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README.md

@@ -1,161 +1,41 @@
----
-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
----
+# Permutation Groups Datasets
 
-# Permutation Groups Composition Dataset
-
-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
-
-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
+This repository contains permutation composition datasets for various symmetric and alternating groups.
 
 ## Usage
 
+You can load individual datasets or all datasets combined:
+
 ```python
 from datasets import load_dataset
 
-# 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 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)
 
-# Example data point
-print(train_data[0])
-# {'input_sequence': '23 45 12', 'target': '67'}
+# Load all datasets combined
+all_datasets = load_dataset("BeeGass/permutation-groups", name="all", trust_remote_code=True)
 ```
 
-## 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
 
-### Configuration Format
-- Base: `{group}_data` (default length 512)
-- Length variants: `{group}_len{n}` where n ∈ {4, 8, 16, 32, 64, 128, 256, 512}
-
-### 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
+- `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
 
-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
+## Dataset Structure
 
-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.
+Each dataset contains:
+- `input_sequence`: Space-separated sequence of permutation IDs
+- `target`: The ID of the composed permutation
 
 ## License
 
-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).
+MIT