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s4_data/README.md

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+---
+pretty_name: Permutation Composition Dataset (S4)
+size_categories:
+  - small
+  - medium
+  - large
+  - xlarge
+  - xxlarge
+tags:
+  - mathematics
+  - group-theory
+  - permutations
+  - sequence-to-sequence
+  - benchmark
+  - generated
+task_categories:
+  - text-generation
+  - sequence-modeling
+annotations_creators:
+  - no-annotations
+language_creators:
+  - other
+language:
+  - en
+licenses:
+  - mit
+--- 
+
+# Permutation Composition Dataset for S4
+
+This dataset contains sequences of permutation IDs and their compositions, designed for benchmarking sequence-to-sequence models on group theory tasks.
+
+## Dataset Structure
+
+The dataset is split into `train` and `test` sets. Each sample in the dataset has the following features:
+
+- `input_sequence`: A space-separated string of integer IDs representing the sequence of permutations to be composed.
+- `target`: An integer ID representing the composition of the `input_sequence` permutations.
+
+## Group Details
+
+- **Group Name**: S4
+- **Group Type**: Symmetric Group
+- **Degree**: 4 (permutations act on 4 elements)
+- **Order**: 24 (total number of elements in the group)
+
+## Data Generation
+
+This dataset was generated using the `s5-data-gen` script. The generation process involves:
+
+1.  Generating all unique permutations for the specified group.
+2.  Mapping each unique permutation to a unique integer ID.
+3.  Randomly sampling sequences of these permutation IDs.
+4.  Composing the permutations in the sequence (from right to left: `p_n o ... o p_2 o p_1`).
+5.  Mapping the resulting composed permutation to its integer ID as the target.
+
+### Generation Parameters:
+
+- **Total Samples**: 50000
+- **Minimum Sequence Length**: 3
+- **Maximum Sequence Length**: 512
+- **Test Split Size**: 0.2
+
+## Dataset Statistics
+
+- **Train Samples**: 40000
+- **Test Samples**: 10000
+
+## Permutation Mapping
+
+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.
+
+Example of `metadata.json` content:
+
+```json
+{
+  "0": "[0, 1, 2, 3, 4]",
+  "1": "[0, 1, 3, 2, 4]",
+  "2": "[0, 1, 4, 3, 2]",
+  "3": "[0, 2, 1, 3, 4]",
+  "4": "[0, 2, 3, 1, 4]"
+  // ... and so on for all 24 permutations
+}
+```
+
+## Usage
+
+You can load this dataset using the Hugging Face `datasets` library:
+
+```python
+from datasets import load_dataset
+import json
+from huggingface_hub import hf_hub_download
+
+# Load the dataset
+dataset = load_dataset("BeeGass/permutation-groups")
+
+# Load the permutation mapping
+metadata_path = hf_hub_download(repo_id="BeeGass/permutation-groups", filename="metadata.json")
+with open(metadata_path, "r") as f:
+    id_to_perm_map = json.load(f)
+
+# Example: Decode a sample
+first_train_sample = dataset["train"][0]
+input_ids = [int(x) for x in first_train_sample["input_sequence"].split(" ")]
+target_id = int(first_train_sample["target"])
+
+print(f"Input sequence IDs: {input_ids}")
+print(f"Target ID: {target_id}")
+
+# Convert IDs back to permutations (example for the first input permutation)
+# Note: SymPy Permutation expects a list of integers, not a string representation
+# You would need to parse the string representation from id_to_perm_map
+# For example: eval(id_to_perm_map[str(input_ids[0])])
+
+print(f"First input permutation (array form): {id_to_perm_map[str(input_ids[0])]}")
+print(f"Target permutation (array form): {id_to_perm_map[str(target_id)]}")
+```
+
+## License
+
+This dataset is licensed under the MIT License.