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+ path: algebra_func_intersection_coords/test_out-*
1201
+ - config_name: algebra_func_zeros
1202
+ data_files:
1203
+ - split: train
1204
+ path: algebra_func_zeros/train-*
1205
+ - split: test_in
1206
+ path: algebra_func_zeros/test_in-*
1207
+ - split: test_out
1208
+ path: algebra_func_zeros/test_out-*
1209
+ - config_name: algebra_linear_equation
1210
+ data_files:
1211
+ - split: train
1212
+ path: algebra_linear_equation/train-*
1213
+ - split: test_in
1214
+ path: algebra_linear_equation/test_in-*
1215
+ - split: test_out
1216
+ path: algebra_linear_equation/test_out-*
1217
+ - config_name: algebra_polynomial_roots
1218
+ data_files:
1219
+ - split: train
1220
+ path: algebra_polynomial_roots/train-*
1221
+ - split: test_in
1222
+ path: algebra_polynomial_roots/test_in-*
1223
+ - split: test_out
1224
+ path: algebra_polynomial_roots/test_out-*
1225
+ - config_name: arithmetic_gcd
1226
+ data_files:
1227
+ - split: train
1228
+ path: arithmetic_gcd/train-*
1229
+ - split: test_in
1230
+ path: arithmetic_gcd/test_in-*
1231
+ - split: test_out
1232
+ path: arithmetic_gcd/test_out-*
1233
+ - config_name: arithmetic_list_prime_factors
1234
+ data_files:
1235
+ - split: train
1236
+ path: arithmetic_list_prime_factors/train-*
1237
+ - split: test_in
1238
+ path: arithmetic_list_prime_factors/test_in-*
1239
+ - split: test_out
1240
+ path: arithmetic_list_prime_factors/test_out-*
1241
+ - config_name: arithmetic_mixed
1242
+ data_files:
1243
+ - split: train
1244
+ path: arithmetic_mixed/train-*
1245
+ - split: test_in
1246
+ path: arithmetic_mixed/test_in-*
1247
+ - split: test_out
1248
+ path: arithmetic_mixed/test_out-*
1249
+ - config_name: arithmetic_matrix_determinant
1250
+ data_files:
1251
+ - split: train
1252
+ path: arithmetic_matrix_determinant/train-*
1253
+ - split: test_in
1254
+ path: arithmetic_matrix_determinant/test_in-*
1255
+ - split: test_out
1256
+ path: arithmetic_matrix_determinant/test_out-*
1257
+ - config_name: arithmetic_matrix_eigenvalues
1258
+ data_files:
1259
+ - split: train
1260
+ path: arithmetic_matrix_eigenvalues/train-*
1261
+ - split: test_in
1262
+ path: arithmetic_matrix_eigenvalues/test_in-*
1263
+ - split: test_out
1264
+ path: arithmetic_matrix_eigenvalues/test_out-*
1265
+ - config_name: arithmetic_matrix_inverse
1266
+ data_files:
1267
+ - split: train
1268
+ path: arithmetic_matrix_inverse/train-*
1269
+ - split: test_in
1270
+ path: arithmetic_matrix_inverse/test_in-*
1271
+ - split: test_out
1272
+ path: arithmetic_matrix_inverse/test_out-*
1273
+ - config_name: arithmetic_matrix_multiplication
1274
+ data_files:
1275
+ - split: train
1276
+ path: arithmetic_matrix_multiplication/train-*
1277
+ - split: test_in
1278
+ path: arithmetic_matrix_multiplication/test_in-*
1279
+ - split: test_out
1280
+ path: arithmetic_matrix_multiplication/test_out-*
1281
+ - config_name: arithmetic_matrix_power
1282
+ data_files:
1283
+ - split: train
1284
+ path: arithmetic_matrix_power/train-*
1285
+ - split: test_in
1286
+ path: arithmetic_matrix_power/test_in-*
1287
+ - split: test_out
1288
+ path: arithmetic_matrix_power/test_out-*
1289
+ - config_name: arithmetic_matrix_rank
1290
+ data_files:
1291
+ - split: train
1292
+ path: arithmetic_matrix_rank/train-*
1293
+ - split: test_in
1294
+ path: arithmetic_matrix_rank/test_in-*
1295
+ - split: test_out
