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Browse files- data/s7_data/README.md +122 -0
- data/s7_data/dataset_dict.json +1 -0
- data/s7_data/metadata.json +0 -0
- data/s7_data/test/data-00000-of-00001.arrow +3 -0
- data/s7_data/test/dataset_info.json +16 -0
- data/s7_data/test/state.json +13 -0
- data/s7_data/train/data-00000-of-00001.arrow +3 -0
- data/s7_data/train/dataset_info.json +16 -0
- data/s7_data/train/state.json +13 -0
data/s7_data/README.md
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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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# Permutation Composition Dataset for S7
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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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## Dataset Structure
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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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- `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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## Group Details
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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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## Data Generation
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This dataset was generated using the `s5-data-gen` script. The generation process involves:
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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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### Generation Parameters:
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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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## Dataset Statistics
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- **Train Samples**: 80000
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- **Test Samples**: 20000
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## Permutation Mapping
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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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Example of `metadata.json` content:
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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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## Usage
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You can load this dataset using the Hugging Face `datasets` library:
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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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# Load the dataset
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dataset = load_dataset("BeeGass/permutation-groups")
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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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# 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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print(f"Input sequence IDs: {input_ids}")
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print(f"Target ID: {target_id}")
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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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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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## License
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This dataset is licensed under the MIT License.
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data/s7_data/dataset_dict.json
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{"splits": ["train", "test"]}
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data/s7_data/metadata.json
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The diff for this file is too large to render.
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data/s7_data/test/data-00000-of-00001.arrow
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version https://git-lfs.github.com/spec/v1
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oid sha256:d0495287c0667e82167d499737b800ad85b1f2c34cb56a557e003c0ae2d60429
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size 24750440
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data/s7_data/test/dataset_info.json
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{
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"citation": "",
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"description": "Permutation composition benchmark for the S7 group.",
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"features": {
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"input_sequence": {
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"dtype": "string",
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"_type": "Value"
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},
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"target": {
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"dtype": "string",
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"_type": "Value"
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}
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},
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"homepage": "https://github.com/your-repo",
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"license": "mit"
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}
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data/s7_data/test/state.json
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{
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"_data_files": [
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{
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"filename": "data-00000-of-00001.arrow"
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}
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],
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"_fingerprint": "1539b9d834783e77",
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"_format_columns": null,
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"_format_kwargs": {},
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"_format_type": null,
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"_output_all_columns": false,
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"_split": null
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}
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data/s7_data/train/data-00000-of-00001.arrow
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version https://git-lfs.github.com/spec/v1
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oid sha256:a0916cdbc72e770c9c1ef6f2c158d1807c5f20a0c38caf2f9d616c21be91a694
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size 99280120
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data/s7_data/train/dataset_info.json
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{
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"citation": "",
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"description": "Permutation composition benchmark for the S7 group.",
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"features": {
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"input_sequence": {
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"dtype": "string",
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"_type": "Value"
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},
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"target": {
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"dtype": "string",
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"_type": "Value"
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}
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},
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"homepage": "https://github.com/your-repo",
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"license": "mit"
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}
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data/s7_data/train/state.json
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{
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"_data_files": [
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{
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"filename": "data-00000-of-00001.arrow"
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}
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],
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"_fingerprint": "9778a883866ed2a4",
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"_format_columns": null,
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"_format_kwargs": {},
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"_format_type": null,
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"_output_all_columns": false,
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"_split": null
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}
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