{ "schema_version": "1.1", "dataset": "LogicBench-1K", "version": "1.0.1", "release": "camera-ready", "generated_at": "2026-06-08T19:05:59Z", "generated_by": "scripts/generate_statistics.py", "num_samples": 1000, "num_images": 1000, "image_format": "JPEG", "image_resolution": [ 512, 512 ], "splits": { "train": 700, "val": 100, "test": 200 }, "gate_vocabulary": [ "AND", "NAND", "NOR", "NOT", "OR", "XNOR", "XOR" ], "definitions": { "gate_mixture": "Sorted multiset of gate types present in one diagram; unique mixtures measure combinatorial diversity.", "directed_density": "edges / (nodes * (nodes - 1)) for n > 1; proportion of possible directed pairs that are annotated edges.", "terminal_degree": "Per-gate in-degree (incoming edges) and out-degree (outgoing edges) aggregated across all diagrams." }, "sample_diversity": { "unique_gate_mixtures": 343, "mixture_coverage": 0.343, "graphs_with_no_edges": 19, "isolated_gate_instances": 232, "graph_size": { "nodes_per_graph": { "min": 1, "max": 31, "mean": 6.174, "median": 5.0, "std": 3.699, "q1": 4.0, "q3": 7.0 }, "edges_per_graph": { "min": 0, "max": 57, "mean": 6.423, "median": 5.0, "std": 5.636, "q1": 3.0, "q3": 8.0 }, "node_count_histogram": { "1-5": 576, "6-10": 343, "11-15": 49, "16-20": 18, "21-31": 14 }, "edge_count_histogram": { "0": 19, "1-5": 544, "6-10": 298, "11-20": 114, "21-57": 25 } } }, "topology_distribution": { "global": { "num_samples": 1000, "totals": { "gates": 6174, "edges": 6423, "avg_gates_per_sample": 6.174, "avg_edges_per_sample": 6.423 }, "sample_diversity": { "unique_gate_mixtures": 343, "mixture_coverage": 0.343, "graphs_with_no_edges": 19, "isolated_gate_instances": 232 }, "graph_size": { "nodes_per_graph": { "min": 1, "max": 31, "mean": 6.174, "median": 5.0, "std": 3.699, "q1": 4.0, "q3": 7.0 }, "edges_per_graph": { "min": 0, "max": 57, "mean": 6.423, "median": 5.0, "std": 5.636, "q1": 3.0, "q3": 8.0 }, "node_count_histogram": { "1-5": 576, "6-10": 343, "11-15": 49, "16-20": 18, "21-31": 14 }, "edge_count_histogram": { "0": 19, "1-5": 544, "6-10": 298, "11-20": 114, "21-57": 25 } }, "topology": { "avg_directed_density": 0.2355, "gate_type_frequencies": { "AND": { "count": 1492, "proportion": 0.2417 }, "NAND": { "count": 915, "proportion": 0.1482 }, "NOR": { "count": 597, "proportion": 0.0967 }, "NOT": { "count": 1389, "proportion": 0.225 }, "OR": { "count": 894, "proportion": 0.1448 }, "XNOR": { "count": 258, "proportion": 0.0418 }, "XOR": { "count": 629, "proportion": 0.1019 } }, "terminal_degree_histogram": { "in_degree": { "0": 2112, "1": 2129, "2": 1634, "3": 207, "4": 70, "5": 14, "6": 5, "7": 1, "8": 1, "10": 1 }, "out_degree": { "0": 1600, "1": 3185, "2": 1125, "3": 152, "4": 79, "5": 15, "6": 6, "8": 7, "9": 4, "13": 1 } } } }, "by_split": { "train": { "num_samples": 700, "totals": { "gates": 4137, "edges": 4256, "avg_gates_per_sample": 5.91, "avg_edges_per_sample": 6.08 }, "sample_diversity": { "unique_gate_mixtures": 261, "mixture_coverage": 0.3729, "graphs_with_no_edges": 14, "isolated_gate_instances": 167 }, "graph_size": { "nodes_per_graph": { "min": 1, "max": 31, "mean": 5.91, "median": 5.0, "std": 3.48, "q1": 4.0, "q3": 7.0 }, "edges_per_graph": { "min": 0, "max": 57, "mean": 6.08, "median": 5.0, "std": 5.434, "q1": 3.0, "q3": 7.0 }, "node_count_histogram": { "1-5": 435, "6-10": 217, "11-15": 28, "16-20": 12, "21-31": 8 }, "edge_count_histogram": { "0": 14, "1-5": 400, "6-10": 199, "11-20": 73, "21-57": 14 } }, "topology": { "avg_directed_density": 0.2399, "gate_type_frequencies": { "AND": { "count": 985, "proportion": 0.2381 }, "NAND": { "count": 668, "proportion": 0.1615 }, "NOR": { "count": 390, "proportion": 0.0943 }, "NOT": { "count": 