README.md

metadata

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

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:

@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 for the complete dataset
• Explorative Dataset: See omega-explorative for explorative reasoning challenges
• Compositional Dataset: See omega-compositional for compositional reasoning challenges
• Transformative Dataset: See omega-transformative for transformative reasoning challenges
• Paper: See the full details in paper
• Code Repository: See generation code on github