---
license: mit
dataset_info:
- config_name: default
  features:
  - name: id
    dtype: string
  - name: original_id
    dtype: string
  - name: family
    dtype: string
  - name: difficulty_level
    dtype: int64
  - name: source_family
    dtype: string
  - name: source_level
    dtype: string
  - name: messages
    list:
    - name: role
      dtype: string
    - name: content
      dtype: string
  - name: ground_truth
    dtype: string
  - name: dataset
    dtype: string
  splits:
  - name: train
    num_bytes: 106157
    num_examples: 500
  download_size: 106157
  dataset_size: 106157
configs:
- config_name: default
  data_files:
  - split: train
    path: train-*
---

# Omega-500: Random Sample of Mathematical Problems

This dataset contains a random sample of 500 mathematical problems selected from the comprehensive OMEGA problem families dataset. It provides a diverse, manageable subset for quick evaluation and experimentation across multiple mathematical domains and difficulty levels.

## Overview

Omega-500 is designed for:
- **Quick Evaluation**: Fast assessment of model capabilities across math domains
- **Prototyping**: Testing new approaches before scaling to larger datasets  
- **Benchmarking**: Standardized subset for fair model comparisons
- **Research**: Focused analysis on a balanced mathematical problem set

The sample maintains diversity across mathematical domains and difficulty levels while keeping the dataset size manageable for rapid iteration.

## Quick Start

```python
from datasets import load_dataset

# Load the Omega-500 sample
dataset = load_dataset("sunyiyou/omega-500")
problems = dataset["train"]

# Access individual problems
first_problem = problems[0]
print("Problem:", first_problem["messages"][0]["content"])
print("Answer:", first_problem["ground_truth"])
print("Family:", first_problem["family"])
print("Difficulty:", first_problem["difficulty_level"])
```

## Dataset Composition

### Total Problems: 500

### Domain Distribution:
- **Algebra**: 106 problems (21.2%)
- **Arithmetic**: 171 problems (34.2%)
- **Combinatorics**: 70 problems (14.0%)
- **Geometry**: 37 problems (7.4%)
- **Logic**: 76 problems (15.2%)
- **Number Theory**: 40 problems (8.0%)


# ### Problem Families Included: 35
# - **algebra_func_area**: 15 problems
- **algebra_func_derivative_sign**: 19 problems
- **algebra_func_extrema**: 9 problems
- **algebra_func_extrema_coords**: 15 problems
- **algebra_func_intersection**: 16 problems
- **algebra_func_intersection_coords**: 11 problems
- **algebra_func_zeros**: 11 problems
- **algebra_linear_equation**: 10 problems
- **arithmetic_gcd**: 11 problems
- **arithmetic_list_prime_factors**: 17 problems
- **arithmetic_matrix_determinant**: 19 problems
- **arithmetic_matrix_eigenvalues**: 24 problems
- **arithmetic_matrix_inverse**: 19 problems
- **arithmetic_matrix_multiplication**: 20 problems
- **arithmetic_matrix_power**: 21 problems
- **arithmetic_matrix_rank**: 14 problems
- **arithmetic_matrix_svd**: 16 problems
- **arithmetic_mixed**: 10 problems
- **combinatory_distribution**: 9 problems
- **combinatory_pattern_matching**: 14 problems
- **combinatory_probability_at_least_n_specific_fixed**: 13 problems
- **combinatory_probability_exactly_n_specific_fixed**: 9 problems
- **combinatory_probability_no_fixed_points**: 13 problems
- **combinatory_probability_no_specific_letter_fixed**: 12 problems
- **geometry_polygon_chords**: 11 problems
- **geometry_polygon_color**: 12 problems
- **geometry_rotation**: 14 problems
- **logic_puzzles_blocked_grid**: 18 problems
- **logic_puzzles_grid_chip**: 21 problems
- **logic_puzzles_grid_knight**: 15 problems
- **logic_puzzles_grid_rook**: 13 problems
- **logic_puzzles_zebralogic**: 9 problems
- **number_theory_digit_sum**: 12 problems
- **number_theory_prime_mod**: 18 problems
- **number_theory_triple_count**: 10 problems


### Sampling Method
- **Source**: Randomly sampled from the complete OMEGA problem families dataset
- **Seed**: Fixed random seed (42) for reproducibility  
- **Strategy**: Simple random sampling across all families and difficulty levels
- **Balance**: Natural distribution reflecting the diversity of the source dataset

## Use Cases

1. **Model Evaluation**: Quick assessment of mathematical reasoning capabilities
2. **Method Development**: Testing new prompting or fine-tuning approaches
3. **Comparative Studies**: Standardized benchmark for fair model comparison
4. **Educational**: Learning about mathematical problem types and difficulties
5. **Debugging**: Smaller dataset for faster debugging and iteration

## Data Fields

Each problem contains:
- `id`: Unique identifier for this sample
- `original_id`: Original identifier from source dataset
- `family`: Problem family (e.g., "algebra_func_area")
- `difficulty_level`: Numeric difficulty level from source
- `source_family`: Source family directory name
- `source_level`: Source difficulty level name
- `messages`: Problem statement in chat format
- `ground_truth`: Correct answer
- `dataset`: Dataset identifier ("OMEGA_500_SAMPLE")

## Citation

If you use this dataset, please cite the original OMEGA work:

```bibtex
@article{sun2024omega,
  title     = {OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization},
  author    = {Yiyou Sun and Shawn Hu and Georgia Zhou and Ken Zheng and Hannaneh Hajishirzi and Nouha Dziri and Dawn Song},
  journal   = {arXiv preprint arXiv:2506.18880},
  year      = {2024},
}
```

## Related Resources

- **Full Problem Families**: See [omega-prob-families](https://huggingface.co/datasets/sunyiyou/omega-prob-families) for the complete dataset
- **Explorative Dataset**: See [omega-explorative](https://huggingface.co/datasets/sunyiyou/omega-explorative) for explorative reasoning challenges
- **Compositional Dataset**: See [omega-compositional](https://huggingface.co/datasets/sunyiyou/omega-compositional) for compositional reasoning challenges  
- **Transformative Dataset**: See [omega-transformative](https://huggingface.co/datasets/sunyiyou/omega-transformative) for transformative reasoning challenges
- **Paper**: See the full details in [paper](https://arxiv.org/pdf/2506.18880)
- **Code Repository**: See generation code on [github](https://github.com/sunblaze-ucb/math_ood)