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README.md

@@ -1,41 +1,161 @@
-# Permutation Groups Datasets
+---
+license: mit
+task_categories:
+- text-generation
+language:
+- en
+tags:
+- mathematics
+- group-theory
+- permutations
+- symbolic-reasoning
+- algebra
+- sequence-modeling
+pretty_name: Permutation Groups Composition Dataset
+size_categories:
+- 10M<n<100M
+---
 
-This repository contains permutation composition datasets for various symmetric and alternating groups.
+# Permutation Groups Composition Dataset
 
-## Usage
+A comprehensive collection of permutation composition datasets for various mathematical groups including symmetric, alternating, cyclic, dihedral, and special groups, with multiple sequence length variants.
+
+## Dataset Description
+
+This dataset contains permutation composition problems across 30 different mathematical groups with 8 different sequence length variants each, totaling 270 distinct configurations.
+
+### Supported Groups
+
+#### Symmetric Groups (Sn)
+- **S3** to **S7**: All permutations of n elements (orders: 6, 24, 120, 720, 5040)
+
+#### Alternating Groups (An)
+- **A3** to **A7**: Even permutations of n elements (orders: 3, 12, 60, 360, 2520)
+
+#### Cyclic Groups (Cn/Zn)
+- **C3** to **C12**: Cyclic groups of order n
+- **Z3** to **Z6**: Alternative notation for cyclic groups
+- Orders: 3, 4, 5, 6, 7, 8, 10, 12
+
+#### Dihedral Groups (Dn)
+- **D3** to **D8**: Symmetries of regular n-gons (orders: 6, 8, 10, 12, 14, 16)
+
+#### Special Groups
+- **PSL(2,5)**: Projective special linear group (order 60)
+- **F20**: Frobenius group F(5,4) (order 20)
+
+### Length Variants
 
-You can load individual datasets or all datasets combined:
+Each group is available with 8 different maximum sequence lengths:
+- 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷, 2⁸, 2⁹ (4, 8, 16, 32, 64, 128, 256, 512)
+
+Each dataset consists of sequences of permutations that need to be composed to produce a target permutation. This is useful for:
+- Training models on algebraic reasoning and symbolic computation
+- Evaluating mathematical understanding and compositional generalization
+- Benchmarking sequence models on structured mathematical tasks
+- Studying group theory properties in neural networks
+- Research in abstract algebra and computational mathematics
+
+## Usage
 
 ```python
 from datasets import load_dataset
 
-# Load a specific dataset
-s3_dataset = load_dataset("BeeGass/permutation-groups", name="s3_data", trust_remote_code=True)
-s7_dataset = load_dataset("BeeGass/permutation-groups", name="s7_data", trust_remote_code=True)
-a7_dataset = load_dataset("BeeGass/permutation-groups", name="a7_data", trust_remote_code=True)
+# Load a specific group with default length (512)
+s5_data = load_dataset("BeeGass/permutation-groups", name="s5_data", trust_remote_code=True)
+
+# Load a specific length variant
+s5_short = load_dataset("BeeGass/permutation-groups", name="s5_len32", trust_remote_code=True)
+
+# Load cyclic group dataset
+c8_data = load_dataset("BeeGass/permutation-groups", name="c8_data", trust_remote_code=True)
+
+# Load dihedral group with specific length
+d4_len64 = load_dataset("BeeGass/permutation-groups", name="d4_len64", trust_remote_code=True)
+
+# Load all groups combined
+all_data = load_dataset("BeeGass/permutation-groups", name="all", trust_remote_code=True)
+
+# Load all groups with specific length
+all_len16 = load_dataset("BeeGass/permutation-groups", name="all_len16", trust_remote_code=True)
+
+# Access the data
+train_data = s5_data["train"]
+test_data = s5_data["test"]
 
-# Load all datasets combined
-all_datasets = load_dataset("BeeGass/permutation-groups", name="all", trust_remote_code=True)
+# Example data point
+print(train_data[0])
+# {'input_sequence': '23 45 12', 'target': '67'}
 ```
 
