metadata
license: mit
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configs:
- config_name: algebra_func_area
data_files:
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path: algebra_func_area/train-*
- split: test_in
path: algebra_func_area/test_in-*
- split: test_out
path: algebra_func_area/test_out-*
- config_name: algebra_func_derivative_sign
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path: algebra_func_derivative_sign/train-*
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path: algebra_func_derivative_sign/test_in-*
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path: algebra_func_derivative_sign/test_out-*
- config_name: algebra_func_extrema
data_files:
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path: algebra_func_extrema/train-*
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path: algebra_func_extrema/test_in-*
- split: test_out
path: algebra_func_extrema/test_out-*
- config_name: algebra_func_extrema_coords
data_files:
- split: train
path: algebra_func_extrema_coords/train-*
- split: test_in
path: algebra_func_extrema_coords/test_in-*
- split: test_out
path: algebra_func_extrema_coords/test_out-*
- config_name: algebra_func_intersection
data_files:
- split: train
path: algebra_func_intersection/train-*
- split: test_in
path: algebra_func_intersection/test_in-*
- split: test_out
path: algebra_func_intersection/test_out-*
- config_name: algebra_func_intersection_coords
data_files:
- split: train
path: algebra_func_intersection_coords/train-*
- split: test_in
path: algebra_func_intersection_coords/test_in-*
- split: test_out
path: algebra_func_intersection_coords/test_out-*
- config_name: algebra_func_zeros
data_files:
- split: train
path: algebra_func_zeros/train-*
- split: test_in
path: algebra_func_zeros/test_in-*
- split: test_out
path: algebra_func_zeros/test_out-*
- config_name: algebra_linear_equation
data_files:
- split: train
path: algebra_linear_equation/train-*
- split: test_in
path: algebra_linear_equation/test_in-*
- split: test_out
path: algebra_linear_equation/test_out-*
- config_name: algebra_polynomial_roots
data_files:
- split: train
path: algebra_polynomial_roots/train-*
- split: test_in
path: algebra_polynomial_roots/test_in-*
- split: test_out
path: algebra_polynomial_roots/test_out-*
- config_name: arithmetic_gcd
data_files:
- split: train
path: arithmetic_gcd/train-*
- split: test_in
path: arithmetic_gcd/test_in-*
- split: test_out
path: arithmetic_gcd/test_out-*
- config_name: arithmetic_list_prime_factors
data_files:
- split: train
path: arithmetic_list_prime_factors/train-*
- split: test_in
path: arithmetic_list_prime_factors/test_in-*
- split: test_out
path: arithmetic_list_prime_factors/test_out-*
- config_name: arithmetic_mixed
data_files:
- split: train
path: arithmetic_mixed/train-*
- split: test_in
path: arithmetic_mixed/test_in-*
- split: test_out
path: arithmetic_mixed/test_out-*
- config_name: arithmetic_matrix_determinant
data_files:
- split: train
path: arithmetic_matrix_determinant/train-*
- split: test_in
path: arithmetic_matrix_determinant/test_in-*
- split: test_out
path: arithmetic_matrix_determinant/test_out-*
- config_name: arithmetic_matrix_eigenvalues
data_files:
- split: train
path: arithmetic_matrix_eigenvalues/train-*
- split: test_in
path: arithmetic_matrix_eigenvalues/test_in-*
- split: test_out
path: arithmetic_matrix_eigenvalues/test_out-*
- config_name: arithmetic_matrix_inverse
data_files:
- split: train
path: arithmetic_matrix_inverse/train-*
- split: test_in
path: arithmetic_matrix_inverse/test_in-*
- split: test_out
path: arithmetic_matrix_inverse/test_out-*
- config_name: arithmetic_matrix_multiplication
data_files:
- split: train
path: arithmetic_matrix_multiplication/train-*
- split: test_in
path: arithmetic_matrix_multiplication/test_in-*
- split: test_out
path: arithmetic_matrix_multiplication/test_out-*
- config_name: arithmetic_matrix_power
data_files:
- split: train
path: arithmetic_matrix_power/train-*
- split: test_in
path: arithmetic_matrix_power/test_in-*
- split: test_out
path: arithmetic_matrix_power/test_out-*
