LLM Broke 10 Circle Packing Records for $28

The Discovery Loop system, featuring an LLM agent and an independent verifier, improved the 10 best known solutions on the Packomania csqv circle packing benchmark by 2.4–5.4% in no more than 15 iterations, with a model call cost of $27.72.

Compiled by Sergey KostenchukPublished 2026-09-08Updated 2026-09-18

2026-09-08 Research

🧠 LLM Broke 10 Circle Packing Records for $28

Discovery Loop by researcher Wes Sander: an LLM agent iteratively improves optimization algorithms — proposing changes based on a scoreboard and history of past ideas, with each candidate checked by an independent verifier. On the Packomania csqv benchmark, the system updated the best known solutions for 10 values of N by 2.4–5.4% in no more than 15 iterations, with $27.72 spent on LLM calls. The records were accepted by the Packomania database.

🌍 LLM + verifier: a reproducible template for automated research in optimization — here, verifiable improvements to classical algorithms cost roughly $2.77 per record.

👤 The arXiv:2609.05093 paper and code with .pck files of accepted solutions are open under the MIT license — the 'LLM + verifier' loop can be cloned for your own optimization problems.

Source 1: https://arxiv.org/abs/2609.05093 Source 2: https://github.com/ucsandman/discovery-loop

Sources