metadata
license: mit
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num_examples: 100
- name: level_5
num_bytes: 9227
num_examples: 100
download_size: 40907
dataset_size: 40907
- config_name: geometry_polygon_color
features:
- name: id
dtype: string
- name: family
dtype: string
- name: difficulty_level
dtype: int64
- name: messages
list:
- name: role
dtype: string
- name: content
dtype: string
- name: ground_truth
dtype: string
- name: dataset
dtype: string
splits:
- name: level_1
num_bytes: 11962
num_examples: 100
- name: level_2
num_bytes: 12716
num_examples: 100
- name: level_3
num_bytes: 13789
num_examples: 100
- name: level_4
num_bytes: 14677
num_examples: 100
- name: level_5
num_bytes: 15388
num_examples: 100
download_size: 68532
dataset_size: 68532
- config_name: number_theory_prime_mod
features:
- name: id
dtype: string
- name: family
dtype: string
- name: difficulty_level
dtype: int64
- name: messages
list:
- name: role
dtype: string
- name: content
dtype: string
- name: ground_truth
dtype: string
- name: dataset
dtype: string
splits:
- name: level_1
num_bytes: 8642
num_examples: 100
- name: level_2
num_bytes: 9036
num_examples: 100
- name: level_3
num_bytes: 8703
num_examples: 100
- name: level_4
num_bytes: 8349
num_examples: 100
- name: level_5
num_bytes: 8441
num_examples: 100
download_size: 43171
dataset_size: 43171
- config_name: logic_puzzles_grid_knight
features:
- name: id
dtype: string
- name: family
dtype: string
- name: difficulty_level
dtype: int64
- name: messages
list:
- name: role
dtype: string
- name: content
dtype: string
- name: ground_truth
dtype: string
- name: dataset
dtype: string
splits:
- name: level_1
num_bytes: 9274
num_examples: 100
- name: level_2
num_bytes: 9573
num_examples: 100
- name: level_3
num_bytes: 9679
num_examples: 100
- name: level_4
num_bytes: 9690
num_examples: 100
- name: level_5
num_bytes: 9713
num_examples: 100
download_size: 47929
dataset_size: 47929
- config_name: geometry_rotation
features:
- name: id
dtype: string
- name: family
dtype: string
- name: difficulty_level
dtype: int64
- name: messages
list:
- name: role
dtype: string
- name: content
dtype: string
- name: ground_truth
dtype: string
- name: dataset
dtype: string
splits:
- name: level_1
num_bytes: 15094
num_examples: 100
- name: level_2
num_bytes: 15790
num_examples: 100
- name: level_3
num_bytes: 16625
num_examples: 100
- name: level_4
num_bytes: 17317
num_examples: 100
- name: level_5
num_bytes: 17934
num_examples: 100
- name: level_6
num_bytes: 10510
num_examples: 10
download_size: 93270
dataset_size: 93270
configs:
- config_name: arithmetic_matrix_rank
data_files:
- split: level_1
path: arithmetic_matrix_rank/level_1-*
- split: level_2
path: arithmetic_matrix_rank/level_2-*
- split: level_3
path: arithmetic_matrix_rank/level_3-*
- split: level_4
path: arithmetic_matrix_rank/level_4-*
- split: level_5
path: arithmetic_matrix_rank/level_5-*
- split: level_6
path: arithmetic_matrix_rank/level_6-*
- split: level_7
path: arithmetic_matrix_rank/level_7-*
- config_name: arithmetic_matrix_multiplication
data_files:
- split: level_1
path: arithmetic_matrix_multiplication/level_1-*
- split: level_2
path: arithmetic_matrix_multiplication/level_2-*
- split: level_3
path: arithmetic_matrix_multiplication/level_3-*
- split: level_4
path: arithmetic_matrix_multiplication/level_4-*
- split: level_5
path: arithmetic_matrix_multiplication/level_5-*
- split: level_6
path: arithmetic_matrix_multiplication/level_6-*
- split: level_7
path: arithmetic_matrix_multiplication/level_7-*
- config_name: algebra_func_derivative_sign
data_files:
- split: level_1
path: algebra_func_derivative_sign/level_1-*
- split: level_2
path: algebra_func_derivative_sign/level_2-*
