More Bang for the Buck: Improving the Inference of Large Language Models at a Fixed Budget using Reset and Discard (ReD)

The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the average number of unique questions answered as a function of the total number of attempts. We connect the two metrics and show that the empirically-observed power-law behavior in pass@k leads to a sublinear growth of the coverage@cost (diminishing returns). To solve this problem, we propose Reset-and-Discard (ReD), a query method of LLMs that increases coverage@cost for a given budget, regardless of the pass@k form. Moreover, given a pass@k, we can quantitatively predict the savings in the total number of attempts using ReD. If pass@k is not available for the model, ReD can infer its power-law exponent. Experiments on three LLMs across coding (HumanEval), math (GSM8K), and reasoning (MMLU-Pro) benchmarks demonstrate that ReD substantially reduces the required attempts, tokens, and USD cost to reach a desired coverage, while also offering an efficient way to measure inference power-laws. ReD's advantage is maintained for imperfect verifiers and outperforms the tested allocation baselines.