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+ - name: level_6
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+ num_examples: 10
1310
+ download_size: 93270
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+ dataset_size: 93270
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1313
+ - config_name: arithmetic_matrix_rank
1314
+ data_files:
1315
+ - split: level_1
1316
+ path: arithmetic_matrix_rank/level_1-*
1317
+ - split: level_2
1318
+ path: arithmetic_matrix_rank/level_2-*
1319
+ - split: level_3
1320
+ path: arithmetic_matrix_rank/level_3-*
1321
+ - split: level_4
1322
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1323
+ - split: level_5
1324
+ path: arithmetic_matrix_rank/level_5-*
1325
+ - split: level_6
1326
+ path: arithmetic_matrix_rank/level_6-*
1327
+ - split: level_7
1328
+ path: arithmetic_matrix_rank/level_7-*
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+ - config_name: arithmetic_matrix_multiplication
1330
+ data_files:
1331
+ - split: level_1
1332
+ path: arithmetic_matrix_multiplication/level_1-*
1333
+ - split: level_2
1334
+ path: arithmetic_matrix_multiplication/level_2-*
1335
+ - split: level_3
1336
+ path: arithmetic_matrix_multiplication/level_3-*
1337
+ - split: level_4
1338
+ path: arithmetic_matrix_multiplication/level_4-*
1339
+ - split: level_5
1340
+ path: arithmetic_matrix_multiplication/level_5-*
1341
+ - split: level_6
1342
+ path: arithmetic_matrix_multiplication/level_6-*
1343
+ - split: level_7
1344
+ path: arithmetic_matrix_multiplication/level_7-*
1345
+ - config_name: algebra_func_derivative_sign
1346
+ data_files:
1347
+ - split: level_1
1348
+ path: algebra_func_derivative_sign/level_1-*
1349
+ - split: level_2
1350
+ path: algebra_func_derivative_sign/level_2-*
1351
+ - split: level_3
1352
+ path: algebra_func_derivative_sign/level_3-*
1353
+ - split: level_4
1354
+ path: algebra_func_derivative_sign/level_4-*
1355
+ - split: level_5
1356
+ path: algebra_func_derivative_sign/level_5-*
1357
+ - config_name: arithmetic_matrix_svd
1358
+ data_files:
1359
+ - split: level_1
1360
+ path: arithmetic_matrix_svd/level_1-*
1361
+ - split: level_2
1362
+ path: arithmetic_matrix_svd/level_2-*
1363
+ - split: level_3
1364
+ path: arithmetic_matrix_svd/level_3-*
1365
+ - split: level_4
1366
+ path: arithmetic_matrix_svd/level_4-*
1367
+ - split: level_5
1368
+ path: arithmetic_matrix_svd/level_5-*
1369
+ - split: level_6
1370
+ path: arithmetic_matrix_svd/level_6-*
1371
+ - split: level_7
1372
+ path: arithmetic_matrix_svd/level_7-*
1373
+ - config_name: algebra_func_extrema_coords
1374
+ data_files:
1375
+ - split: level_1
1376
+ path: algebra_func_extrema_coords/level_1-*
1377
+ - split: level_2
1378
+ path: algebra_func_extrema_coords/level_2-*
1379
+ - split: level_3
1380
+ path: algebra_func_extrema_coords/level_3-*
1381
+ - split: level_4
1382
+ path: algebra_func_extrema_coords/level_4-*
1383
+ - split: level_5
1384
+ path: algebra_func_extrema_coords/level_5-*
1385
+ - config_name: geometry_polygon_chords
1386
+ data_files:
1387
+ - split: level_1
1388
+ path: geometry_polygon_chords/level_1-*
1389
+ - split: level_2
1390
+ path: geometry_polygon_chords/level_2-*
1391
+ - split: level_3
1392