- split: level_3
path: algebra_func_derivative_sign/level_3-*
- split: level_4
path: algebra_func_derivative_sign/level_4-*
- split: level_5
path: algebra_func_derivative_sign/level_5-*
- config_name: arithmetic_matrix_svd
data_files:
- split: level_1
path: arithmetic_matrix_svd/level_1-*
- split: level_2
path: arithmetic_matrix_svd/level_2-*
- split: level_3
path: arithmetic_matrix_svd/level_3-*
- split: level_4
path: arithmetic_matrix_svd/level_4-*
- split: level_5
path: arithmetic_matrix_svd/level_5-*
- split: level_6
path: arithmetic_matrix_svd/level_6-*
- split: level_7
path: arithmetic_matrix_svd/level_7-*
- config_name: algebra_func_extrema_coords
data_files:
- split: level_1
path: algebra_func_extrema_coords/level_1-*
- split: level_2
path: algebra_func_extrema_coords/level_2-*
- split: level_3
path: algebra_func_extrema_coords/level_3-*
- split: level_4
path: algebra_func_extrema_coords/level_4-*
- split: level_5
path: algebra_func_extrema_coords/level_5-*
- config_name: geometry_polygon_chords
data_files:
- split: level_1
path: geometry_polygon_chords/level_1-*
- split: level_2
path: geometry_polygon_chords/level_2-*
- split: level_3
path: geometry_polygon_chords/level_3-*
- split: level_4
path: geometry_polygon_chords/level_4-*
- split: level_5
path: geometry_polygon_chords/level_5-*
- config_name: logic_puzzles_blocked_grid
data_files:
- split: level_1
path: logic_puzzles_blocked_grid/level_1-*
- split: level_2
path: logic_puzzles_blocked_grid/level_2-*
- split: level_3
path: logic_puzzles_blocked_grid/level_3-*
- split: level_4
path: logic_puzzles_blocked_grid/level_4-*
- split: level_5
path: logic_puzzles_blocked_grid/level_5-*
- config_name: arithmetic_matrix_eigenvalues
data_files:
- split: level_1
path: arithmetic_matrix_eigenvalues/level_1-*
- split: level_2
path: arithmetic_matrix_eigenvalues/level_2-*
- split: level_3
path: arithmetic_matrix_eigenvalues/level_3-*
- split: level_4
path: arithmetic_matrix_eigenvalues/level_4-*
- split: level_5
path: arithmetic_matrix_eigenvalues/level_5-*
- split: level_6
path: arithmetic_matrix_eigenvalues/level_6-*
- split: level_7
path: arithmetic_matrix_eigenvalues/level_7-*
- config_name: algebra_func_intersection
data_files:
- split: level_1
path: algebra_func_intersection/level_1-*
- split: level_2
path: algebra_func_intersection/level_2-*
- split: level_3
path: algebra_func_intersection/level_3-*
- split: level_4
path: algebra_func_intersection/level_4-*
- split: level_5
path: algebra_func_intersection/level_5-*
- config_name: number_theory_digit_sum
data_files:
- split: level_1
path: number_theory_digit_sum/level_1-*
- split: level_2
path: number_theory_digit_sum/level_2-*
- split: level_3
path: number_theory_digit_sum/level_3-*
- split: level_4
path: number_theory_digit_sum/level_4-*
- split: level_5
path: number_theory_digit_sum/level_5-*
- config_name: combinatory_probability_no_specific_letter_fixed
data_files:
- split: level_1
path: combinatory_probability_no_specific_letter_fixed/level_1-*
- split: level_2
path: combinatory_probability_no_specific_letter_fixed/level_2-*
- split: level_3
path: combinatory_probability_no_specific_letter_fixed/level_3-*
- split: level_4
path: combinatory_probability_no_specific_letter_fixed/level_4-*
- split: level_5
path: combinatory_probability_no_specific_letter_fixed/level_5-*
- config_name: combinatory_probability_at_least_n_specific_fixed
data_files:
- split: level_1
path: combinatory_probability_at_least_n_specific_fixed/level_1-*
- split: level_2
path: combinatory_probability_at_least_n_specific_fixed/level_2-*
- split: level_3
path: combinatory_probability_at_least_n_specific_fixed/level_3-*
- split: level_4
path: combinatory_probability_at_least_n_specific_fixed/level_4-*
