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- README.md +1839 -0
- algebra_func_area/level_1-00000-of-00001.parquet +3 -0
- algebra_func_area/level_2-00000-of-00001.parquet +3 -0
- algebra_func_area/level_3-00000-of-00001.parquet +3 -0
- algebra_func_area/level_4-00000-of-00001.parquet +3 -0
- algebra_func_area/level_5-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/level_1-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/level_2-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/level_3-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/level_4-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/level_5-00000-of-00001.parquet +3 -0
- algebra_func_extrema/level_1-00000-of-00001.parquet +3 -0
- algebra_func_extrema/level_2-00000-of-00001.parquet +3 -0
- algebra_func_extrema/level_3-00000-of-00001.parquet +3 -0
- algebra_func_extrema/level_4-00000-of-00001.parquet +3 -0
- algebra_func_extrema/level_5-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/level_1-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/level_2-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/level_3-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/level_4-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/level_5-00000-of-00001.parquet +3 -0
- algebra_func_intersection/level_1-00000-of-00001.parquet +3 -0
- algebra_func_intersection/level_2-00000-of-00001.parquet +3 -0
- algebra_func_intersection/level_3-00000-of-00001.parquet +3 -0
- algebra_func_intersection/level_4-00000-of-00001.parquet +3 -0
- algebra_func_intersection/level_5-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/level_1-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/level_2-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/level_3-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/level_4-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/level_5-00000-of-00001.parquet +3 -0
- algebra_func_zeros/level_1-00000-of-00001.parquet +3 -0
- algebra_func_zeros/level_2-00000-of-00001.parquet +3 -0
- algebra_func_zeros/level_3-00000-of-00001.parquet +3 -0
- algebra_func_zeros/level_4-00000-of-00001.parquet +3 -0
- algebra_func_zeros/level_5-00000-of-00001.parquet +3 -0
- algebra_linear_equation/level_1-00000-of-00001.parquet +3 -0
- algebra_linear_equation/level_2-00000-of-00001.parquet +3 -0
- algebra_linear_equation/level_3-00000-of-00001.parquet +3 -0
- algebra_linear_equation/level_4-00000-of-00001.parquet +3 -0
- algebra_linear_equation/level_5-00000-of-00001.parquet +3 -0
- arithmetic_gcd/level_1-00000-of-00001.parquet +3 -0
- arithmetic_gcd/level_2-00000-of-00001.parquet +3 -0
- arithmetic_gcd/level_3-00000-of-00001.parquet +3 -0
- arithmetic_gcd/level_4-00000-of-00001.parquet +3 -0
- arithmetic_gcd/level_5-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/level_1-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/level_2-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/level_3-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/level_4-00000-of-00001.parquet +3 -0
README.md
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1 |
+
---
|
2 |
+
license: mit
|
3 |
+
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|
1561 |
+
- split: level_5
|
1562 |
+
path: arithmetic_gcd/level_5-*
|
1563 |
+
- config_name: arithmetic_list_prime_factors
|
1564 |
+
data_files:
|
1565 |
+
- split: level_1
|
1566 |
+
path: arithmetic_list_prime_factors/level_1-*
|
1567 |
+
- split: level_2
|
1568 |
+
path: arithmetic_list_prime_factors/level_2-*
|
1569 |
+
- split: level_3
|
1570 |
+
path: arithmetic_list_prime_factors/level_3-*
|
1571 |
+
- split: level_4
|
1572 |
+
path: arithmetic_list_prime_factors/level_4-*
|
1573 |
+
