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Hill Sampling for Test-Time Scaling: A Simple and Better Alternative to Repeated Sampling, Evolution, and Training

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

Large language models (LLMs) can improve solutions to verifiable scientific and algorithmic problems by spending additional computation at test time. Recent systems achieve strong results with increasingly elaborate evolutionary search harnesses or by updating model parameters during test-time training. We ask how much of this machinery is necessary. We introduce Hill Sampling, a simple procedure that repeatedly samples candidate program edits from a frozen LLM, retains the best program found so far, and conditions all subsequent samples on that program. We evaluate the method on circle packin

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