Hill Sampling, Which Only Samples Edits to the Best Program So Far, Beats AlphaEvolve's Reference on Erdős Minimum Overlap

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Beck, Ogren and Kobren repeatedly sample program edits from a frozen open-weight LLM, keep the best verified program, and condition every later sample on it. With no archives, evolutionary scaffold or test-time training, the method set a published state of the art on circle packing and improved on AlphaEvolve's Erdős minimum-overlap result in hours on eight H100s. Evolution strategies on the weights did worse than running the same loop at a zero learning rate. For any task with a verifier, try greedy hill-climbing over the best solution before building an evolutionary harness.