Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit models to making only one attempt at a problem. Here, we explore inference compute as another axis for scaling, using the simple technique of repeatedly sampling candidate solutions from a model. Across multiple tasks and models, we observe that coverage -- the fraction of problems that are solved by any generated sample -- scales with the number of samples over four orders of magnitude. Interestingly, the relationship between coverage and the number of samples is often log-linear and can be modelled with an exponentiated power law, suggesting the existence of inference-time scaling laws. In domains like coding and formal proofs, where answers can be automatically verified, these increases in coverage directly translate into improved performance. When we apply repeated sampling to SWE-bench Lite, the fraction of issues solved with DeepSeek-Coder-V2-Instruct increases from 15.9% with one sample to 56% with 250 samples, outperforming the single-sample state-of-the-art of 43%. In domains without automatic verifiers, we find that common methods for picking from a sample collection (majority voting and reward models) plateau beyond several hundred samples and fail to fully scale with the sample budget.
Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inference
Institute of Foundation Models, MBZUAI（基础模型研究所，MBZUAI）；Huawei Lagrange Mathematics and Computing Research Center, Paris, France（华为拉格朗日数学与计算研究中心，法国巴黎）；Mohamed Bin Zayed University of AI, Chair of the ML Department, EPITA, Laboratoire Recherche de l'EPITA（穆罕默德·本·扎耶德人工智能大学，机器学习系主任，EPITA，EPITA研究实验室）
FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling
School of Life Science and Technology, Institute of Science Tokyo（生命科学与技术学院，科学东京研究所）；Department of Computational Biology and Medical Sciences, Graduate School of Frontier Sciences（计算生物学与医学科学系，前沿科学研究生院）
Is Thompson Sampling Susceptible to Algorithmic Collusion?
School of Information Management and Engineering, Shanghai University of Finance and Economics（上海财经大学信息管理与工程学院）；The Rotman School of Management, University of Toronto（多伦多大学罗特曼管理学院）；Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong（香港中文大学系统工程与工程管理学系）
