allenai/omega-explorative

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