1296
+ path: arithmetic_matrix_rank/test_out-*
1297
+ - config_name: arithmetic_matrix_svd
1298
+ data_files:
1299
+ - split: train
1300
+ path: arithmetic_matrix_svd/train-*
1301
+ - split: test_in
1302
+ path: arithmetic_matrix_svd/test_in-*
1303
+ - split: test_out
1304
+ path: arithmetic_matrix_svd/test_out-*
1305
+ - config_name: combinatory_distribution
1306
+ data_files:
1307
+ - split: train
1308
+ path: combinatory_distribution/train-*
1309
+ - split: test_in
1310
+ path: combinatory_distribution/test_in-*
1311
+ - split: test_out
1312
+ path: combinatory_distribution/test_out-*
1313
+ - config_name: combinatory_pattern_matching
1314
+ data_files:
1315
+ - split: train
1316
+ path: combinatory_pattern_matching/train-*
1317
+ - split: test_in
1318
+ path: combinatory_pattern_matching/test_in-*
1319
+ - split: test_out
1320
+ path: combinatory_pattern_matching/test_out-*
1321
+ - config_name: combinatory_probability_at_least_n_specific_fixed
1322
+ data_files:
1323
+ - split: train
1324
+ path: combinatory_probability_at_least_n_specific_fixed/train-*
1325
+ - split: test_in
1326
+ path: combinatory_probability_at_least_n_specific_fixed/test_in-*
1327
+ - split: test_out
1328
+ path: combinatory_probability_at_least_n_specific_fixed/test_out-*
1329
+ - config_name: combinatory_probability_exactly_n_specific_fixed
1330
+ data_files:
1331
+ - split: train
1332
+ path: combinatory_probability_exactly_n_specific_fixed/train-*
1333
+ - split: test_in
1334
+ path: combinatory_probability_exactly_n_specific_fixed/test_in-*
1335
+ - split: test_out
1336
+ path: combinatory_probability_exactly_n_specific_fixed/test_out-*
1337
+ - config_name: combinatory_probability_no_fixed_points
1338
+ data_files:
1339
+ - split: train
1340
+ path: combinatory_probability_no_fixed_points/train-*
1341
+ - split: test_in
1342
+ path: combinatory_probability_no_fixed_points/test_in-*
1343
+ - split: test_out
1344
+ path: combinatory_probability_no_fixed_points/test_out-*
1345
+ - config_name: combinatory_probability_no_specific_letter_fixed
1346
+ data_files:
1347
+ - split: train
1348
+ path: combinatory_probability_no_specific_letter_fixed/train-*
1349
+ - split: test_in
1350
+ path: combinatory_probability_no_specific_letter_fixed/test_in-*
1351
+ - split: test_out
1352
+ path: combinatory_probability_no_specific_letter_fixed/test_out-*
1353
+ - config_name: geometry_basic
1354
+ data_files:
1355
+ - split: train
1356
+ path: geometry_basic/train-*
1357
+ - split: test_in
1358
+ path: geometry_basic/test_in-*
1359
+ - split: test_out
1360
+ path: geometry_basic/test_out-*
1361
+ - config_name: geometry_circle
1362
+ data_files:
1363
+ - split: train
1364
+ path: geometry_circle/train-*
1365
+ - split: test_in
1366
+ path: geometry_circle/test_in-*
1367
+ - split: test_out
1368
+ path: geometry_circle/test_out-*
1369
+ - config_name: geometry_perpendicular_intersection
1370
+ data_files:
1371
+ - split: train
1372
+ path: geometry_perpendicular_intersection/train-*
1373
+ - split: test_in
1374
+ path: geometry_perpendicular_intersection/test_in-*
1375
+ - split: test_out
1376
+ path: geometry_perpendicular_intersection/test_out-*
1377
+ - config_name: geometry_polygon
1378
+ data_files:
1379
+ - split: train
1380
+ path: geometry_polygon/train-*
1381
+ - split: test_in
1382
+ path: geometry_polygon/test_in-*
1383
+ - split: test_out
1384