- split: level_5
|
1574 |
+
path: arithmetic_list_prime_factors/level_5-*
|
1575 |
+
- config_name: logic_puzzles_zebralogic
|
1576 |
+
data_files:
|
1577 |
+
- split: level_1
|
1578 |
+
path: logic_puzzles_zebralogic/level_1-*
|
1579 |
+
- split: level_2
|
1580 |
+
path: logic_puzzles_zebralogic/level_2-*
|
1581 |
+
- split: level_3
|
1582 |
+
path: logic_puzzles_zebralogic/level_3-*
|
1583 |
+
- split: level_4
|
1584 |
+
path: logic_puzzles_zebralogic/level_4-*
|
1585 |
+
- split: level_5
|
1586 |
+
path: logic_puzzles_zebralogic/level_5-*
|
1587 |
+
- config_name: arithmetic_matrix_inverse
|
1588 |
+
data_files:
|
1589 |
+
- split: level_1
|
1590 |
+
path: arithmetic_matrix_inverse/level_1-*
|
1591 |
+
- split: level_2
|
1592 |
+
path: arithmetic_matrix_inverse/level_2-*
|
1593 |
+
- split: level_3
|
1594 |
+
path: arithmetic_matrix_inverse/level_3-*
|
1595 |
+
- split: level_4
|
1596 |
+
path: arithmetic_matrix_inverse/level_4-*
|
1597 |
+
- split: level_5
|
1598 |
+
path: arithmetic_matrix_inverse/level_5-*
|
1599 |
+
- split: level_6
|
1600 |
+
path: arithmetic_matrix_inverse/level_6-*
|
1601 |
+
- split: level_7
|
1602 |
+
path: arithmetic_matrix_inverse/level_7-*
|
1603 |
+
- config_name: algebra_func_extrema
|
1604 |
+
data_files:
|
1605 |
+
- split: level_1
|
1606 |
+
path: algebra_func_extrema/level_1-*
|
1607 |
+
- split: level_2
|
1608 |
+
path: algebra_func_extrema/level_2-*
|
1609 |
+
- split: level_3
|
1610 |
+
path: algebra_func_extrema/level_3-*
|
1611 |
+
- split: level_4
|
1612 |
+
path: algebra_func_extrema/level_4-*
|
1613 |
+
- split: level_5
|
1614 |
+
path: algebra_func_extrema/level_5-*
|
1615 |
+
- config_name: algebra_func_zeros
|
1616 |
+
data_files:
|
1617 |
+
- split: level_1
|
1618 |
+
path: algebra_func_zeros/level_1-*
|
1619 |
+
- split: level_2
|
1620 |
+
path: algebra_func_zeros/level_2-*
|
1621 |
+
- split: level_3
|
1622 |
+
path: algebra_func_zeros/level_3-*
|
1623 |
+
- split: level_4
|
1624 |
+
path: algebra_func_zeros/level_4-*
|
1625 |
+
- split: level_5
|
1626 |
+
path: algebra_func_zeros/level_5-*
|
1627 |
+
- config_name: arithmetic_matrix_power
|
1628 |
+
data_files:
|
1629 |
+
- split: level_1
|
1630 |
+
path: arithmetic_matrix_power/level_1-*
|
1631 |
+
- split: level_2
|
1632 |
+
path: arithmetic_matrix_power/level_2-*
|
1633 |
+
- split: level_3
|
1634 |
+
path: arithmetic_matrix_power/level_3-*
|
1635 |
+
- split: level_4
|
1636 |
+
path: arithmetic_matrix_power/level_4-*
|
1637 |
+
- split: level_5
|
1638 |
+
path: arithmetic_matrix_power/level_5-*
|
1639 |
+
- split: level_6
|
1640 |
+
path: arithmetic_matrix_power/level_6-*
|
1641 |
+
- split: level_7
|
1642 |
+
path: arithmetic_matrix_power/level_7-*
|
1643 |
+
- config_name: combinatory_pattern_matching
|
1644 |
+
data_files:
|
1645 |
+
- split: level_1
|
1646 |
+
path: combinatory_pattern_matching/level_1-*
|
1647 |
+
- split: level_2
|
1648 |
+
path: combinatory_pattern_matching/level_2-*
|
1649 |
+
- split: level_3
|
1650 |
+
path: combinatory_pattern_matching/level_3-*
|
1651 |
+
- split: level_4
|
1652 |
+
path: combinatory_pattern_matching/level_4-*
|
1653 |
+
- split: level_5
|
1654 |
+
path: combinatory_pattern_matching/level_5-*
|
1655 |
+
- config_name: algebra_func_area
|
1656 |
+
data_files:
|
1657 |
+
- split: level_1
|
1658 |
+
path: algebra_func_area/level_1-*
|
1659 |
+
- split: level_2
|
1660 |
+
path: algebra_func_area/level_2-*
|
1661 |
+
- split: level_3
|
1662 |
+
path: algebra_func_area/level_3-*
|
1663 |
+
- split: level_4
|
1664 |
+
path: algebra_func_area/level_4-*
|
1665 |
+
- split: level_5
|
1666 |
+
path: algebra_func_area/level_5-*
|
1667 |
+
- config_name: algebra_func_intersection_coords
|
1668 |
