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data/s7_data/README.md ADDED
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+ ---
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+ pretty_name: Permutation Composition Dataset (S7)
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+ size_categories:
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+ - small
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+ - medium
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+ - large
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+ - xlarge
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+ - xxlarge
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+ tags:
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+ - mathematics
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+ - group-theory
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+ - permutations
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+ - sequence-to-sequence
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+ - benchmark
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+ - generated
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+ task_categories:
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+ - text-generation
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+ - sequence-modeling
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+ annotations_creators:
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+ - no-annotations
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+ language_creators:
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+ - other
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+ language:
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+ - en
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+ licenses:
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+ - mit
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+ ---
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+
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+ # Permutation Composition Dataset for S7
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+
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+ This dataset contains sequences of permutation IDs and their compositions, designed for benchmarking sequence-to-sequence models on group theory tasks.
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+
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+ ## Dataset Structure
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+
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+ The dataset is split into `train` and `test` sets. Each sample in the dataset has the following features:
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+
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+ - `input_sequence`: A space-separated string of integer IDs representing the sequence of permutations to be composed.
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+ - `target`: An integer ID representing the composition of the `input_sequence` permutations.
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+
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+ ## Group Details
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+
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+ - **Group Name**: S7
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+ - **Group Type**: Symmetric Group
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+ - **Degree**: 7 (permutations act on 7 elements)
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+ - **Order**: 5040 (total number of elements in the group)
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+
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+ ## Data Generation
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+
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+ This dataset was generated using the `s5-data-gen` script. The generation process involves:
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+
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+ 1. Generating all unique permutations for the specified group.
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+ 2. Mapping each unique permutation to a unique integer ID.
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+ 3. Randomly sampling sequences of these permutation IDs.
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+ 4. Composing the permutations in the sequence (from right to left: `p_n o ... o p_2 o p_1`).
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+ 5. Mapping the resulting composed permutation to its integer ID as the target.
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+
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+ ### Generation Parameters:
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+
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+ - **Total Samples**: 100000
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+ - **Minimum Sequence Length**: 3
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+ - **Maximum Sequence Length**: 512
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+ - **Test Split Size**: 0.2
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+
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+ ## Dataset Statistics
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+
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+ - **Train Samples**: 80000
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+ - **Test Samples**: 20000
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+
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+ ## Permutation Mapping
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+
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+ The mapping from integer IDs to their corresponding permutation array forms is provided in the `metadata.json` file alongside the dataset. This file is crucial for interpreting the `input_sequence` and `target` IDs.
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+
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+ Example of `metadata.json` content:
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+
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+ ```json
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+ {
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+ "0": "[0, 1, 2, 3, 4]",
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+ "1": "[0, 1, 3, 2, 4]",
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+ "2": "[0, 1, 4, 3, 2]",
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+ "3": "[0, 2, 1, 3, 4]",
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+ "4": "[0, 2, 3, 1, 4]"
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+ // ... and so on for all 5040 permutations
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+ }
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+ ```
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+
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+ ## Usage
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+
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+ You can load this dataset using the Hugging Face `datasets` library:
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+
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+ ```python
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+ from datasets import load_dataset
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+ import json
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+ from huggingface_hub import hf_hub_download
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+
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+ # Load the dataset
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+ dataset = load_dataset("BeeGass/permutation-groups")
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+
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+ # Load the permutation mapping
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+ metadata_path = hf_hub_download(repo_id="BeeGass/permutation-groups", filename="metadata.json")
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+ with open(metadata_path, "r") as f:
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+ id_to_perm_map = json.load(f)
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+
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+ # Example: Decode a sample
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+ first_train_sample = dataset["train"][0]
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+ input_ids = [int(x) for x in first_train_sample["input_sequence"].split(" ")]
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+ target_id = int(first_train_sample["target"])
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+
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+ print(f"Input sequence IDs: {input_ids}")
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+ print(f"Target ID: {target_id}")
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+
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+ # Convert IDs back to permutations (example for the first input permutation)
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+ # Note: SymPy Permutation expects a list of integers, not a string representation
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+ # You would need to parse the string representation from id_to_perm_map
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+ # For example: eval(id_to_perm_map[str(input_ids[0])])
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+
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+ print(f"First input permutation (array form): {id_to_perm_map[str(input_ids[0])]}")
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+ print(f"Target permutation (array form): {id_to_perm_map[str(target_id)]}")
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+ ```
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+
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+ ## License
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+
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+ This dataset is licensed under the MIT License.
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