- split: level_5
path: combinatory_probability_at_least_n_specific_fixed/level_5-*
- config_name: logic_puzzles_grid_rook
data_files:
- split: level_1
path: logic_puzzles_grid_rook/level_1-*
- split: level_2
path: logic_puzzles_grid_rook/level_2-*
- split: level_3
path: logic_puzzles_grid_rook/level_3-*
- split: level_4
path: logic_puzzles_grid_rook/level_4-*
- split: level_5
path: logic_puzzles_grid_rook/level_5-*
- config_name: combinatory_distribution
data_files:
- split: level_1
path: combinatory_distribution/level_1-*
- split: level_2
path: combinatory_distribution/level_2-*
- split: level_3
path: combinatory_distribution/level_3-*
- split: level_4
path: combinatory_distribution/level_4-*
- split: level_5
path: combinatory_distribution/level_5-*
- split: level_6
path: combinatory_distribution/level_6-*
- config_name: arithmetic_mixed
data_files:
- split: level_1
path: arithmetic_mixed/level_1-*
- split: level_2
path: arithmetic_mixed/level_2-*
- split: level_3
path: arithmetic_mixed/level_3-*
- split: level_4
path: arithmetic_mixed/level_4-*
- split: level_5
path: arithmetic_mixed/level_5-*
- config_name: arithmetic_matrix_determinant
data_files:
- split: level_1
path: arithmetic_matrix_determinant/level_1-*
- split: level_2
path: arithmetic_matrix_determinant/level_2-*
- split: level_3
path: arithmetic_matrix_determinant/level_3-*
- split: level_4
path: arithmetic_matrix_determinant/level_4-*
- split: level_5
path: arithmetic_matrix_determinant/level_5-*
- split: level_6
path: arithmetic_matrix_determinant/level_6-*
- split: level_7
path: arithmetic_matrix_determinant/level_7-*
- config_name: algebra_linear_equation
data_files:
- split: level_1
path: algebra_linear_equation/level_1-*
- split: level_2
path: algebra_linear_equation/level_2-*
- split: level_3
path: algebra_linear_equation/level_3-*
- split: level_4
path: algebra_linear_equation/level_4-*
- split: level_5
path: algebra_linear_equation/level_5-*
- config_name: logic_puzzles_grid_chip
data_files:
- split: level_1
path: logic_puzzles_grid_chip/level_1-*
- split: level_2
path: logic_puzzles_grid_chip/level_2-*
- split: level_3
path: logic_puzzles_grid_chip/level_3-*
- split: level_4
path: logic_puzzles_grid_chip/level_4-*
- split: level_5
path: logic_puzzles_grid_chip/level_5-*
- config_name: arithmetic_gcd
data_files:
- split: level_1
path: arithmetic_gcd/level_1-*
- split: level_2
path: arithmetic_gcd/level_2-*
- split: level_3
path: arithmetic_gcd/level_3-*
- split: level_4
path: arithmetic_gcd/level_4-*
- split: level_5
path: arithmetic_gcd/level_5-*
- config_name: arithmetic_list_prime_factors
data_files:
- split: level_1
path: arithmetic_list_prime_factors/level_1-*
- split: level_2
path: arithmetic_list_prime_factors/level_2-*
- split: level_3
path: arithmetic_list_prime_factors/level_3-*
- split: level_4
path: arithmetic_list_prime_factors/level_4-*
- split: level_5
path: arithmetic_list_prime_factors/level_5-*
- config_name: logic_puzzles_zebralogic
data_files:
- split: level_1
path: logic_puzzles_zebralogic/level_1-*
- split: level_2
path: logic_puzzles_zebralogic/level_2-*
- split: level_3
path: logic_puzzles_zebralogic/level_3-*
- split: level_4
path: logic_puzzles_zebralogic/level_4-*
- split: level_5
path: logic_puzzles_zebralogic/level_5-*
- config_name: arithmetic_matrix_inverse
data_files:
- split: level_1
path: arithmetic_matrix_inverse/level_1-*
- split: level_2
path: arithmetic_matrix_inverse/level_2-*
- split: level_3
path: arithmetic_matrix_inverse/level_3-*
- split: level_4
path: arithmetic_matrix_inverse/level_4-*
- split: level_5
path: arithmetic_matrix_inverse/level_5-*
- split: level_6
path: arithmetic_matrix_inverse/level_6-*
- split: level_7