- config_name: arithmetic_matrix_rank
data_files:
- split: train
path: arithmetic_matrix_rank/train-*
- split: test_in
path: arithmetic_matrix_rank/test_in-*
- split: test_out
path: arithmetic_matrix_rank/test_out-*
- config_name: arithmetic_matrix_svd
data_files:
- split: train
path: arithmetic_matrix_svd/train-*
- split: test_in
path: arithmetic_matrix_svd/test_in-*
- split: test_out
path: arithmetic_matrix_svd/test_out-*
- config_name: combinatory_distribution
data_files:
- split: train
path: combinatory_distribution/train-*
- split: test_in
path: combinatory_distribution/test_in-*
- split: test_out
path: combinatory_distribution/test_out-*
- config_name: combinatory_pattern_matching
data_files:
- split: train
path: combinatory_pattern_matching/train-*
- split: test_in
path: combinatory_pattern_matching/test_in-*
- split: test_out
path: combinatory_pattern_matching/test_out-*
- config_name: combinatory_probability_at_least_n_specific_fixed
data_files:
- split: train
path: combinatory_probability_at_least_n_specific_fixed/train-*
- split: test_in
path: combinatory_probability_at_least_n_specific_fixed/test_in-*
- split: test_out
path: combinatory_probability_at_least_n_specific_fixed/test_out-*
- config_name: combinatory_probability_exactly_n_specific_fixed
data_files:
- split: train
path: combinatory_probability_exactly_n_specific_fixed/train-*
- split: test_in
path: combinatory_probability_exactly_n_specific_fixed/test_in-*
- split: test_out
path: combinatory_probability_exactly_n_specific_fixed/test_out-*
- config_name: combinatory_probability_no_fixed_points
data_files:
- split: train
path: combinatory_probability_no_fixed_points/train-*
- split: test_in
path: combinatory_probability_no_fixed_points/test_in-*
- split: test_out
path: combinatory_probability_no_fixed_points/test_out-*
- config_name: combinatory_probability_no_specific_letter_fixed
data_files:
- split: train
path: combinatory_probability_no_specific_letter_fixed/train-*
- split: test_in
path: combinatory_probability_no_specific_letter_fixed/test_in-*
- split: test_out
path: combinatory_probability_no_specific_letter_fixed/test_out-*
- config_name: geometry_basic
data_files:
- split: train
path: geometry_basic/train-*
- split: test_in
path: geometry_basic/test_in-*
- split: test_out
path: geometry_basic/test_out-*
- config_name: geometry_circle
data_files:
- split: train
path: geometry_circle/train-*
- split: test_in
path: geometry_circle/test_in-*
- split: test_out
path: geometry_circle/test_out-*
- config_name: geometry_perpendicular_intersection
data_files:
- split: train
path: geometry_perpendicular_intersection/train-*
- split: test_in
path: geometry_perpendicular_intersection/test_in-*
- split: test_out
path: geometry_perpendicular_intersection/test_out-*
- config_name: geometry_polygon
data_files:
- split: train
path: geometry_polygon/train-*
- split: test_in
path: geometry_polygon/test_in-*
- split: test_out
path: geometry_polygon/test_out-*
- config_name: geometry_polygon_rotation
data_files:
- split: train
path: geometry_polygon_rotation/train-*
- split: test_in
path: geometry_polygon_rotation/test_in-*
- split: test_out
path: geometry_polygon_rotation/test_out-*
- config_name: geometry_triangle
data_files:
- split: train
path: geometry_triangle/train-*
- split: test_in
path: geometry_triangle/test_in-*
- split: test_out
path: geometry_triangle/test_out-*
- config_name: geometry_polygon_chords
data_files:
- split: train
path: geometry_polygon_chords/train-*
- split: test_in
path: geometry_polygon_chords/test_in-*
- split: test_out
path: geometry_polygon_chords/test_out-*
- config_name: geometry_polygon_color
data_files:
- split: train
path: geometry_polygon_color/train-*
- split: test_in
path: geometry_polygon_color/test_in-*
- split: test_out
path: geometry_polygon_color/test_out-*
- config_name: logic_gridworld_blocked
data_files:
- split: train
path: logic_gridworld_blocked/train-*
- split: test_in
path: logic_gridworld_blocked/test_in-*
- split: test_out
path: logic_gridworld_blocked/test_out-*
- config_name: logic_gridworld_knight_move
data_files:
