arXiv:2610.12536v1 Announce Type: new Abstract: EliteTable is a self-improving program-search algorithm guided by large language models (LLMs) that uses a fixed-capacity table of high-scoring solutions to guide new proposals, edits of existing solutions, and remixes of several solutions. Performance was evaluated across six Gymnasium control tasks, each with ten generations and fifty candidate slots per generation. Each task was evaluated across ten independently initialized searches. Candidate-score medians rose between the first and final generations in all six tasks, and selected-winner search-score medians rose in five. In CartPole-v1, the selected winner reached the search-score ceiling in the first generation of all ten searches. All ten paired held-out endpoints improved in four of the six tasks. BipedalWalker-v3 and CarRacing-v3 improved without reaching their reporting targets. Six of ten Acrobot-v1 searches declined on held-out episodes, and the median paired change was negat...