path: arithmetic_matrix_inverse/level_7-*
- config_name: algebra_func_extrema
data_files:
- split: level_1
path: algebra_func_extrema/level_1-*
- split: level_2
path: algebra_func_extrema/level_2-*
- split: level_3
path: algebra_func_extrema/level_3-*
- split: level_4
path: algebra_func_extrema/level_4-*
- split: level_5
path: algebra_func_extrema/level_5-*
- config_name: algebra_func_zeros
data_files:
- split: level_1
path: algebra_func_zeros/level_1-*
- split: level_2
path: algebra_func_zeros/level_2-*
- split: level_3
path: algebra_func_zeros/level_3-*
- split: level_4
path: algebra_func_zeros/level_4-*
- split: level_5
path: algebra_func_zeros/level_5-*
- config_name: arithmetic_matrix_power
data_files:
- split: level_1
path: arithmetic_matrix_power/level_1-*
- split: level_2
path: arithmetic_matrix_power/level_2-*
- split: level_3
path: arithmetic_matrix_power/level_3-*
- split: level_4
path: arithmetic_matrix_power/level_4-*
- split: level_5
path: arithmetic_matrix_power/level_5-*
- split: level_6
path: arithmetic_matrix_power/level_6-*
- split: level_7
path: arithmetic_matrix_power/level_7-*
- config_name: combinatory_pattern_matching
data_files:
- split: level_1
path: combinatory_pattern_matching/level_1-*
- split: level_2
path: combinatory_pattern_matching/level_2-*
- split: level_3
path: combinatory_pattern_matching/level_3-*
- split: level_4
path: combinatory_pattern_matching/level_4-*
- split: level_5
path: combinatory_pattern_matching/level_5-*
- config_name: algebra_func_area
data_files:
- split: level_1
path: algebra_func_area/level_1-*
- split: level_2
path: algebra_func_area/level_2-*
- split: level_3
path: algebra_func_area/level_3-*
- split: level_4
path: algebra_func_area/level_4-*
- split: level_5
path: algebra_func_area/level_5-*
- config_name: algebra_func_intersection_coords
data_files:
- split: level_1
path: algebra_func_intersection_coords/level_1-*
- split: level_2
path: algebra_func_intersection_coords/level_2-*
- split: level_3
path: algebra_func_intersection_coords/level_3-*
- split: level_4
path: algebra_func_intersection_coords/level_4-*
- split: level_5
path: algebra_func_intersection_coords/level_5-*
- config_name: combinatory_probability_exactly_n_specific_fixed
data_files:
- split: level_1
path: combinatory_probability_exactly_n_specific_fixed/level_1-*
- split: level_2
path: combinatory_probability_exactly_n_specific_fixed/level_2-*
- split: level_3
path: combinatory_probability_exactly_n_specific_fixed/level_3-*
- split: level_4
path: combinatory_probability_exactly_n_specific_fixed/level_4-*
- split: level_5
path: combinatory_probability_exactly_n_specific_fixed/level_5-*
- config_name: combinatory_probability_no_fixed_points
data_files:
- split: level_1
path: combinatory_probability_no_fixed_points/level_1-*
- split: level_2
path: combinatory_probability_no_fixed_points/level_2-*
- split: level_3
path: combinatory_probability_no_fixed_points/level_3-*
- split: level_4
path: combinatory_probability_no_fixed_points/level_4-*
- split: level_5
path: combinatory_probability_no_fixed_points/level_5-*
- config_name: number_theory_triple_count
data_files:
- split: level_1
path: number_theory_triple_count/level_1-*
- split: level_2
path: number_theory_triple_count/level_2-*
- split: level_3
path: number_theory_triple_count/level_3-*
- split: level_4
path: number_theory_triple_count/level_4-*
- split: level_5
path: number_theory_triple_count/level_5-*
- config_name: geometry_polygon_color
data_files:
- split: level_1
path: geometry_polygon_color/level_1-*
- split: level_2
path: geometry_polygon_color/level_2-*
- split: level_3
path: geometry_polygon_color/level_3-*
- split: level_4
path: geometry_polygon_color/level_4-*
- split: level_5
