given_not_H": 0.024629}, {"E_given_H": 0.530049, "E_given_not_H": 0.251686}, {"E_given_H": 0.619193, "E_given_not_H": 0.323881}, {"E_given_H": 0.845869, "E_given_not_H": 0.546818}, {"E_given_H": 0.912848, "E_given_not_H": 0.658795}], "observed_prefix_length": 5, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994], "prior_H": 0.031994}, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994]}, "gold_argmax": "H", "gold_distribution": {"H": 0.8003900273948994, "not_H": 0.1996099726051006}, "instance_id": "sequential_bayes__seed_000049__repr_direct", "latent_instance_id": "sequential_bayes__seed_000049", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 49, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.346234, "E_given_not_H": 0.024629}, {"E_given_H": 0.530049, "E_given_not_H": 0.251686}, {"E_given_H": 0.619193, "E_given_not_H": 0.323881}, {"E_given_H": 0.845869, "E_given_not_H": 0.546818}, {"E_given_H": 0.912848, "E_given_not_H": 0.658795}], "observed_prefix_length": 5, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994], "prior_H": 0.031994}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.346234, "E_given_not_H": 0.024629}, {"E_given_H": 0.530049, "E_given_not_H": 0.251686}, {"E_given_H": 0.619193, "E_given_not_H": 0.323881}, {"E_given_H": 0.845869, "E_given_not_H": 0.546818}, {"E_given_H": 0.912848, "E_given_not_H": 0.658795}], "observed_prefix_length": 5, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994], "prior_H": 0.031994}, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994]}, "gold_argmax": "H", "gold_distribution": {"H": 0.8003900273948994, "not_H": 0.1996099726051006}, "instance_id": "sequential_bayes__seed_000049__repr_table", "latent_instance_id": "sequential_bayes__seed_000049", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 49, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.346234, "E_given_not_H": 0.024629}, {"E_given_H": 0.530049, "E_given_not_H": 0.251686}, {"E_given_H": 0.619193, "E_given_not_H": 0.323881}, {"E_given_H": 0.845869, "E_given_not_H": 0.546818}, {"E_given_H": 0.912848, "E_given_not_H": 0.658795}], "observed_prefix_length": 5, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994], "prior_H": 0.031994}, "table": [{"E_given_H": 0.346234, "E_given_not_H": 0.024629, "step": 1}, {"E_given_H": 0.530049, "E_given_not_H": 0.251686, "step": 2}, {"E_given_H": 0.619193, "E_given_not_H": 0.323881, "step": 3}, {"E_given_H": 0.845869, "E_given_not_H": 0.546818, "step": 4}, {"E_given_H": 0.912848, "E_given_not_H": 0.658795, "step": 5}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.346234, "E_given_not_H": 0.024629}, {"E_given_H": 0.530049, "E_given_not_H": 0.251686}, {"E_given_H": 0.619193, "E_given_not_H": 0.323881}, {"E_given_H": 0.845869, "E_given_not_H": 0.546818}, {"E_given_H": 0.912848, "E_given_not_H": 0.658795}], "observed_prefix_length": 5, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994], "prior_H": 0.031994}, "posterior_trajectory": [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994]}, "gold_argmax": "H", "gold_distribution": {"H": 0.8003900273948994, "not_H": 0.1996099726051006}, "instance_id": "sequential_bayes__seed_000049__repr_prose", "latent_instance_id": "sequential_bayes__seed_000049", "outcomes": ["H", "not_H"], "probability_band": "(0.70,0.90]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 49, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.800390027395, and the remaining probability belongs to the other outcome. {'prior_H': 0.031994, 'evidence_sequence': [{'E_given_H': 0.346234, 'E_given_not_H': 0.024629}, {'E_given_H': 0.530049, 'E_given_not_H': 0.251686}, {'E_given_H': 0.619193, 'E_given_not_H': 0.323881}, {'E_given_H': 0.845869, 'E_given_not_H': 0.546818}, {'E_given_H': 0.912848, 'E_given_not_H': 0.658795}], 'observed_prefix_length': 5, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.031994, 0.3172367852341124, 0.49457209137119523, 0.6516564647592755, 0.7431826754290087, 0.8003900273948994]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.472127, "E_given_not_H": 0.191458}, {"E_given_H": 0.631191, "E_given_not_H": 0.405093}, {"E_given_H": 0.870541, "E_given_not_H": 0.546792}, {"E_given_H": 0.93722, "E_given_not_H": 0.612099}, {"E_given_H": 0.075121, "E_given_not_H": 0.763611}, {"E_given_H": 0.115737, "E_given_not_H": 0.962357}], "observed_prefix_length": 6, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506], "prior_H": 0.204042}, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.02762280113741506, "not_H": 0.9723771988625849}, "instance_id": "sequential_bayes__seed_000050__repr_direct", "latent_instance_id": "sequential_bayes__seed_000050", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 50, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.472127, "E_given_not_H": 0.191458}, {"E_given_H": 0.631191, "E_given_not_H": 0.405093}, {"E_given_H": 0.870541, "E_given_not_H": 0.546792}, {"E_given_H": 0.93722, "E_given_not_H": 0.612099}, {"E_given_H": 0.075121, "E_given_not_H": 0.763611}, {"E_given_H": 0.115737, "E_given_not_H": 0.962357}], "observed_prefix_length": 6, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506], "prior_H": 0.204042}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.472127, "E_given_not_H": 0.191458}, {"E_given_H": 0.631191, "E_given_not_H": 0.405093}, {"E_given_H": 0.870541, "E_given_not_H": 0.546792}, {"E_given_H": 0.93722, "E_given_not_H": 0.612099}, {"E_given_H": 0.075121, "E_given_not_H": 0.763611}, {"E_given_H": 0.115737, "E_given_not_H": 0.962357}], "observed_prefix_length": 6, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506], "prior_H": 0.204042}, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.02762280113741506, "not_H": 0.9723771988625849}, "instance_id": "sequential_bayes__seed_000050__repr_table", "latent_instance_id": "sequential_bayes__seed_000050", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 50, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.472127, "E_given_not_H": 0.191458}, {"E_given_H": 0.631191, "E_given_not_H": 0.405093}, {"E_given_H": 0.870541, "E_given_not_H": 0.546792}, {"E_given_H": 0.93722, "E_given_not_H": 0.612099}, {"E_given_H": 0.075121, "E_given_not_H": 0.763611}, {"E_given_H": 0.115737, "E_given_not_H": 0.962357}], "observed_prefix_length": 6, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506], "prior_H": 0.204042}, "table": [{"E_given_H": 0.472127, "E_given_not_H": 0.191458, "step": 1}, {"E_given_H": 0.631191, "E_given_not_H": 0.405093, "step": 2}, {"E_given_H": 0.870541, "E_given_not_H": 0.546792, "step": 3}, {"E_given_H": 0.93722, "E_given_not_H": 0.612099, "step": 4}, {"E_given_H": 0.075121, "E_given_not_H": 0.763611, "step": 5}, {"E_given_H": 0.115737, "E_given_not_H": 0.962357, "step": 6}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.472127, "E_given_not_H": 0.191458}, {"E_given_H": 0.631191, "E_given_not_H": 0.405093}, {"E_given_H": 0.870541, "E_given_not_H": 0.546792}, {"E_given_H": 0.93722, "E_given_not_H": 0.612099}, {"E_given_H": 0.075121, "E_given_not_H": 0.763611}, {"E_given_H": 0.115737, "E_given_not_H": 0.962357}], "observed_prefix_length": 6, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506], "prior_H": 0.204042}, "posterior_trajectory": [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.02762280113741506, "not_H": 0.9723771988625849}, "instance_id": "sequential_bayes__seed_000050__repr_prose", "latent_instance_id": "sequential_bayes__seed_000050", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 50, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.0276228011374, and the remaining probability belongs to the other outcome. {'prior_H': 0.204042, 'evidence_sequence': [{'E_given_H': 0.472127, 'E_given_not_H': 0.191458}, {'E_given_H': 0.631191, 'E_given_not_H': 0.405093}, {'E_given_H': 0.870541, 'E_given_not_H': 0.546792}, {'E_given_H': 0.93722, 'E_given_not_H': 0.612099}, {'E_given_H': 0.075121, 'E_given_not_H': 0.763611}, {'E_given_H': 0.115737, 'E_given_not_H': 0.962357}], 'observed_prefix_length': 6, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.204042, 0.3873082630953835, 0.4962127795907569, 0.6106147948908568, 0.7059762861319588, 0.1910754727564699, 0.02762280113741506]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.556613, "E_given_not_H": 0.401197}, {"E_given_H": 0.788138, "E_given_not_H": 0.49524}, {"E_given_H": 0.968742, "E_given_not_H": 0.55418}, {"E_given_H": 0.022217, "E_given_not_H": 0.870351}, {"E_given_H": 0.19125, "E_given_not_H": 0.946898}, {"E_given_H": 0.32951, "E_given_not_H": 0.055451}], "observed_prefix_length": 6, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873], "prior_H": 0.410511}, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.07608014616604873, "not_H": 0.9239198538339513}, "instance_id": "sequential_bayes__seed_000051__repr_direct", "latent_instance_id": "sequential_bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 51, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.556613, "E_given_not_H": 0.401197}, {"E_given_H": 0.788138, "E_given_not_H": 0.49524}, {"E_given_H": 0.968742, "E_given_not_H": 0.55418}, {"E_given_H": 0.022217, "E_given_not_H": 0.870351}, {"E_given_H": 0.19125, "E_given_not_H": 0.946898}, {"E_given_H": 0.32951, "E_given_not_H": 0.055451}], "observed_prefix_length": 6, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873], "prior_H": 0.410511}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.556613, "E_given_not_H": 0.401197}, {"E_given_H": 0.788138, "E_given_not_H": 0.49524}, {"E_given_H": 0.968742, "E_given_not_H": 0.55418}, {"E_given_H": 0.022217, "E_given_not_H": 0.870351}, {"E_given_H": 0.19125, "E_given_not_H": 0.946898}, {"E_given_H": 0.32951, "E_given_not_H": 0.055451}], "observed_prefix_length": 6, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873], "prior_H": 0.410511}, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.07608014616604873, "not_H": 0.9239198538339513}, "instance_id": "sequential_bayes__seed_000051__repr_table", "latent_instance_id": "sequential_bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 51, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.556613, "E_given_not_H": 0.401197}, {"E_given_H": 0.788138, "E_given_not_H": 0.49524}, {"E_given_H": 0.968742, "E_given_not_H": 0.55418}, {"E_given_H": 0.022217, "E_given_not_H": 0.870351}, {"E_given_H": 0.19125, "E_given_not_H": 0.946898}, {"E_given_H": 0.32951, "E_given_not_H": 0.055451}], "observed_prefix_length": 6, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873], "prior_H": 0.410511}, "table": [{"E_given_H": 0.556613, "E_given_not_H": 0.401197, "step": 1}, {"E_given_H": 0.788138, "E_given_not_H": 0.49524, "step": 2}, {"E_given_H": 0.968742, "E_given_not_H": 0.55418, "step": 3}, {"E_given_H": 0.022217, "E_given_not_H": 0.870351, "step": 4}, {"E_given_H": 0.19125, "E_given_not_H": 0.946898, "step": 5}, {"E_given_H": 0.32951, "E_given_not_H": 0.055451, "step": 6}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.556613, "E_given_not_H": 0.401197}, {"E_given_H": 0.788138, "E_given_not_H": 0.49524}, {"E_given_H": 0.968742, "E_given_not_H": 0.55418}, {"E_given_H": 0.022217, "E_given_not_H": 0.870351}, {"E_given_H": 0.19125, "E_given_not_H": 0.946898}, {"E_given_H": 0.32951, "E_given_not_H": 0.055451}], "observed_prefix_length": 6, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873], "prior_H": 0.410511}, "posterior_trajectory": [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.07608014616604873, "not_H": 0.9239198538339513}, "instance_id": "sequential_bayes__seed_000051__repr_prose", "latent_instance_id": "sequential_bayes__seed_000051", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 51, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.076080146166, and the remaining probability belongs to the