- split: train
path: logic_gridworld_knight_move/train-*
- split: test_in
path: logic_gridworld_knight_move/test_in-*
- split: test_out
path: logic_gridworld_knight_move/test_out-*
- config_name: logic_gridworld_rookmove
data_files:
- split: train
path: logic_gridworld_rookmove/train-*
- split: test_in
path: logic_gridworld_rookmove/test_in-*
- split: test_out
path: logic_gridworld_rookmove/test_out-*
- config_name: logic_zebralogic
data_files:
- split: train
path: logic_zebralogic/train-*
- split: test_in
path: logic_zebralogic/test_in-*
- split: test_out
path: logic_zebralogic/test_out-*
- config_name: logic_puzzles_grid_chip
data_files:
- split: train
path: logic_puzzles_grid_chip/train-*
- split: test_in
path: logic_puzzles_grid_chip/test_in-*
- split: test_out
path: logic_puzzles_grid_chip/test_out-*
- config_name: numbertheory_lte_qr
data_files:
- split: train
path: numbertheory_lte_qr/train-*
- split: test_in
path: numbertheory_lte_qr/test_in-*
- split: test_out
path: numbertheory_lte_qr/test_out-*
- config_name: numbertheory_ordered_lte
data_files:
- split: train
path: numbertheory_ordered_lte/train-*
- split: test_in
path: numbertheory_ordered_lte/test_in-*
- split: test_out
path: numbertheory_ordered_lte/test_out-*
- config_name: numbertheory_qr_sum
data_files:
- split: train
path: numbertheory_qr_sum/train-*
- split: test_in
path: numbertheory_qr_sum/test_in-*
- split: test_out
path: numbertheory_qr_sum/test_out-*
Explorative Math Problems
This dataset contains explorative mathematical problem settings in paper "OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization" that assess whether a model can faithfully extend a single reasoning strategy beyond the range of complexities seen during training.
Overview
Exploratory generalization assesses whether a model can faithfully extend a single reasoning strategy beyond the range of complexities seen during training. Concretely, the model is exposed to problems drawn from one template, all lying within a "low-complexity" regime, and is then evaluated on harder instances from the same family. This axis probes robustness: does the model generalize the same algorithm to higher complexity problems? or does it merely memorize solutions at a fixed difficulty level?
Each explorative setting consists of:
- Training Dataset: Low-complexity problems from a specific mathematical domain
- Test In-Distribution: Problems of similar complexity to training data (test-in)
- Test Out-of-Distribution: Higher complexity problems from the same domain/template (test-out)
Quick Start
from datasets import load_dataset
# Load all explorative settings
dataset = load_dataset("allenai/omega-explorative")
# Load a specific explorative setting with all splits
func_area_data = load_dataset("allenai/omega-explorative", "algebra_func_area")
train_data = func_area_data["train"] # Low complexity training problems
test_in_data = func_area_data["test_in"] # Similar complexity test problems
test_out_data = func_area_data["test_out"] # Higher complexity test problems
# Load just specific splits
train_only = load_dataset("allenai/omega-explorative", "algebra_func_area", split="train")
test_out_only = load_dataset("allenai/omega-explorative", "algebra_func_area", split="test_out")
Dataset Description
Each explorative setting provides three splits to evaluate different aspects of generalization:
- Train: Low-complexity problems used for training/few-shot learning
- Test-in: Problems of similar complexity to training data (in-distribution evaluation)
- Test-out: Higher complexity problems from the same template (out-of-distribution evaluation)
The key challenge is whether models can extend the same reasoning strategy from low-complexity training problems to higher-complexity test problems in the same domain.
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
- Transformative Dataset: See omega-transformative for transformative reasoning challenges
- Compositional Dataset: See omega-compositional for compositional reasoning challenges
- Paper: See the full details in paper
- Code Repository: See generation code on github