NEURAL NETWORK METHODS FOR SELECTING AND GENERATING SYNTHETIC VARIATIONS OF COMBINATORIAL PROBLEMS

This study explores neural network methods for selecting and generating synthetic variations of mathematical combinatorial problems using large language models. We filter 1000 problems from the NuminaMath-CoT dataset and introduce three new variations: fictional, adversarial, and contextual disguise. We propose the Variation Consistency Score to measure the accuracy in the solution generation rate of the variations and their correlation rate with the original problems. Experiments with GPT-4o-mini showed consistent performance in the generation process, demonstrating the highest score on the fictional variation with the greatest average statement length and the lowest score on the contextual disguise variation. The model demonstrates the ability to generate diverse variations while preserving their mathematical core. Keywords: Neural Network Methods; Natural Language Processing; Large Language Models; Synthetic Data Generation; Mathematical Problems.