+
data_files:
|
1669 |
+
- split: level_1
|
1670 |
+
path: algebra_func_intersection_coords/level_1-*
|
1671 |
+
- split: level_2
|
1672 |
+
path: algebra_func_intersection_coords/level_2-*
|
1673 |
+
- split: level_3
|
1674 |
+
path: algebra_func_intersection_coords/level_3-*
|
1675 |
+
- split: level_4
|
1676 |
+
path: algebra_func_intersection_coords/level_4-*
|
1677 |
+
- split: level_5
|
1678 |
+
path: algebra_func_intersection_coords/level_5-*
|
1679 |
+
- config_name: combinatory_probability_exactly_n_specific_fixed
|
1680 |
+
data_files:
|
1681 |
+
- split: level_1
|
1682 |
+
path: combinatory_probability_exactly_n_specific_fixed/level_1-*
|
1683 |
+
- split: level_2
|
1684 |
+
path: combinatory_probability_exactly_n_specific_fixed/level_2-*
|
1685 |
+
- split: level_3
|
1686 |
+
path: combinatory_probability_exactly_n_specific_fixed/level_3-*
|
1687 |
+
- split: level_4
|
1688 |
+
path: combinatory_probability_exactly_n_specific_fixed/level_4-*
|
1689 |
+
- split: level_5
|
1690 |
+
path: combinatory_probability_exactly_n_specific_fixed/level_5-*
|
1691 |
+
- config_name: combinatory_probability_no_fixed_points
|
1692 |
+
data_files:
|
1693 |
+
- split: level_1
|
1694 |
+
path: combinatory_probability_no_fixed_points/level_1-*
|
1695 |
+
- split: level_2
|
1696 |
+
path: combinatory_probability_no_fixed_points/level_2-*
|
1697 |
+
- split: level_3
|
1698 |
+
path: combinatory_probability_no_fixed_points/level_3-*
|
1699 |
+
- split: level_4
|
1700 |
+
path: combinatory_probability_no_fixed_points/level_4-*
|
1701 |
+
- split: level_5
|
1702 |
+
path: combinatory_probability_no_fixed_points/level_5-*
|
1703 |
+
- config_name: number_theory_triple_count
|
1704 |
+
data_files:
|
1705 |
+
- split: level_1
|
1706 |
+
path: number_theory_triple_count/level_1-*
|
1707 |
+
- split: level_2
|
1708 |
+
path: number_theory_triple_count/level_2-*
|
1709 |
+
- split: level_3
|
1710 |
+
path: number_theory_triple_count/level_3-*
|
1711 |
+
- split: level_4
|
1712 |
+
path: number_theory_triple_count/level_4-*
|
1713 |
+
- split: level_5
|
1714 |
+
path: number_theory_triple_count/level_5-*
|
1715 |
+
- config_name: geometry_polygon_color
|
1716 |
+
data_files:
|
1717 |
+
- split: level_1
|
1718 |
+
path: geometry_polygon_color/level_1-*
|
1719 |
+
- split: level_2
|
1720 |
+
path: geometry_polygon_color/level_2-*
|
1721 |
+
- split: level_3
|
1722 |
+
path: geometry_polygon_color/level_3-*
|
1723 |
+
- split: level_4
|
1724 |
+
path: geometry_polygon_color/level_4-*
|
1725 |
+
- split: level_5
|
1726 |
+
path: geometry_polygon_color/level_5-*
|
1727 |
+
- config_name: number_theory_prime_mod
|
1728 |
+
data_files:
|
1729 |
+
- split: level_1
|
1730 |
+
path: number_theory_prime_mod/level_1-*
|
1731 |
+
- split: level_2
|
1732 |
+
path: number_theory_prime_mod/level_2-*
|
1733 |
+
- split: level_3
|
1734 |
+
path: number_theory_prime_mod/level_3-*
|
1735 |
+
- split: level_4
|
1736 |
+
path: number_theory_prime_mod/level_4-*
|
1737 |
+
- split: level_5
|
1738 |
+
path: number_theory_prime_mod/level_5-*
|
1739 |
+
- config_name: logic_puzzles_grid_knight
|
1740 |
+
data_files:
|
1741 |
+
- split: level_1
|
1742 |
+
path: logic_puzzles_grid_knight/level_1-*
|
1743 |
+
- split: level_2
|
1744 |
+
path: logic_puzzles_grid_knight/level_2-*
|
1745 |
+
- split: level_3
|
1746 |
+
path: logic_puzzles_grid_knight/level_3-*
|
1747 |
+
- split: level_4
|
1748 |
+
path: logic_puzzles_grid_knight/level_4-*
|
1749 |
+
- split: level_5
|
1750 |
+
path: logic_puzzles_grid_knight/level_5-*
|
1751 |
+
- config_name: geometry_rotation
|
1752 |
+
data_files:
|
1753 |
+
- split: level_1
|
1754 |
+
path: geometry_rotation/level_1-*
|
1755 |
+
- split: level_2
