LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28
2026-09-07 12:00Science🔥 42.2 heat score
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The researchers released the Discovery Loop system, which uses large language model iterative optimization algorithms to set new best records for 10 N values (101-114) in the Packomania circular filling benchmark test. The system starts with a simple seed solver and proposes improvements based on the result scoreboard and historical solutions. After being screened by an independent verifier, valid solutions are retained and failed ones are eliminated. The improvement rate compared to prior records was 2.4%-5.4%, and all improvements were completed within 15 iterations, with a total LLM cost of $27.72. These results have been independently recognized by Packomania. The study also analyzed the cost-efficiency dynamics, including an adaptive platform detection mechanism, and discussed its impact on the democratization of automated scientific discovery.