other outcome. {'prior_H': 0.410511, 'evidence_sequence': [{'E_given_H': 0.556613, 'E_given_not_H': 0.401197}, {'E_given_H': 0.788138, 'E_given_not_H': 0.49524}, {'E_given_H': 0.968742, 'E_given_not_H': 0.55418}, {'E_given_H': 0.022217, 'E_given_not_H': 0.870351}, {'E_given_H': 0.19125, 'E_given_not_H': 0.946898}, {'E_given_H': 0.32951, 'E_given_not_H': 0.055451}], 'observed_prefix_length': 6, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.410511, 0.49139192352202815, 0.6059202315489085, 0.7288318182873215, 0.06420381683042299, 0.013667875069321786, 0.07608014616604873]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.879365, "E_given_not_H": 0.462544}, {"E_given_H": 0.979216, "E_given_not_H": 0.624609}, {"E_given_H": 0.059074, "E_given_not_H": 0.804877}], "observed_prefix_length": 3, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008], "prior_H": 0.453999}, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.15389933510803008, "not_H": 0.8461006648919699}, "instance_id": "sequential_bayes__seed_000052__repr_direct", "latent_instance_id": "sequential_bayes__seed_000052", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 52, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.879365, "E_given_not_H": 0.462544}, {"E_given_H": 0.979216, "E_given_not_H": 0.624609}, {"E_given_H": 0.059074, "E_given_not_H": 0.804877}], "observed_prefix_length": 3, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008], "prior_H": 0.453999}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.879365, "E_given_not_H": 0.462544}, {"E_given_H": 0.979216, "E_given_not_H": 0.624609}, {"E_given_H": 0.059074, "E_given_not_H": 0.804877}], "observed_prefix_length": 3, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008], "prior_H": 0.453999}, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.15389933510803008, "not_H": 0.8461006648919699}, "instance_id": "sequential_bayes__seed_000052__repr_table", "latent_instance_id": "sequential_bayes__seed_000052", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 52, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.879365, "E_given_not_H": 0.462544}, {"E_given_H": 0.979216, "E_given_not_H": 0.624609}, {"E_given_H": 0.059074, "E_given_not_H": 0.804877}], "observed_prefix_length": 3, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008], "prior_H": 0.453999}, "table": [{"E_given_H": 0.879365, "E_given_not_H": 0.462544, "step": 1}, {"E_given_H": 0.979216, "E_given_not_H": 0.624609, "step": 2}, {"E_given_H": 0.059074, "E_given_not_H": 0.804877, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.879365, "E_given_not_H": 0.462544}, {"E_given_H": 0.979216, "E_given_not_H": 0.624609}, {"E_given_H": 0.059074, "E_given_not_H": 0.804877}], "observed_prefix_length": 3, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008], "prior_H": 0.453999}, "posterior_trajectory": [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.15389933510803008, "not_H": 0.8461006648919699}, "instance_id": "sequential_bayes__seed_000052__repr_prose", "latent_instance_id": "sequential_bayes__seed_000052", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 52, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.153899335108, and the remaining probability belongs to the other outcome. {'prior_H': 0.453999, 'evidence_sequence': [{'E_given_H': 0.879365, 'E_given_not_H': 0.462544}, {'E_given_H': 0.979216, 'E_given_not_H': 0.624609}, {'E_given_H': 0.059074, 'E_given_not_H': 0.804877}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.453999, 0.6125236066700036, 0.7125003896742405, 0.15389933510803008]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.925288, "E_given_not_H": 0.660119}, {"E_given_H": 0.031742, "E_given_not_H": 0.822326}, {"E_given_H": 0.24875, "E_given_not_H": 0.954675}], "observed_prefix_length": 3, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456], "prior_H": 0.619861}, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.02247158859218456, "not_H": 0.9775284114078154}, "instance_id": "sequential_bayes__seed_000053__repr_direct", "latent_instance_id": "sequential_bayes__seed_000053", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 53, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.925288, "E_given_not_H": 0.660119}, {"E_given_H": 0.031742, "E_given_not_H": 0.822326}, {"E_given_H": 0.24875, "E_given_not_H": 0.954675}], "observed_prefix_length": 3, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456], "prior_H": 0.619861}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.925288, "E_given_not_H": 0.660119}, {"E_given_H": 0.031742, "E_given_not_H": 0.822326}, {"E_given_H": 0.24875, "E_given_not_H": 0.954675}], "observed_prefix_length": 3, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456], "prior_H": 0.619861}, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.02247158859218456, "not_H": 0.9775284114078154}, "instance_id": "sequential_bayes__seed_000053__repr_table", "latent_instance_id": "sequential_bayes__seed_000053", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 53, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.925288, "E_given_not_H": 0.660119}, {"E_given_H": 0.031742, "E_given_not_H": 0.822326}, {"E_given_H": 0.24875, "E_given_not_H": 0.954675}], "observed_prefix_length": 3, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456], "prior_H": 0.619861}, "table": [{"E_given_H": 0.925288, "E_given_not_H": 0.660119, "step": 1}, {"E_given_H": 0.031742, "E_given_not_H": 0.822326, "step": 2}, {"E_given_H": 0.24875, "E_given_not_H": 0.954675, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.925288, "E_given_not_H": 0.660119}, {"E_given_H": 0.031742, "E_given_not_H": 0.822326}, {"E_given_H": 0.24875, "E_given_not_H": 0.954675}], "observed_prefix_length": 3, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456], "prior_H": 0.619861}, "posterior_trajectory": [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.02247158859218456, "not_H": 