+ path: geometry_polygon_chords/level_3-*
1393
+ - split: level_4
1394
+ path: geometry_polygon_chords/level_4-*
1395
+ - split: level_5
1396
+ path: geometry_polygon_chords/level_5-*
1397
+ - config_name: logic_puzzles_blocked_grid
1398
+ data_files:
1399
+ - split: level_1
1400
+ path: logic_puzzles_blocked_grid/level_1-*
1401
+ - split: level_2
1402
+ path: logic_puzzles_blocked_grid/level_2-*
1403
+ - split: level_3
1404
+ path: logic_puzzles_blocked_grid/level_3-*
1405
+ - split: level_4
1406
+ path: logic_puzzles_blocked_grid/level_4-*
1407
+ - split: level_5
1408
+ path: logic_puzzles_blocked_grid/level_5-*
1409
+ - config_name: arithmetic_matrix_eigenvalues
1410
+ data_files:
1411
+ - split: level_1
1412
+ path: arithmetic_matrix_eigenvalues/level_1-*
1413
+ - split: level_2
1414
+ path: arithmetic_matrix_eigenvalues/level_2-*
1415
+ - split: level_3
1416
+ path: arithmetic_matrix_eigenvalues/level_3-*
1417
+ - split: level_4
1418
+ path: arithmetic_matrix_eigenvalues/level_4-*
1419
+ - split: level_5
1420
+ path: arithmetic_matrix_eigenvalues/level_5-*
1421
+ - split: level_6
1422
+ path: arithmetic_matrix_eigenvalues/level_6-*
1423
+ - split: level_7
1424
+ path: arithmetic_matrix_eigenvalues/level_7-*
1425
+ - config_name: algebra_func_intersection
1426
+ data_files:
1427
+ - split: level_1
1428
+ path: algebra_func_intersection/level_1-*
1429
+ - split: level_2
1430
+ path: algebra_func_intersection/level_2-*
1431
+ - split: level_3
1432
+ path: algebra_func_intersection/level_3-*
1433
+ - split: level_4
1434
+ path: algebra_func_intersection/level_4-*
1435
+ - split: level_5
1436
+ path: algebra_func_intersection/level_5-*
1437
+ - config_name: number_theory_digit_sum
1438
+ data_files:
1439
+ - split: level_1
1440
+ path: number_theory_digit_sum/level_1-*
1441
+ - split: level_2
1442
+ path: number_theory_digit_sum/level_2-*
1443
+ - split: level_3
1444
+ path: number_theory_digit_sum/level_3-*
1445
+ - split: level_4
1446
+ path: number_theory_digit_sum/level_4-*
1447
+ - split: level_5
1448
+ path: number_theory_digit_sum/level_5-*
1449
+ - config_name: combinatory_probability_no_specific_letter_fixed
1450
+ data_files:
1451
+ - split: level_1
1452
+ path: combinatory_probability_no_specific_letter_fixed/level_1-*
1453
+ - split: level_2
1454
+ path: combinatory_probability_no_specific_letter_fixed/level_2-*
1455
+ - split: level_3
1456
+ path: combinatory_probability_no_specific_letter_fixed/level_3-*
1457
+ - split: level_4
1458
+ path: combinatory_probability_no_specific_letter_fixed/level_4-*
1459
+ - split: level_5
1460
+ path: combinatory_probability_no_specific_letter_fixed/level_5-*
1461
+ - config_name: combinatory_probability_at_least_n_specific_fixed
1462
+ data_files:
1463
+ - split: level_1
1464
+ path: combinatory_probability_at_least_n_specific_fixed/level_1-*
1465
+ - split: level_2
1466
+ path: combinatory_probability_at_least_n_specific_fixed/level_2-*
1467
+ - split: level_3
1468
+ path: combinatory_probability_at_least_n_specific_fixed/level_3-*
1469
+ - split: level_4
1470
+ path: combinatory_probability_at_least_n_specific_fixed/level_4-*
1471
+ - split: level_5
1472
+ path: combinatory_probability_at_least_n_specific_fixed/level_5-*
1473
+ - config_name: logic_puzzles_grid_rook
