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README.md

@@ -1,41 +1,181 @@
-# Permutation Groups Datasets
+---
+license: mit
+task_categories:
+- text-generation
+language:
+- en
+tags:
+- mathematics
+- group-theory
+- permutations
+- symbolic-reasoning
+pretty_name: Permutation Groups Dataset
+size_categories:
+- 100K<n<1M
+configs:
+- config_name: s3_data
+  data_files:
+    - split: train
+      path: data/s3_data/train/*
+    - split: test
+      path: data/s3_data/test/*
+- config_name: s4_data
+  data_files:
+    - split: train
+      path: data/s4_data/train/*
+    - split: test
+      path: data/s4_data/test/*
+- config_name: s5_data
+  data_files:
+    - split: train
+      path: data/s5_data/train/*
+    - split: test
+      path: data/s5_data/test/*
+- config_name: s6_data
+  data_files:
+    - split: train
+      path: data/s6_data/train/*
+    - split: test
+      path: data/s6_data/test/*
+- config_name: s7_data
+  data_files:
+    - split: train
+      path: data/s7_data/train/*
+    - split: test
+      path: data/s7_data/test/*
+- config_name: a3_data
+  data_files:
+    - split: train
+      path: data/a3_data/train/*
+    - split: test
+      path: data/a3_data/test/*
+- config_name: a4_data
+  data_files:
+    - split: train
+      path: data/a4_data/train/*
+    - split: test
+      path: data/a4_data/test/*
+- config_name: a5_data
+  data_files:
+    - split: train
+      path: data/a5_data/train/*
+    - split: test
+      path: data/a5_data/test/*
+- config_name: a6_data
+  data_files:
+    - split: train
+      path: data/a6_data/train/*
+    - split: test
+      path: data/a6_data/test/*
+- config_name: a7_data
+  data_files:
+    - split: train
+      path: data/a7_data/train/*
+    - split: test
+      path: data/a7_data/test/*
+---
 
-This repository contains permutation composition datasets for various symmetric and alternating groups.
+# Permutation Groups Dataset
 
-## Usage
+A comprehensive collection of permutation composition datasets for symmetric and alternating groups, designed for training and evaluating models on group theory operations.
+
+## Dataset Description
+
+This dataset contains permutation composition problems for various mathematical groups:
+- **Symmetric Groups**: S3, S4, S5, S6, S7
+- **Alternating Groups**: A3, A4, A5, A6, A7
 
-You can load individual datasets or all datasets combined:
+Each dataset consists of sequences of permutations that need to be composed to produce a target permutation. This is useful for:
+- Training models on symbolic reasoning
+- Evaluating mathematical understanding
+- Testing compositional generalization
+- Studying group theory properties in neural networks
+
+## 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 dataset
+s5_dataset = load_dataset("BeeGass/permutation-groups", name="s5_data", trust_remote_code=True)
+
+# Load alternating group A5
+a5_dataset = load_dataset("BeeGass/permutation-groups", name="a5_data", trust_remote_code=True)
 
 # Load all datasets combined
 all_datasets = load_dataset("BeeGass/permutation-groups", name="all", trust_remote_code=True)
+
+# Access the data
+train_data = s5_dataset["train"]
+test_data = s5_dataset["test"]
+
+# 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 | Group Type | Group Order | Elements | Train Samples | Test Samples |
+|--------------|------------|-------------|----------|---------------|--------------|
+| `s3_data` | Symmetric | S3 | 6 | 8,000 | 2,000 |
+| `s4_data` | Symmetric | S4 | 24 | 16,000 | 4,000 |
+| `s5_data` | Symmetric | S5 | 120 | 40,000 | 10,000 |
+| `s6_data` | Symmetric | S6 | 720 | 80,000 | 20,000 |
+| `s7_data` | Symmetric | S7 | 5,040 | 160,000 | 40,000 |
+| `a3_data` | Alternating | A3 | 3 | 4,000 | 1,000 |
+| `a4_data` | Alternating | A4 | 12 | 12,000 | 3,000 |
+| `a5_data` | Alternating | A5 | 60 | 24,000 | 6,000 |
+| `a6_data` | Alternating | A6 | 360 | 64,000 | 16,000 |
+| `a7_data` | Alternating | A7 | 2,520 | 120,000 | 30,000 |
+| `all` | Combined | - | - | 528,000 | 132,000 |
 
-## Dataset Structure
+## Dataset Features
+
+- **Variable sequence length**: Input sequences range from 3 to 512 permutations
+- **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
+
+## Understanding the Data
+
+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
 
-Each dataset contains:
-- `input_sequence`: Space-separated sequence of permutation IDs
-- `target`: The ID of the composed permutation
+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).