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Jun 26

OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization

Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA-Out-of-distribution Math Problems Evaluation with 3 Generalization Axes-a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory-applying known problem solving skills to more complex instances within the same problem domain; (2) Compositional-combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative-adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

What Should Data Science Education Do with Large Language Models?

The rapid advances of large language models (LLMs), such as ChatGPT, are revolutionizing data science and statistics. These state-of-the-art tools can streamline complex processes. As a result, it reshapes the role of data scientists. We argue that LLMs are transforming the responsibilities of data scientists, shifting their focus from hands-on coding, data-wrangling and conducting standard analyses to assessing and managing analyses performed by these automated AIs. This evolution of roles is reminiscent of the transition from a software engineer to a product manager. We illustrate this transition with concrete data science case studies using LLMs in this paper. These developments necessitate a meaningful evolution in data science education. Pedagogy must now place greater emphasis on cultivating diverse skillsets among students, such as LLM-informed creativity, critical thinking, AI-guided programming. LLMs can also play a significant role in the classroom as interactive teaching and learning tools, contributing to personalized education. This paper discusses the opportunities, resources and open challenges for each of these directions. As with any transformative technology, integrating LLMs into education calls for careful consideration. While LLMs can perform repetitive tasks efficiently, it's crucial to remember that their role is to supplement human intelligence and creativity, not to replace it. Therefore, the new era of data science education should balance the benefits of LLMs while fostering complementary human expertise and innovations. In conclusion, the rise of LLMs heralds a transformative period for data science and its education. This paper seeks to shed light on the emerging trends, potential opportunities, and challenges accompanying this paradigm shift, hoping to spark further discourse and investigation into this exciting, uncharted territory.