+ path: geometry_polygon/test_out-*
1385
+ - config_name: geometry_polygon_rotation
1386
+ data_files:
1387
+ - split: train
1388
+ path: geometry_polygon_rotation/train-*
1389
+ - split: test_in
1390
+ path: geometry_polygon_rotation/test_in-*
1391
+ - split: test_out
1392
+ path: geometry_polygon_rotation/test_out-*
1393
+ - config_name: geometry_triangle
1394
+ data_files:
1395
+ - split: train
1396
+ path: geometry_triangle/train-*
1397
+ - split: test_in
1398
+ path: geometry_triangle/test_in-*
1399
+ - split: test_out
1400
+ path: geometry_triangle/test_out-*
1401
+ - config_name: geometry_polygon_chords
1402
+ data_files:
1403
+ - split: train
1404
+ path: geometry_polygon_chords/train-*
1405
+ - split: test_in
1406
+ path: geometry_polygon_chords/test_in-*
1407
+ - split: test_out
1408
+ path: geometry_polygon_chords/test_out-*
1409
+ - config_name: geometry_polygon_color
1410
+ data_files:
1411
+ - split: train
1412
+ path: geometry_polygon_color/train-*
1413
+ - split: test_in
1414
+ path: geometry_polygon_color/test_in-*
1415
+ - split: test_out
1416
+ path: geometry_polygon_color/test_out-*
1417
+ - config_name: logic_gridworld_blocked
1418
+ data_files:
1419
+ - split: train
1420
+ path: logic_gridworld_blocked/train-*
1421
+ - split: test_in
1422
+ path: logic_gridworld_blocked/test_in-*
1423
+ - split: test_out
1424
+ path: logic_gridworld_blocked/test_out-*
1425
+ - config_name: logic_gridworld_knight_move
1426
+ data_files:
1427
+ - split: train
1428
+ path: logic_gridworld_knight_move/train-*
1429
+ - split: test_in
1430
+ path: logic_gridworld_knight_move/test_in-*
1431
+ - split: test_out
1432
+ path: logic_gridworld_knight_move/test_out-*
1433
+ - config_name: logic_gridworld_rookmove
1434
+ data_files:
1435
+ - split: train
1436
+ path: logic_gridworld_rookmove/train-*
1437
+ - split: test_in
1438
+ path: logic_gridworld_rookmove/test_in-*
1439
+ - split: test_out
1440
+ path: logic_gridworld_rookmove/test_out-*
1441
+ - config_name: logic_zebralogic
1442
+ data_files:
1443
+ - split: train
1444
+ path: logic_zebralogic/train-*
1445
+ - split: test_in
1446
+ path: logic_zebralogic/test_in-*
1447
+ - split: test_out
1448
+ path: logic_zebralogic/test_out-*
1449
+ - config_name: logic_puzzles_grid_chip
1450
+ data_files:
1451
+ - split: train
1452
+ path: logic_puzzles_grid_chip/train-*
1453
+ - split: test_in
1454
+ path: logic_puzzles_grid_chip/test_in-*
1455
+ - split: test_out
1456
+ path: logic_puzzles_grid_chip/test_out-*
1457
+ - config_name: numbertheory_lte_qr
1458
+ data_files:
1459
+ - split: train
1460
+ path: numbertheory_lte_qr/train-*
1461
+ - split: test_in
1462
+ path: numbertheory_lte_qr/test_in-*
1463
+ - split: test_out
1464
+ path: numbertheory_lte_qr/test_out-*
1465
+ - config_name: numbertheory_ordered_lte
1466
+ data_files:
1467
+ - split: train
1468
+ path: numbertheory_ordered_lte/train-*
1469
+ - split: test_in
1470
+ path: numbertheory_ordered_lte/test_in-*
1471
+ - split: test_out
1472
+ path: numbertheory_ordered_lte/test_out-*
1473
+ - config_name: numbertheory_qr_sum
1474
+ data_files:
1475
+ - split: train
1476
+ path: numbertheory_qr_sum/train-*
1477
+ - split: test_in
1478
+ path: numbertheory_qr_sum/test_in-*
1479
+ - split: test_out
1480
+ path: numbertheory_qr_sum/test_out-*
1481
+ ---
1482
+
1483
+ # Explorative Math Problems
1484
+
1485
+ 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.
