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 any 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 using HumanEval 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.

Optimizing Perturbations for Improved Training of Machine Learning Models

Machine learning models have become indispensable tools in applications across the physical sciences. Their training is often time-consuming, vastly exceeding the inference timescales. Several protocols have been developed to perturb the learning process and improve the training, such as shrink and perturb, warm restarts, and stochastic resetting. For classifiers, these perturbations have been shown to result in enhanced speedups or improved generalization. However, the design of such perturbations is usually done \textit{ad hoc} by intuition and trial and error. To rationally optimize training protocols, we frame them as first-passage processes and consider their response to perturbations. We show that if the unperturbed learning process reaches a quasi-steady state, the response at a single perturbation frequency can predict the behavior at a wide range of frequencies. We demonstrate that this is the case when training a CIFAR-10 classifier using the ResNet-18 model and use this approach to identify an optimal perturbation and frequency. Our work allows optimization of training protocols of machine learning models using a statistical mechanical approach.