+## Dataset Structure
+
+Each example contains:
+- `input_sequence`: A space-separated sequence of permutation IDs to be composed
+- `target`: The ID of the resulting permutation after composition
+
+The composition follows standard mathematical convention: for input `[p1, p2, p3]`, the result is `p3 ∘ p2 ∘ p1`.
+
 ## Available Configurations
 
-- `s3_data`: Symmetric Group S3
-- `s4_data`: Symmetric Group S4
-- `s5_data`: Symmetric Group S5
-- `s6_data`: Symmetric Group S6
-- `s7_data`: Symmetric Group S7
-- `a5_data`: Alternating Group A5
-- `a6_data`: Alternating Group A6
-- `a7_data`: Alternating Group A7
-- `all`: All datasets combined
+### Configuration Format
+- Base: `{group}_data` (default length 512)
+- Length variants: `{group}_len{n}` where n ∈ {4, 8, 16, 32, 64, 128, 256, 512}
 
-## Dataset Structure
+### All Groups (30 total)
+| Group | Type | Order | Configurations |
+|-------|------|-------|----------------|
+| S3-S7 | Symmetric | 6-5040 | s3_data, s3_len4, ..., s3_len512 |
+| A3-A7 | Alternating | 3-2520 | a3_data, a3_len4, ..., a3_len512 |
+| C3-C12 | Cyclic | 3-12 | c3_data, c3_len4, ..., c3_len512 |
+| Z3-Z6 | Cyclic (alt) | 3-6 | z3_data, z3_len4, ..., z3_len512 |
+| D3-D8 | Dihedral | 6-16 | d3_data, d3_len4, ..., d3_len512 |
+| PSL25 | PSL(2,5) | 60 | psl25_data, psl25_len4, ..., psl25_len512 |
+| F20 | Frobenius | 20 | f20_data, f20_len4, ..., f20_len512 |
+| all | Combined | - | all, all_len4, ..., all_len512 |
+
+**Total configurations**: 270 (30 groups × 9 length variants)
+
+## Dataset Features
+
+- **Variable sequence length**: Input sequences range from 3 to maximum configured length
+- **Length-specific variants**: 8 different maximum lengths for each group (2² to 2⁹)
+- **Consistent formatting**: All permutations use space-separated integer IDs
+- **Metadata included**: Each dataset includes a `metadata.json` file mapping IDs to permutation array forms
+- **Train/test split**: 80/20 split for all configurations
+- **Scaled sample sizes**: Shorter sequences have more samples for efficient training
+
+## Understanding the Data
 
-Each dataset contains:
-- `input_sequence`: Space-separated sequence of permutation IDs
-- `target`: The ID of the composed permutation
+Each permutation is represented by a unique integer ID. The `metadata.json` file in each dataset folder provides the mapping from IDs to permutation array forms.
+
+For example, in S3:
+- ID 0 might map to `[0, 1, 2]` (identity)
+- ID 1 might map to `[0, 2, 1]` (transpose elements 1 and 2)
+- etc.
+
+## Citation
+
+If you use this dataset in your research, please cite:
+
+```bibtex
+@software{permutation_groups_dataset,
+  author = {Bryan Gass},
+  title = {Permutation Groups Dataset},
+  year = {2024},
+  publisher = {Hugging Face},
+  url = {https://huggingface.co/datasets/BeeGass/permutation-groups}
+}
+```
+
+## Acknowledgments
+
+This dataset was inspired by the work of [William Merrill](https://github.com/viking-sudo-rm) and his paper ["The Illusion of State in State-Space Models"](https://arxiv.org/abs/2404.08819), which explores the computational properties of state-space models through group theory.
 
 ## License
 
-MIT
+This dataset is released under the MIT License.
+
+## Contact
+
+For questions or issues, please open an issue on the [GitHub repository](https://github.com/BeeGass/permutation-groups).