path: geometry_polygon_color/level_5-*
- config_name: number_theory_prime_mod
data_files:
- split: level_1
path: number_theory_prime_mod/level_1-*
- split: level_2
path: number_theory_prime_mod/level_2-*
- split: level_3
path: number_theory_prime_mod/level_3-*
- split: level_4
path: number_theory_prime_mod/level_4-*
- split: level_5
path: number_theory_prime_mod/level_5-*
- config_name: logic_puzzles_grid_knight
data_files:
- split: level_1
path: logic_puzzles_grid_knight/level_1-*
- split: level_2
path: logic_puzzles_grid_knight/level_2-*
- split: level_3
path: logic_puzzles_grid_knight/level_3-*
- split: level_4
path: logic_puzzles_grid_knight/level_4-*
- split: level_5
path: logic_puzzles_grid_knight/level_5-*
- config_name: geometry_rotation
data_files:
- split: level_1
path: geometry_rotation/level_1-*
- split: level_2
path: geometry_rotation/level_2-*
- split: level_3
path: geometry_rotation/level_3-*
- split: level_4
path: geometry_rotation/level_4-*
- split: level_5
path: geometry_rotation/level_5-*
- split: level_6
path: geometry_rotation/level_6-*
Mathematical Problem Families by Difficulty
This dataset contains mathematical problems organized by problem families, with each family spanning multiple difficulty levels. This organization allows for studying how mathematical reasoning scales with problem complexity within specific mathematical domains.
Overview
Each problem family represents a specific type of mathematical problem (e.g., function area calculation, matrix operations, probability calculations) with problems spanning multiple difficulty levels. This structure enables researchers to study:
- Difficulty Scaling: How mathematical reasoning changes as problems become more complex
- Domain-Specific Learning: How models learn within specific mathematical areas
- Progressive Training: Training on easier levels and testing on harder ones
- Curriculum Learning: Gradually increasing difficulty within problem types
Quick Start
from datasets import load_dataset
# Load all problem families
dataset = load_dataset("allenai/omega-prob-families")
# Load a specific problem family with all difficulty levels
func_area_data = load_dataset("allenai/omega-prob-families", "algebra_func_area")
level_1_data = func_area_data["level_1"] # Easiest problems
level_5_data = func_area_data["level_5"] # Hardest problems
# Load just a specific difficulty level
level_3_only = load_dataset("allenai/omega-prob-families", "algebra_func_area", split="level_3")
# Get all available families
available_families = list(dataset.keys())
print(f"Available families: {available_families}")
Dataset Description
Each problem family contains exactly 100 problems per difficulty level (or fewer if the original file contained fewer than 100), allowing for systematic study of how mathematical reasoning scales with complexity. The families cover various mathematical domains including:
- Algebra: Function analysis, polynomial operations, linear equations
- Arithmetic: Matrix operations, number theory, basic calculations
- Geometry: Shape analysis, transformations, spatial reasoning
- Combinatorics: Probability, pattern matching, counting problems
- Logic: Grid-based puzzles, constraint satisfaction
Family Structure
Each family is organized as:
- Family Name: Descriptive identifier (e.g.,
algebra_func_area) - Difficulty Levels: Progressive levels from 1 (easiest) to N (hardest)
- Problem Count: Exactly 100 problems per level (or fewer if original file had fewer)
- Consistent Format: Same problem type across all levels, increasing in complexity
Citation
If you use this dataset, please cite the original 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
- 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