1486
+
1487
+ ## Overview
1488
+
1489
+ 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?
1490
+
1491
+ Each explorative setting consists of:
1492
+ - **Training Dataset**: Low-complexity problems from a specific mathematical domain
1493
+ - **Test In-Distribution**: Problems of similar complexity to training data (test-in)
1494
+ - **Test Out-of-Distribution**: Higher complexity problems from the same domain/template (test-out)
1495
+
1496
+ ## Quick Start
1497
+
1498
+ ```python
1499
+ from datasets import load_dataset
1500
+
1501
+ # Load all explorative settings
1502
+ dataset = load_dataset("sunyiyou/omega-explorative")
1503
+
1504
+ # Load a specific explorative setting with all splits
1505
+ func_area_data = load_dataset("sunyiyou/omega-explorative", "algebra_func_area")
1506
+ train_data = func_area_data["train"] # Low complexity training problems
1507
+ test_in_data = func_area_data["test_in"] # Similar complexity test problems
1508
+ test_out_data = func_area_data["test_out"] # Higher complexity test problems
1509
+
1510
+ # Load just specific splits
1511
+ train_only = load_dataset("sunyiyou/omega-explorative", "algebra_func_area", split="train")
1512
+ test_out_only = load_dataset("sunyiyou/omega-explorative", "algebra_func_area", split="test_out")
1513
+ ```
1514
+
1515
+ ## Dataset Description
1516
+
1517
+ Each explorative setting provides three splits to evaluate different aspects of generalization:
1518
+
1519
+ - **Train**: Low-complexity problems used for training/few-shot learning
1520
+ - **Test-in**: Problems of similar complexity to training data (in-distribution evaluation)
1521
+ - **Test-out**: Higher complexity problems from the same template (out-of-distribution evaluation)
1522
+
1523
+ 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.
1524
+
1525
+ ## Citation
1526
+
1527
+ If you use this dataset, please cite the original work:
1528
+
1529
+ ```bibtex
1530
+ @article{sun2024omega,
1531
+ title = {OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization},
1532
+ author = {Yiyou Sun and Shawn Hu and Georgia Zhou and Ken Zheng and Hannaneh Hajishirzi and Nouha Dziri and Dawn Song},
1533
+ journal = {arXiv preprint arXiv:2506.18880},
1534
+ year = {2024},
1535
+ }
1536
+ ```
1537
+
1538
+ ## Related Resources
1539
+
1540
+ - **Transformative Dataset**: See [omega-transformative](https://huggingface.co/datasets/sunyiyou/omega-transformative) for transformative reasoning challenges
1541
+ - **Compositional Dataset**: See [omega-compositional](https://huggingface.co/datasets/sunyiyou/omega-compositional) for compositional reasoning challenges
1542
+ - **Paper**: See the full details in [paper](https://arxiv.org/pdf/2506.18880)
1543
+ - **Code Repository**: See generation code on [github](https://github.com/sunblaze-ucb/math_ood)
1544
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