Large language models that employ extended chain-of-thought reasoning, exemplified by DeepSeek-R1, have achieved strong results on math competition problems. But models tuned with supervised fine-tuning or reinforcement learning often rely on a fixed set of tactics—repeating algebra rules or switching to coordinate geometry for diagram questions—rather than demonstrating genuine mathematical invention.
As these tuned systems replicate familiar reasoning sequences, they struggle with tasks demanding fresh insights. Existing math benchmarks fall short of measuring the skills that reinforcement learning can instill, and massive question collections mix topics and difficulties in ways that obscure individual capabilities.
Practices like out-of-distribution generalization aim to prepare models for test sets that depart from training examples, a need that spans fields from math reasoning to physics modeling and economic forecasting. Compositional generalization methods work to teach models how to assemble basic tactics into new solutions. To assess these properties, past efforts have produced datasets via human problem writing (GSM8K, MinervaMath), exam question curation (AIME, OlympiadBench) or large-scale exam scraping (NuminaMath, BigMath). Many of these either fall short of challenging today’s language models or lack the fine-grained analysis required for pinpointing reasoning strengths.
A coalition of researchers from the University of California, Ai2, the University of Washington and dmodel.ai introduced OMEGA, a specialized benchmark that probes three facets of out-of-distribution generalization based on Boden’s creativity framework. OMEGA generates paired training and test questions that isolate exploratory, compositional and transformative reasoning skills. Each problem is drawn from one of 40 template generators spanning six mathematical areas—arithmetic, algebra, combinatorics, number theory, geometry and logic and puzzles—enabling careful control over variety, difficulty and the precise methods needed for a solution.
In their evaluation, the team tested four leading models—DeepSeek-R1, Claude-3.7-Sonnet, OpenAI-o3-mini and OpenAI-o4-mini—across multiple complexity tiers. They applied the GRPO reinforcement algorithm on 1,000 training templates with Qwen2.5-7B-Instruct and Qwen2.5-Math-7B backbones. Exploratory generalization training used simpler problems and measured performance on harder variants. Compositional experiments taught models individual skills separately before assessing how well those skills were combined. Transformative setups exposed models to classic solution patterns then challenged them with prompts that demanded unconventional techniques.
The results reveal a clear trend: as the puzzle difficulty climbs, reasoning models often spot the correct path early yet expend extra tokens on needless checks. Reinforcement learning fine-tuned on low-difficulty questions boosts accuracy on medium-difficulty ones, showing bigger gains within the same distribution than on truly novel problem sets. For example, in a Zebra Logic scenario the base system reached just 30% success, but RL tuning lifted that rate by 61 points on familiar templates and by 53 points on out-of-distribution cases.
OMEGA’s analysis highlights three key observations. First, reinforcement learning tuning delivers substantial improvements on both in-distribution and exploratory generalization challenges. Second, it offers only modest benefits for compositional tasks. Third, it does little to spark new reasoning pathways required for transformational performance. This suggests that RL is able to deepen and broaden existing skills, but it falls short of prompting the creative leaps needed for truly novel mathematical reasoning. Future directions may include layered curriculum strategies and meta-reasoning architectures.
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