|
1756 |
+
path: geometry_rotation/level_2-*
|
1757 |
+
- split: level_3
|
1758 |
+
path: geometry_rotation/level_3-*
|
1759 |
+
- split: level_4
|
1760 |
+
path: geometry_rotation/level_4-*
|
1761 |
+
- split: level_5
|
1762 |
+
path: geometry_rotation/level_5-*
|
1763 |
+
- split: level_6
|
1764 |
+
path: geometry_rotation/level_6-*
|
1765 |
+
---
|
1766 |
+
|
1767 |
+
# Mathematical Problem Families by Difficulty
|
1768 |
+
|
1769 |
+
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.
|
1770 |
+
|
1771 |
+
## Overview
|
1772 |
+
|
1773 |
+
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:
|
1774 |
+
|
1775 |
+
- **Difficulty Scaling**: How mathematical reasoning changes as problems become more complex
|
1776 |
+
- **Domain-Specific Learning**: How models learn within specific mathematical areas
|
1777 |
+
- **Progressive Training**: Training on easier levels and testing on harder ones
|
1778 |
+
- **Curriculum Learning**: Gradually increasing difficulty within problem types
|
1779 |
+
|
1780 |
+
## Quick Start
|
1781 |
+
|
1782 |
+
```python
|
1783 |
+
from datasets import load_dataset
|
1784 |
+
|
1785 |
+
# Load all problem families
|
1786 |
+
dataset = load_dataset("allenai/omega-prob-families")
|
1787 |
+
|
1788 |
+
# Load a specific problem family with all difficulty levels
|
1789 |
+
func_area_data = load_dataset("allenai/omega-prob-families", "algebra_func_area")
|
1790 |
+
level_1_data = func_area_data["level_1"] # Easiest problems
|
1791 |
+
level_5_data = func_area_data["level_5"] # Hardest problems
|
1792 |
+
|
1793 |
+
# Load just a specific difficulty level
|
1794 |
+
level_3_only = load_dataset("allenai/omega-prob-families", "algebra_func_area", split="level_3")
|
1795 |
+
|
1796 |
+
# Get all available families
|
1797 |
+
available_families = list(dataset.keys())
|
1798 |
+
print(f"Available families: {available_families}")
|
1799 |
+
```
|
1800 |
+
|
1801 |
+
## Dataset Description
|
1802 |
+
|
1803 |
+
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:
|
1804 |
+
|
1805 |
+
- **Algebra**: Function analysis, polynomial operations, linear equations
|
1806 |
+
- **Arithmetic**: Matrix operations, number theory, basic calculations
|
1807 |
+
- **Geometry**: Shape analysis, transformations, spatial reasoning
|
1808 |
+
- **Combinatorics**: Probability, pattern matching, counting problems
|
1809 |
+
- **Logic**: Grid-based puzzles, constraint satisfaction
|
1810 |
+
|
1811 |
+
## Family Structure
|
1812 |
+
|
1813 |
+
Each family is organized as:
|
1814 |
+
- **Family Name**: Descriptive identifier (e.g., `algebra_func_area`)
|
1815 |
+
- **Difficulty Levels**: Progressive levels from 1 (easiest) to N (hardest)
|
1816 |
+
- **Problem Count**: Exactly 100 problems per level (or fewer if original file had fewer)
|
1817 |
+
- **Consistent Format**: Same problem type across all levels, increasing in complexity
|
1818 |
+
|
1819 |
+
## Citation
|
1820 |
+
|
1821 |
+
If you use this dataset, please cite the original work:
|
1822 |
+
|
1823 |
+
```bibtex
|
1824 |
+
@article{sun2024omega,
|
1825 |
+
title = {OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization},
|
1826 |
+
author = {Yiyou Sun and Shawn Hu and Georgia Zhou and Ken Zheng and Hannaneh Hajishirzi and Nouha Dziri and Dawn Song},
|
1827 |
+
journal = {arXiv preprint arXiv:2506.18880},
|
1828 |
+
year = {2024},
|
1829 |
+
}
|
1830 |
+
```
|
1831 |
+
|
1832 |
+
## Related Resources
|
1833 |
+
|
1834 |
+
- **Explorative Dataset**: See [omega-explorative](https://huggingface.co/datasets/allenai/omega-explorative) for explorative reasoning challenges
|
1835 |
+
- **Compositional Dataset**: See [omega-compositional](https://huggingface.co/datasets/allenai/omega-compositional) for compositional reasoning challenges