0.9775284114078154}, "instance_id": "sequential_bayes__seed_000053__repr_prose", "latent_instance_id": "sequential_bayes__seed_000053", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 53, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.0224715885922, and the remaining probability belongs to the other outcome. {'prior_H': 0.619861, 'evidence_sequence': [{'E_given_H': 0.925288, 'E_given_not_H': 0.660119}, {'E_given_H': 0.031742, 'E_given_not_H': 0.822326}, {'E_given_H': 0.24875, 'E_given_not_H': 0.954675}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.619861, 0.6956446852040687, 0.08107327708820022, 0.02247158859218456]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.093764, "E_given_not_H": 0.771322}, {"E_given_H": 0.243778, "E_given_not_H": 0.924411}, {"E_given_H": 0.325247, "E_given_not_H": 0.026323}], "observed_prefix_length": 3, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295], "prior_H": 0.808057}, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6251234123859295, "not_H": 0.3748765876140705}, "instance_id": "sequential_bayes__seed_000054__repr_direct", "latent_instance_id": "sequential_bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 54, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.093764, "E_given_not_H": 0.771322}, {"E_given_H": 0.243778, "E_given_not_H": 0.924411}, {"E_given_H": 0.325247, "E_given_not_H": 0.026323}], "observed_prefix_length": 3, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295], "prior_H": 0.808057}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.093764, "E_given_not_H": 0.771322}, {"E_given_H": 0.243778, "E_given_not_H": 0.924411}, {"E_given_H": 0.325247, "E_given_not_H": 0.026323}], "observed_prefix_length": 3, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295], "prior_H": 0.808057}, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6251234123859295, "not_H": 0.3748765876140705}, "instance_id": "sequential_bayes__seed_000054__repr_table", "latent_instance_id": "sequential_bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 54, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.093764, "E_given_not_H": 0.771322}, {"E_given_H": 0.243778, "E_given_not_H": 0.924411}, {"E_given_H": 0.325247, "E_given_not_H": 0.026323}], "observed_prefix_length": 3, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295], "prior_H": 0.808057}, "table": [{"E_given_H": 0.093764, "E_given_not_H": 0.771322, "step": 1}, {"E_given_H": 0.243778, "E_given_not_H": 0.924411, "step": 2}, {"E_given_H": 0.325247, "E_given_not_H": 0.026323, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.093764, "E_given_not_H": 0.771322}, {"E_given_H": 0.243778, "E_given_not_H": 0.924411}, {"E_given_H": 0.325247, "E_given_not_H": 0.026323}], "observed_prefix_length": 3, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295], "prior_H": 0.808057}, "posterior_trajectory": [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6251234123859295, "not_H": 0.3748765876140705}, "instance_id": "sequential_bayes__seed_000054__repr_prose", "latent_instance_id": "sequential_bayes__seed_000054", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 54, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.625123412386, and the remaining probability belongs to the other outcome. {'prior_H': 0.808057, 'evidence_sequence': [{'E_given_H': 0.093764, 'E_given_not_H': 0.771322}, {'E_given_H': 0.243778, 'E_given_not_H': 0.924411}, {'E_given_H': 0.325247, 'E_given_not_H': 0.026323}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.808057, 0.33852129492020233, 0.1189103435331514, 0.6251234123859295]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.218221, "E_given_not_H": 0.987522}, {"E_given_H": 0.403645, "E_given_not_H": 0.018042}, {"E_given_H": 0.467266, "E_given_not_H": 0.150138}], "observed_prefix_length": 3, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025], "prior_H": 0.92575}, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025]}, "gold_argmax": "H", "gold_distribution": {"H": 0.9948143100686025, "not_H": 0.0051856899313974525}, "instance_id": "sequential_bayes__seed_000055__repr_direct", "latent_instance_id": "sequential_bayes__seed_000055", "outcomes": ["H", "not_H"], "probability_band": "(0.99,1)", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 55, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.218221, "E_given_not_H": 0.987522}, {"E_given_H": 0.403645, "E_given_not_H": 0.018042}, {"E_given_H": 0.467266, "E_given_not_H": 0.150138}], "observed_prefix_length": 3, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025], "prior_H": 0.92575}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.218221, "E_given_not_H": 0.987522}, {"E_given_H": 0.403645, "E_given_not_H": 0.018042}, {"E_given_H": 0.467266, "E_given_not_H": 0.150138}], "observed_prefix_length": 3, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025], "prior_H": 0.92575}, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025]}, "gold_argmax": "H", "gold_distribution": {"H": 0.9948143100686025, "not_H": 0.0051856899313974525}, "instance_id": "sequential_bayes__seed_000055__repr_table", "latent_instance_id": "sequential_bayes__seed_000055", "outcomes": ["H", "not_H"], "probability_band": "(0.99,1)", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 55, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.218221, "E_given_not_H": 0.987522}, {"E_given_H": 0.403645, "E_given_not_H": 0.018042}, {"E_given_H": 0.467266, "E_given_not_H": 0.150138}], "observed_prefix_length": 3, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025], "prior_H": 0.92575}, "table": [{"E_given_H": 0.218221, "E_given_not_H": 0.987522, "step": 1}, {"E_given_H": 0.403645, "E_given_not_H": 0.018042, "step": 2}, {"E_given_H": 0.467266, "E_given_not_H": 0.150138, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.218221, "E_given_not_H": 