879, "proportion": 0.2125 }, "OR": { "count": 606, "proportion": 0.1465 }, "XNOR": { "count": 177, "proportion": 0.0428 }, "XOR": { "count": 432, "proportion": 0.1044 } }, "terminal_degree_histogram": { "in_degree": { "0": 1448, "1": 1398, "2": 1088, "3": 146, "4": 44, "5": 10, "6": 3 }, "out_degree": { "0": 1105, "1": 2125, "2": 733, "3": 101, "4": 49, "5": 11, "6": 1, "8": 7, "9": 4, "13": 1 } } } }, "val": { "num_samples": 100, "totals": { "gates": 677, "edges": 704, "avg_gates_per_sample": 6.77, "avg_edges_per_sample": 7.04 }, "sample_diversity": { "unique_gate_mixtures": 73, "mixture_coverage": 0.73, "graphs_with_no_edges": 3, "isolated_gate_instances": 23 }, "graph_size": { "nodes_per_graph": { "min": 2, "max": 29, "mean": 6.77, "median": 6.0, "std": 3.911, "q1": 4.0, "q3": 9.0 }, "edges_per_graph": { "min": 0, "max": 47, "mean": 7.04, "median": 6.0, "std": 6.071, "q1": 3.0, "q3": 9.5 }, "node_count_histogram": { "1-5": 43, "6-10": 44, "11-15": 11, "16-20": 0, "21-31": 2 }, "edge_count_histogram": { "0": 3, "1-5": 46, "6-10": 36, "11-20": 13, "21-57": 2 } }, "topology": { "avg_directed_density": 0.2148, "gate_type_frequencies": { "AND": { "count": 179, "proportion": 0.2644 }, "NAND": { "count": 62, "proportion": 0.0916 }, "NOR": { "count": 69, "proportion": 0.1019 }, "NOT": { "count": 182, "proportion": 0.2688 }, "OR": { "count": 96, "proportion": 0.1418 }, "XNOR": { "count": 13, "proportion": 0.0192 }, "XOR": { "count": 76, "proportion": 0.1123 } }, "terminal_degree_histogram": { "in_degree": { "0": 220, "1": 249, "2": 182, "3": 14, "4": 11, "5": 1 }, "out_degree": { "0": 169, "1": 347, "2": 135, "3": 17, "4": 9 } } } }, "test": { "num_samples": 200, "totals": { "gates": 1360, "edges": 1463, "avg_gates_per_sample": 6.8, "avg_edges_per_sample": 7.315 }, "sample_diversity": { "unique_gate_mixtures": 128, "mixture_coverage": 0.64, "graphs_with_no_edges": 2, "isolated_gate_instances": 42 }, "graph_size": { "nodes_per_graph": { "min": 2, "max": 29, "mean": 6.8, "median": 6.0, "std": 4.19, "q1": 4.0, "q3": 8.0 }, "edges_per_graph": { "min": 0, "max": 48, "mean": 7.315, "median": 5.5, "std": 5.973, "q1": 4.0, "q3": 9.0 }, "node_count_histogram": { "1-5": 98, "6-10": 82, "11-15": 10, "16-20": 6, "21-31": 4 }, "edge_count_histogram": { "0": 2, "1-5": 98, "6-10": 63, "11-20": 28, "21-57": 9 } }, "topology": { "avg_directed_density": 0.2305, "gate_type_frequencies": { "AND": { "count": 328, "proportion": 0.2412 }, "NAND": { "count": 185, "proportion": 0.136 }, "NOR": { "count": 138, "proportion": 0.1015 }, "NOT": { "count": 328, "proportion": 0.2412 }, "OR": { "count": 192, "proportion": 0.1412 }, "XNOR": { "count": 68, "proportion": 0.05 }, "XOR": { "count": 121, "proportion": 0.089 } }, "terminal_degree_histogram": { "in_degree": { "0": 444, "1": 482, "2": 364, "3": 47, "4": 15, "5": 3, "6": 2, "7": 1, "8": 1, "10": 1 }, "out_degree": { "0": 326, "1": 713, "2": 257, "3": 34, "4": 21, "5": 4, "6": 5 } } } } } }, "paper_summary": { "unique_gate_mixtures": 343, "gates_per_diagram": { "range": [ 1, 31 ], "mean": 6.174, "median": 5.0, "std": 3.699 }, "edges_per_diagram": { "range": [ 0, 57 ], "mean": 6.423, "median": 5.0, "std": 5.636 }, "total_gates": 6174, "total_edges": 6423, "mean_directed_density": 0.2355, "data_availability_paragraph": "The corpus comprises 1,000 annotated diagrams with 6,174 gates and 6,423 directed edges. Sample diversity spans 343 unique gate mixtures (34.3% coverage). Diagrams contain 1\u201331 gates (mean 6.174, median 5.0) and 0\u201357 edges (mean 6.423, median 5.0). Gate-type and topology statistics are stratified by the official 700/100/200 train/validation/test split in `metadata/statistics.json`." } }