|
1836 |
+
- **Transformative Dataset**: See [omega-transformative](https://huggingface.co/datasets/allenai/omega-transformative) for transformative reasoning challenges
|
1837 |
+
- **Paper**: See the full details in [paper](https://arxiv.org/pdf/2506.18880)
|
1838 |
+
- **Code Repository**: See generation code on [github](https://github.com/sunblaze-ucb/math_ood)
|
1839 |
+
|
algebra_func_area/level_1-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
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+
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|
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oid sha256:f6f4ae2dbc3f7ddf9739dc1bf14f6d1fe73d1e0602fb98f0e576fa66e2bc7095
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size 11344
|
algebra_func_area/level_2-00000-of-00001.parquet
ADDED
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|
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|
|
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+
version https://git-lfs.github.com/spec/v1
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oid sha256:50aef59721a957a45ea4725567c9c58674d53fa8139b286ef7e2a6e0444093cb
|
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size 13559
|
algebra_func_area/level_3-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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oid sha256:59e7e4883fca9c3002c26eb21557260f3ca7c9eac189bff70bd0999472fb4f75
|
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size 15395
|
algebra_func_area/level_4-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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oid sha256:af14977d5201f85c153d815e5ca7f0ec0a770eedb7a4a9420bbedd259d687a3d
|
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+
size 17998
|
algebra_func_area/level_5-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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oid sha256:eb3890d04074ed70b306b2a3d895ae92b05fbbad2a392bca1a26dbe15641f73a
|
3 |
+
size 20299
|
algebra_func_derivative_sign/level_1-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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oid sha256:45b20262caf875bc573c8f4c86dbe784d8efaae2b16eeae4ef60caa15752d64f
|
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+
size 9441
|
algebra_func_derivative_sign/level_2-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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+
oid sha256:8855eaf10a05fe51d9bc20229b596ca2aeeee2f1611eeaf22119c6f162736794
|
3 |
+
size 10566
|
algebra_func_derivative_sign/level_3-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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+
oid sha256:7094df45473c548bd28ee2dc9dd52293b6dc976f184dbc08de830370bc8a1be2
|
3 |
+
size 11744
|
algebra_func_derivative_sign/level_4-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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+
oid sha256:9964f875dbb1268bb54ef093fd309ad3281cf475e97c18c644082737e60b84e7
|
3 |
+
size 13171
|
algebra_func_derivative_sign/level_5-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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+
oid sha256:7532c9db4923322a828bc2ad6fc4a40d95619f9ed57040d2f7365f216aada897
|
3 |
+
size 14233
|
algebra_func_extrema/level_1-00000-of-00001.parquet
ADDED
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
1 |
+
version https://git-lfs.github.com/spec/v1
|
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+
oid sha256:cd65dd9b816b4ce1cf8a827b13b02facd1c3a7ef1aae9c33c913976f49bbbf17
|
3 |
+
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