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- .DS_Store +0 -0
- README.md +1544 -0
- algebra_func_area/test_in-00000-of-00001.parquet +3 -0
- algebra_func_area/test_out-00000-of-00001.parquet +3 -0
- algebra_func_area/train-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/test_in-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/test_out-00000-of-00001.parquet +3 -0
- algebra_func_derivative_sign/train-00000-of-00001.parquet +3 -0
- algebra_func_extrema/test_in-00000-of-00001.parquet +3 -0
- algebra_func_extrema/test_out-00000-of-00001.parquet +3 -0
- algebra_func_extrema/train-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/test_in-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/test_out-00000-of-00001.parquet +3 -0
- algebra_func_extrema_coords/train-00000-of-00001.parquet +3 -0
- algebra_func_intersection/test_in-00000-of-00001.parquet +3 -0
- algebra_func_intersection/test_out-00000-of-00001.parquet +3 -0
- algebra_func_intersection/train-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/test_in-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/test_out-00000-of-00001.parquet +3 -0
- algebra_func_intersection_coords/train-00000-of-00001.parquet +3 -0
- algebra_func_zeros/test_in-00000-of-00001.parquet +3 -0
- algebra_func_zeros/test_out-00000-of-00001.parquet +3 -0
- algebra_func_zeros/train-00000-of-00001.parquet +3 -0
- algebra_linear_equation/test_in-00000-of-00001.parquet +3 -0
- algebra_linear_equation/test_out-00000-of-00001.parquet +3 -0
- algebra_linear_equation/train-00000-of-00001.parquet +3 -0
- algebra_polynomial_roots/test_in-00000-of-00001.parquet +3 -0
- algebra_polynomial_roots/test_out-00000-of-00001.parquet +3 -0
- algebra_polynomial_roots/train-00000-of-00001.parquet +3 -0
- arithmetic_gcd/test_in-00000-of-00001.parquet +3 -0
- arithmetic_gcd/test_out-00000-of-00001.parquet +3 -0
- arithmetic_gcd/train-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/test_in-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/test_out-00000-of-00001.parquet +3 -0
- arithmetic_list_prime_factors/train-00000-of-00001.parquet +3 -0
- arithmetic_matrix_determinant/test_in-00000-of-00001.parquet +3 -0
- arithmetic_matrix_determinant/test_out-00000-of-00001.parquet +3 -0
- arithmetic_matrix_determinant/train-00000-of-00001.parquet +3 -0
- arithmetic_matrix_eigenvalues/test_in-00000-of-00001.parquet +3 -0
- arithmetic_matrix_eigenvalues/test_out-00000-of-00001.parquet +3 -0
- arithmetic_matrix_eigenvalues/train-00000-of-00001.parquet +3 -0
- arithmetic_matrix_inverse/test_in-00000-of-00001.parquet +3 -0
- arithmetic_matrix_inverse/test_out-00000-of-00001.parquet +3 -0
- arithmetic_matrix_inverse/train-00000-of-00001.parquet +3 -0
- arithmetic_matrix_multiplication/test_in-00000-of-00001.parquet +3 -0
- arithmetic_matrix_multiplication/test_out-00000-of-00001.parquet +3 -0
- arithmetic_matrix_multiplication/train-00000-of-00001.parquet +3 -0
- arithmetic_matrix_power/test_in-00000-of-00001.parquet +3 -0
- arithmetic_matrix_power/test_out-00000-of-00001.parquet +3 -0
- arithmetic_matrix_power/train-00000-of-00001.parquet +3 -0
.DS_Store
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README.md
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|
| 1 |
+
---
|
| 2 |
+
license: mit
|
| 3 |
+
dataset_info:
|
| 4 |
+
- config_name: algebra_func_area
|
| 5 |
+
features:
|
| 6 |
+
- name: id
|
| 7 |
+
dtype: string
|
| 8 |
+
- name: setting_key
|
| 9 |
+
dtype: string
|
| 10 |
+
- name: messages
|
| 11 |
+
list:
|
| 12 |
+
- name: role
|
| 13 |
+
dtype: string
|
| 14 |
+
- name: content
|
| 15 |
+
dtype: string
|
| 16 |
+
- name: ground_truth
|
| 17 |
+
dtype: string
|
| 18 |
+
- name: dataset
|
| 19 |
+
dtype: string
|
| 20 |
+
splits:
|
| 21 |
+
- name: train
|
| 22 |
+
num_bytes: 78799
|
| 23 |
+
num_examples: 1000
|
| 24 |
+
- name: test_in
|
| 25 |
+
num_bytes: 12587
|
| 26 |
+
num_examples: 100
|
| 27 |
+
- name: test_out
|
| 28 |
+
num_bytes: 9518
|
| 29 |
+
num_examples: 50
|
| 30 |
+
download_size: 100904
|
| 31 |
+
dataset_size: 100904
|
| 32 |
+
- config_name: algebra_func_derivative_sign
|
| 33 |
+
features:
|
| 34 |
+
- name: id
|
| 35 |
+
dtype: string
|
| 36 |
+
- name: setting_key
|
| 37 |
+
dtype: string
|
| 38 |
+
- name: messages
|
| 39 |
+
list:
|
| 40 |
+
- name: role
|
| 41 |
+
dtype: string
|
| 42 |
+
- name: content
|
| 43 |
+
dtype: string
|
| 44 |
+
- name: ground_truth
|
| 45 |
+
dtype: string
|
| 46 |
+
- name: dataset
|
| 47 |
+
dtype: string
|
| 48 |
+
splits:
|
| 49 |
+
- name: train
|
| 50 |
+
num_bytes: 54517
|
| 51 |
+
num_examples: 1000
|
| 52 |
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- name: test_in
|
| 53 |
+
num_bytes: 9942
|
| 54 |
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num_examples: 100
|
| 55 |
+
- name: test_out
|
| 56 |
+
num_bytes: 8135
|
| 57 |
+
num_examples: 50
|
| 58 |
+
download_size: 72594
|
| 59 |
+
dataset_size: 72594
|
| 60 |
+
- config_name: algebra_func_extrema
|
| 61 |
+
features:
|
| 62 |
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| 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 |
+
|
algebra_func_area/test_in-00000-of-00001.parquet
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|
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algebra_func_extrema/test_in-00000-of-00001.parquet
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|
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ADDED
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algebra_func_extrema/train-00000-of-00001.parquet
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ADDED
|
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|
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|
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ADDED
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algebra_func_intersection/train-00000-of-00001.parquet
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|
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|
algebra_func_intersection_coords/test_out-00000-of-00001.parquet
ADDED
|
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|
algebra_func_intersection_coords/train-00000-of-00001.parquet
ADDED
|
@@ -0,0 +1,3 @@
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|
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|
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|
|
|
|
|
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|
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|
algebra_func_zeros/test_in-00000-of-00001.parquet
ADDED
|
@@ -0,0 +1,3 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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size 9688
|
algebra_func_zeros/test_out-00000-of-00001.parquet
ADDED
|
@@ -0,0 +1,3 @@
|
|
|
|
|
|
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