0.987522}, {"E_given_H": 0.403645, "E_given_not_H": 0.018042}, {"E_given_H": 0.467266, "E_given_not_H": 0.150138}], "observed_prefix_length": 3, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025], "prior_H": 0.92575}, "posterior_trajectory": [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025]}, "gold_argmax": "H", "gold_distribution": {"H": 0.9948143100686025, "not_H": 0.0051856899313974525}, "instance_id": "sequential_bayes__seed_000055__repr_prose", "latent_instance_id": "sequential_bayes__seed_000055", "outcomes": ["H", "not_H"], "probability_band": "(0.99,1)", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 55, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.994814310069, and the remaining probability belongs to the other outcome. {'prior_H': 0.92575, 'evidence_sequence': [{'E_given_H': 0.218221, 'E_given_not_H': 0.987522}, {'E_given_H': 0.403645, 'E_given_not_H': 0.018042}, {'E_given_H': 0.467266, 'E_given_not_H': 0.150138}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.92575, 0.7336998524751613, 0.9840357343380087, 0.9948143100686025]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.396464, "E_given_not_H": 0.059517}, {"E_given_H": 0.532697, "E_given_not_H": 0.217707}, {"E_given_H": 0.581599, "E_given_not_H": 0.387297}, {"E_given_H": 0.845928, "E_given_not_H": 0.547247}], "observed_prefix_length": 4, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328], "prior_H": 0.052477}, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6769462255144328, "not_H": 0.32305377448556716}, "instance_id": "sequential_bayes__seed_000056__repr_direct", "latent_instance_id": "sequential_bayes__seed_000056", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 56, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.396464, "E_given_not_H": 0.059517}, {"E_given_H": 0.532697, "E_given_not_H": 0.217707}, {"E_given_H": 0.581599, "E_given_not_H": 0.387297}, {"E_given_H": 0.845928, "E_given_not_H": 0.547247}], "observed_prefix_length": 4, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328], "prior_H": 0.052477}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.396464, "E_given_not_H": 0.059517}, {"E_given_H": 0.532697, "E_given_not_H": 0.217707}, {"E_given_H": 0.581599, "E_given_not_H": 0.387297}, {"E_given_H": 0.845928, "E_given_not_H": 0.547247}], "observed_prefix_length": 4, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328], "prior_H": 0.052477}, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6769462255144328, "not_H": 0.32305377448556716}, "instance_id": "sequential_bayes__seed_000056__repr_table", "latent_instance_id": "sequential_bayes__seed_000056", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 56, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.396464, "E_given_not_H": 0.059517}, {"E_given_H": 0.532697, "E_given_not_H": 0.217707}, {"E_given_H": 0.581599, "E_given_not_H": 0.387297}, {"E_given_H": 0.845928, "E_given_not_H": 0.547247}], "observed_prefix_length": 4, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328], "prior_H": 0.052477}, "table": [{"E_given_H": 0.396464, "E_given_not_H": 0.059517, "step": 1}, {"E_given_H": 0.532697, "E_given_not_H": 0.217707, "step": 2}, {"E_given_H": 0.581599, "E_given_not_H": 0.387297, "step": 3}, {"E_given_H": 0.845928, "E_given_not_H": 0.547247, "step": 4}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.396464, "E_given_not_H": 0.059517}, {"E_given_H": 0.532697, "E_given_not_H": 0.217707}, {"E_given_H": 0.581599, "E_given_not_H": 0.387297}, {"E_given_H": 0.845928, "E_given_not_H": 0.547247}], "observed_prefix_length": 4, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328], "prior_H": 0.052477}, "posterior_trajectory": [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6769462255144328, "not_H": 0.32305377448556716}, "instance_id": "sequential_bayes__seed_000056__repr_prose", "latent_instance_id": "sequential_bayes__seed_000056", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 56, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.676946225514, and the remaining probability belongs to the other outcome. {'prior_H': 0.052477, 'evidence_sequence': [{'E_given_H': 0.396464, 'E_given_not_H': 0.059517}, {'E_given_H': 0.532697, 'E_given_not_H': 0.217707}, {'E_given_H': 0.581599, 'E_given_not_H': 0.387297}, {'E_given_H': 0.845928, 'E_given_not_H': 0.547247}], 'observed_prefix_length': 4, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.052477, 0.2695015483073548, 0.474434734683435, 0.5754784594058879, 0.6769462255144328]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.461393, "E_given_not_H": 0.20014}, {"E_given_H": 0.559031, "E_given_not_H": 0.358382}, {"E_given_H": 0.85315, "E_given_not_H": 0.467545}], "observed_prefix_length": 3, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412], "prior_H": 0.226962}, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6583011485114412, "not_H": 0.34169885148855883}, "instance_id": "sequential_bayes__seed_000057__repr_direct", "latent_instance_id": "sequential_bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 57, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.461393, "E_given_not_H": 0.20014}, {"E_given_H": 0.559031, "E_given_not_H": 0.358382}, {"E_given_H": 0.85315, "E_given_not_H": 0.467545}], "observed_prefix_length": 3, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412], "prior_H": 0.226962}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.461393, "E_given_not_H": 0.20014}, {"E_given_H": 0.559031, "E_given_not_H": 0.358382}, {"E_given_H": 0.85315, "E_given_not_H": 0.467545}], "observed_prefix_length": 3, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412], "prior_H": 0.226962}, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6583011485114412, "not_H": 0.34169885148855883}, "instance_id": "sequential_bayes__seed_000057__repr_table", "latent_instance_id": "sequential_bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 57, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.461393, "E_given_not_H": 0.20014}, {"E_given_H": 0.559031, "E_given_not_H": 0.358382}, {"E_given_H": 0.85315, "E_given_not_H": 0.467545}], "observed_prefix_length": 3, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412], "prior_H": 0.226962}, "table": [{"E_given_H": 0.461393, "E_given_not_H": 0.20014, "step": 1}, {"E_given_H": 0.559031, "E_given_not_H": 0.358382, "step": 2}, {"E_given_H": 0.85315, "E_given_not_H": 0.467545, "step": 3}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.461393, "E_given_not_H": 0.20014}, {"E_given_H": 0.559031, "E_given_not_H": 0.358382}, {"E_given_H": 0.85315, "E_given_not_H": 0.467545}], "observed_prefix_length": 3, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412], "prior_H": 0.226962}, "posterior_trajectory": [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6583011485114412, "not_H": 0.34169885148855883}, "instance_id": "sequential_bayes__seed_000057__repr_prose", "latent_instance_id": "sequential_bayes__seed_000057", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 57, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.658301148511, and the remaining probability belongs to the other outcome. {'prior_H': 0.226962, 'evidence_sequence': [{'E_given_H': 0.461393, 'E_given_not_H': 0.20014}, {'E_given_H': 0.559031, 'E_given_not_H': 0.358382}, {'E_given_H': 0.85315, 'E_given_not_H': 0.467545}], 'observed_prefix_length': 3, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.226962, 0.4036420626372667, 0.5135698968067423, 0.6583011485114412]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.563625, "E_given_not_H": 0.328919}, {"E_given_H": 0.816449, "E_given_not_H": 0.498419}, {"E_given_H": 0.940724, "E_given_not_H": 0.681408}, {"E_given_H": 0.013363, "E_given_not_H": 0.757399}, {"E_given_H": 0.145011, "E_given_not_H": 0.927249}], "observed_prefix_length": 5, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283], "prior_H": 0.448231}, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.008611190063057283, "not_H": 0.9913888099369427}, "instance_id": "sequential_bayes__seed_000058__repr_direct", "latent_instance_id": "sequential_bayes__seed_000058", "outcomes": ["H", "not_H"], "probability_band": "(0,0.01)", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 58, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.563625, "E_given_not_H": 0.328919}, {"E_given_H": 0.816449, "E_given_not_H": 0.498419}, {"E_given_H": 0.940724, "E_given_not_H": 0.681408}, {"E_given_H": 0.013363, "E_given_not_H": 0.757399}, {"E_given_H": 0.145011, "E_given_not_H": 0.927249}], "observed_prefix_length": 5, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283], "prior_H": 0.448231}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.563625, "E_given_not_H": 0.328919}, {"E_given_H": 0.816449, "E_given_not_H": 0.498419}, {"E_given_H": 0.940724, "E_given_not_H": 0.681408}, {"E_given_H": 0.013363, "E_given_not_H": 0.757399}, {"E_given_H": 0.145011, "E_given_not_H": 0.927249}], "observed_prefix_length": 5, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283], "prior_H": 0.448231}, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.008611190063057283, "not_H": 0.9913888099369427}, "instance_id": "sequential_bayes__seed_000058__repr_table", "latent_instance_id": "sequential_bayes__seed_000058", "outcomes": ["H", "not_H"], "probability_band": "(0,0.01)", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 58, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.563625, "E_given_not_H": 0.328919}, {"E_given_H": 0.816449, "E_given_not_H": 0.498419}, {"E_given_H": 0.940724, "E_given_not_H": 0.681408}, {"E_given_H": 0.013363, "E_given_not_H": 0.757399}, {"E_given_H": 0.145011, "E_given_not_H": 0.927249}], "observed_prefix_length": 5, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283], "prior_H": 0.448231}, "table": [{"E_given_H": 0.563625, "E_given_not_H": 0.328919, "step": 1}, {"E_given_H": 0.816449, "E_given_not_H": 0.498419, "step": 2}, {"E_given_H": 0.940724, "E_given_not_H": 0.681408, "step": 3}, {"E_given_H": 0.013363, "E_given_not_H": 0.757399, "step": 4}, {"E_given_H": 0.145011, "E_given_not_H": 0.927249, "step": 5}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.563625, "E_given_not_H": 0.328919}, {"E_given_H": 0.816449, "E_given_not_H": 0.498419}, {"E_given_H": 0.940724, "E_given_not_H": 0.681408}, {"E_given_H": 0.013363, "E_given_not_H": 0.757399}, {"E_given_H": 0.145011, "E_given_not_H": 0.927249}], "observed_prefix_length": 5, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283], "prior_H": 0.448231}, "posterior_trajectory": [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.008611190063057283, "not_H": 0.9913888099369427}, "instance_id": "sequential_bayes__seed_000058__repr_prose", "latent_instance_id": "sequential_bayes__seed_000058", "outcomes": ["H", "not_H"], "probability_band": "(0,0.01)", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 58, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.00861119006306, and the remaining probability belongs to the other outcome. {'prior_H': 0.448231, 'evidence_sequence': [{'E_given_H': 0.563625, 'E_given_not_H': 0.328919}, {'E_given_H': 0.816449, 'E_given_not_H': 0.498419}, {'E_given_H': 0.940724, 'E_given_not_H': 0.681408}, {'E_given_H': 0.013363, 'E_given_not_H': 0.757399}, {'E_given_H': 0.145011, 'E_given_not_H': 0.927249}], 'observed_prefix_length': 5, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.448231, 0.5819435213764701, 0.6951441561018219, 0.7589202242149086, 0.05261861763270556, 0.008611190063057283]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.837044, "E_given_not_H": 0.496548}, {"E_given_H": 0.931117, "E_given_not_H": 0.572808}, {"E_given_H": 0.053668, "E_given_not_H": 0.816594}, {"E_given_H": 0.231918, "E_given_not_H": 0.961978}], "observed_prefix_length": 4, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422], "prior_H": 0.479732}, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.03849325907238422, "not_H": 0.9615067409276158}, "instance_id": "sequential_bayes__seed_000059__repr_direct", "latent_instance_id": "sequential_bayes__seed_000059", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 59, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.837044, "E_given_not_H": 0.496548}, {"E_given_H": 0.931117, "E_given_not_H": 0.572808}, {"E_given_H": 0.053668, "E_given_not_H": 0.816594}, {"E_given_H": 0.231918, "E_given_not_H": 0.961978}], "observed_prefix_length": 4, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422], "prior_H": 0.479732}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.837044, "E_given_not_H": 0.496548}, {"E_given_H": 0.931117, "E_given_not_H": 0.572808}, {"E_given_H": 0.053668, "E_given_not_H": 0.816594}, {"E_given_H": 0.231918, "E_given_not_H": 0.961978}], "observed_prefix_length": 4, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422], "prior_H": 0.479732}, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.03849325907238422, "not_H": 0.9615067409276158}, "instance_id": "sequential_bayes__seed_000059__repr_table", "latent_instance_id": "sequential_bayes__seed_000059", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 59, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.837044, "E_given_not_H": 0.496548}, {"E_given_H": 0.931117, "E_given_not_H": 0.572808}, {"E_given_H": 0.053668, "E_given_not_H": 0.816594}, {"E_given_H": 0.231918, "E_given_not_H": 0.961978}], "observed_prefix_length": 4, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422], "prior_H": 0.479732}, "table": [{"E_given_H": 0.837044, "E_given_not_H": 0.496548, "step": 1}, {"E_given_H": 0.931117, "E_given_not_H": 0.572808, "step": 2}, {"E_given_H": 0.053668, "E_given_not_H": 0.816594, "step": 3}, {"E_given_H": 0.231918, "E_given_not_H": 0.961978, "step": 4}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.837044, "E_given_not_H": 0.496548}, {"E_given_H": 0.931117, "E_given_not_H": 0.572808}, {"E_given_H": 0.053668, "E_given_not_H": 0.816594}, {"E_given_H": 0.231918, "E_given_not_H": 0.961978}], "observed_prefix_length": 4, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422], "prior_H": 0.479732}, "posterior_trajectory": [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.03849325907238422, "not_H": 0.9615067409276158}, "instance_id": "sequential_bayes__seed_000059__repr_prose", "latent_instance_id": "sequential_bayes__seed_000059", "outcomes": ["H", "not_H"], "probability_band": "[0.01,0.10]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 59, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.0384932590724, and the remaining probability belongs to the other outcome. {'prior_H': 0.479732, 'evidence_sequence': [{'E_given_H': 0.837044, 'E_given_not_H': 0.496548}, {'E_given_H': 0.931117, 'E_given_not_H': 0.572808}, {'E_given_H': 0.053668, 'E_given_not_H': 0.816594}, {'E_given_H': 0.231918, 'E_given_not_H': 0.961978}], 'observed_prefix_length': 4, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.479732, 0.6085163509914692, 0.7164488634677464, 0.1424106338677888, 0.03849325907238422]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.939675, "E_given_not_H": 0.667868}, {"E_given_H": 0.01395, "E_given_not_H": 0.793417}, {"E_given_H": 0.196268, "E_given_not_H": 0.914188}, {"E_given_H": 0.328341, "E_given_not_H": 0.022257}], "observed_prefix_length": 4, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172], "prior_H": 0.59555}, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.10343497142093172, "not_H": 0.8965650285790683}, "instance_id": "sequential_bayes__seed_000060__repr_direct", "latent_instance_id": "sequential_bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 60, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.939675, "E_given_not_H": 0.667868}, {"E_given_H": 0.01395, "E_given_not_H": 0.793417}, {"E_given_H": 0.196268, "E_given_not_H": 0.914188}, {"E_given_H": 0.328341, "E_given_not_H": 0.022257}], "observed_prefix_length": 4, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172], "prior_H": 0.59555}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.939675, "E_given_not_H": 0.667868}, {"E_given_H": 0.01395, "E_given_not_H": 0.793417}, {"E_given_H": 0.196268, "E_given_not_H": 0.914188}, {"E_given_H": 0.328341, "E_given_not_H": 0.022257}], "observed_prefix_length": 4, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172], "prior_H": 0.59555}, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.10343497142093172, "not_H": 0.8965650285790683}, "instance_id": "sequential_bayes__seed_000060__repr_table", "latent_instance_id": "sequential_bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 60, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.939675, "E_given_not_H": 0.667868}, {"E_given_H": 0.01395, "E_given_not_H": 0.793417}, {"E_given_H": 0.196268, "E_given_not_H": 0.914188}, {"E_given_H": 0.328341, "E_given_not_H": 0.022257}], "observed_prefix_length": 4, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172], "prior_H": 0.59555}, "table": [{"E_given_H": 0.939675, "E_given_not_H": 0.667868, "step": 1}, {"E_given_H": 0.01395, "E_given_not_H": 0.793417, "step": 2}, {"E_given_H": 0.196268, "E_given_not_H": 0.914188, "step": 3}, {"E_given_H": 0.328341, "E_given_not_H": 0.022257, "step": 4}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.939675, "E_given_not_H": 0.667868}, {"E_given_H": 0.01395, "E_given_not_H": 0.793417}, {"E_given_H": 0.196268, "E_given_not_H": 0.914188}, {"E_given_H": 0.328341, "E_given_not_H": 0.022257}], "observed_prefix_length": 4, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172], "prior_H": 0.59555}, "posterior_trajectory": [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172]}, "gold_argmax": "not_H", "gold_distribution": {"H": 