CogAtom is a novel problem generation framework for enhancing the mathematical reasoning capabilities of large-scale language models (LLMs). Unlike existing methods, CogAtom generates problems by selecting and recombining "cognitive atoms," basic inference units extracted from human-written solutions. A random walk algorithm that promotes diversity and a constraint-based recombination mechanism ensure logical consistency and structural validity, and the difficulty of the problem can be precisely adjusted by adjusting the number of cognitive atoms. Experimental results show that CogAtom outperforms existing methods in accuracy, inference depth, and diversity, generating problems approaching the AIME level of difficulty while exhibiting superior structural variation. The code is publicly available on GitHub.