1474
+ data_files:
1475
+ - split: level_1
1476
+ path: logic_puzzles_grid_rook/level_1-*
1477
+ - split: level_2
1478
+ path: logic_puzzles_grid_rook/level_2-*
1479
+ - split: level_3
1480
+ path: logic_puzzles_grid_rook/level_3-*
1481
+ - split: level_4
1482
+ path: logic_puzzles_grid_rook/level_4-*
1483
+ - split: level_5
1484
+ path: logic_puzzles_grid_rook/level_5-*
1485
+ - config_name: combinatory_distribution
1486
+ data_files:
1487
+ - split: level_1
1488
+ path: combinatory_distribution/level_1-*
1489
+ - split: level_2
1490
+ path: combinatory_distribution/level_2-*
1491
+ - split: level_3
1492
+ path: combinatory_distribution/level_3-*
1493
+ - split: level_4
1494
+ path: combinatory_distribution/level_4-*
1495
+ - split: level_5
1496
+ path: combinatory_distribution/level_5-*
1497
+ - split: level_6
1498
+ path: combinatory_distribution/level_6-*
1499
+ - config_name: arithmetic_mixed
1500
+ data_files:
1501
+ - split: level_1
1502
+ path: arithmetic_mixed/level_1-*
1503
+ - split: level_2
1504
+ path: arithmetic_mixed/level_2-*
1505
+ - split: level_3
1506
+ path: arithmetic_mixed/level_3-*
1507
+ - split: level_4
1508
+ path: arithmetic_mixed/level_4-*
1509
+ - split: level_5
1510
+ path: arithmetic_mixed/level_5-*
1511
+ - config_name: arithmetic_matrix_determinant
1512
+ data_files:
1513
+ - split: level_1
1514
+ path: arithmetic_matrix_determinant/level_1-*
1515
+ - split: level_2
1516
+ path: arithmetic_matrix_determinant/level_2-*
1517
+ - split: level_3
1518
+ path: arithmetic_matrix_determinant/level_3-*
1519
+ - split: level_4
1520
+ path: arithmetic_matrix_determinant/level_4-*
1521
+ - split: level_5
1522
+ path: arithmetic_matrix_determinant/level_5-*
1523
+ - split: level_6
1524
+ path: arithmetic_matrix_determinant/level_6-*
1525
+ - split: level_7
1526
+ path: arithmetic_matrix_determinant/level_7-*
1527
+ - config_name: algebra_linear_equation
1528
+ data_files:
1529
+ - split: level_1
1530
+ path: algebra_linear_equation/level_1-*
1531
+ - split: level_2
1532
+ path: algebra_linear_equation/level_2-*
1533
+ - split: level_3
1534
+ path: algebra_linear_equation/level_3-*
1535
+ - split: level_4
1536
+ path: algebra_linear_equation/level_4-*
1537
+ - split: level_5
1538
+ path: algebra_linear_equation/level_5-*
1539
+ - config_name: logic_puzzles_grid_chip
1540
+ data_files:
1541
+ - split: level_1
1542
+ path: logic_puzzles_grid_chip/level_1-*
1543
+ - split: level_2
1544
+ path: logic_puzzles_grid_chip/level_2-*
1545
+ - split: level_3
1546
+ path: logic_puzzles_grid_chip/level_3-*
1547
+ - split: level_4
1548
+ path: logic_puzzles_grid_chip/level_4-*
1549
+ - split: level_5
1550
+ path: logic_puzzles_grid_chip/level_5-*
1551
+ - config_name: arithmetic_gcd
1552
+ data_files:
1553
+ - split: level_1
1554
+ path: arithmetic_gcd/level_1-*
1555
+ - split: level_2
1556
+ path: arithmetic_gcd/level_2-*
1557
+ - split: level_3
1558
+ path: arithmetic_gcd/level_3-*
1559
+ - split: level_4
1560
+ path: arithmetic_gcd/level_4-*
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-*
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+ - 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
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