An LLM evolution loop broke 10 standing Packomania circle-packing records in 15 iterations for $27.72

arXiv 2609.05093·medium signalXBlueskyLinkedInCopy link

Discovery Loop starts from a simple seed solver and has an LLM propose algorithmic improvements guided by a scoreboard of results and a history of prior ideas, with every candidate scored by an independent verifier so improvements are kept and failures discarded. Applied to the Packomania csqv benchmark it improved the best known solutions for 10 values of N between 101 and 114 by 2.4%-5.4%, all inside 15 iterations at a total LLM cost of $27.72, and Packomania independently accepted the results. The reusable pieces are the external verifier (not the model judging itself), the idea-history file that prevents re-proposing dead ends, and an adaptive plateau detector that stops the loop when gains flatten.