0.10343497142093172, "not_H": 0.8965650285790683}, "instance_id": "sequential_bayes__seed_000060__repr_prose", "latent_instance_id": "sequential_bayes__seed_000060", "outcomes": ["H", "not_H"], "probability_band": "(0.10,0.30]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 60, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.103434971421, and the remaining probability belongs to the other outcome. {'prior_H': 0.59555, 'evidence_sequence': [{'E_given_H': 0.939675, 'E_given_not_H': 0.667868}, {'E_given_H': 0.01395, 'E_given_not_H': 0.793417}, {'E_given_H': 0.196268, 'E_given_not_H': 0.914188}, {'E_given_H': 0.328341, 'E_given_not_H': 0.022257}], 'observed_prefix_length': 4, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.59555, 0.6744542302135247, 0.035145908606276956, 0.007759683052744734, 0.10343497142093172]}", "representation": "natural_language"}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.088961, "E_given_not_H": 0.893826}, {"E_given_H": 0.12922, "E_given_not_H": 0.986114}, {"E_given_H": 0.36327, "E_given_not_H": 0.085042}, {"E_given_H": 0.527252, "E_given_not_H": 0.126874}, {"E_given_H": 0.554853, "E_given_not_H": 0.334595}, {"E_given_H": 0.748268, "E_given_not_H": 0.515369}], "observed_prefix_length": 6, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491], "prior_H": 0.772461}, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6542643257081491, "not_H": 0.3457356742918509}, "instance_id": "sequential_bayes__seed_000061__repr_direct", "latent_instance_id": "sequential_bayes__seed_000061", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "direct", "seed": 61, "state": {"representation": "direct", "sufficient_statistics": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.088961, "E_given_not_H": 0.893826}, {"E_given_H": 0.12922, "E_given_not_H": 0.986114}, {"E_given_H": 0.36327, "E_given_not_H": 0.085042}, {"E_given_H": 0.527252, "E_given_not_H": 0.126874}, {"E_given_H": 0.554853, "E_given_not_H": 0.334595}, {"E_given_H": 0.748268, "E_given_not_H": 0.515369}], "observed_prefix_length": 6, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491], "prior_H": 0.772461}}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.088961, "E_given_not_H": 0.893826}, {"E_given_H": 0.12922, "E_given_not_H": 0.986114}, {"E_given_H": 0.36327, "E_given_not_H": 0.085042}, {"E_given_H": 0.527252, "E_given_not_H": 0.126874}, {"E_given_H": 0.554853, "E_given_not_H": 0.334595}, {"E_given_H": 0.748268, "E_given_not_H": 0.515369}], "observed_prefix_length": 6, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491], "prior_H": 0.772461}, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6542643257081491, "not_H": 0.3457356742918509}, "instance_id": "sequential_bayes__seed_000061__repr_table", "latent_instance_id": "sequential_bayes__seed_000061", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "table", "seed": 61, "state": {"representation": "table", "state": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.088961, "E_given_not_H": 0.893826}, {"E_given_H": 0.12922, "E_given_not_H": 0.986114}, {"E_given_H": 0.36327, "E_given_not_H": 0.085042}, {"E_given_H": 0.527252, "E_given_not_H": 0.126874}, {"E_given_H": 0.554853, "E_given_not_H": 0.334595}, {"E_given_H": 0.748268, "E_given_not_H": 0.515369}], "observed_prefix_length": 6, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491], "prior_H": 0.772461}, "table": [{"E_given_H": 0.088961, "E_given_not_H": 0.893826, "step": 1}, {"E_given_H": 0.12922, "E_given_not_H": 0.986114, "step": 2}, {"E_given_H": 0.36327, "E_given_not_H": 0.085042, "step": 3}, {"E_given_H": 0.527252, "E_given_not_H": 0.126874, "step": 4}, {"E_given_H": 0.554853, "E_given_not_H": 0.334595, "step": 5}, {"E_given_H": 0.748268, "E_given_not_H": 0.515369, "step": 6}]}} | |
| {"benchmark_version": "0.1.0", "difficulty": 6, "family": "sequential_bayes", "generator_metadata": {"parameters": {"conditional_independence": "Evidence items are conditionally independent given H or not_H.", "evidence_sequence": [{"E_given_H": 0.088961, "E_given_not_H": 0.893826}, {"E_given_H": 0.12922, "E_given_not_H": 0.986114}, {"E_given_H": 0.36327, "E_given_not_H": 0.085042}, {"E_given_H": 0.527252, "E_given_not_H": 0.126874}, {"E_given_H": 0.554853, "E_given_not_H": 0.334595}, {"E_given_H": 0.748268, "E_given_not_H": 0.515369}], "observed_prefix_length": 6, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491], "prior_H": 0.772461}, "posterior_trajectory": [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491]}, "gold_argmax": "H", "gold_distribution": {"H": 0.6542643257081491, "not_H": 0.3457356742918509}, "instance_id": "sequential_bayes__seed_000061__repr_prose", "latent_instance_id": "sequential_bayes__seed_000061", "outcomes": ["H", "not_H"], "probability_band": "(0.55,0.70]", "prompt": "After all listed conditionally independent evidence items are observed, what is the posterior distribution over H versus not_H? Return a normalized probability for each of: H, not_H.", "representation": "prose", "seed": 61, "state": {"description": "The state fully determines the target distribution. The probability of H is 0.654264325708, and the remaining probability belongs to the other outcome. {'prior_H': 0.772461, 'evidence_sequence': [{'E_given_H': 0.088961, 'E_given_not_H': 0.893826}, {'E_given_H': 0.12922, 'E_given_not_H': 0.986114}, {'E_given_H': 0.36327, 'E_given_not_H': 0.085042}, {'E_given_H': 0.527252, 'E_given_not_H': 0.126874}, {'E_given_H': 0.554853, 'E_given_not_H': 0.334595}, {'E_given_H': 0.748268, 'E_given_not_H': 0.515369}], 'observed_prefix_length': 6, 'conditional_independence': 'Evidence items are conditionally independent given H or not_H.', 'posterior_trajectory': [0.772461, 0.2525509401362523, 0.04239890454210647, 0.159050792052575, 0.4400834170144869, 0.5658548933841624, 0.6542643257081491]}", "representation": "natural_language"}} | |