Inside the Colosseum's Passage of Commodus, where emperors once walked One theory suggests the infamous Roman emperor survived an assassination attempt in the tunnel now open to the public. From October 2024 to September 2025, a team of experts restored part of the tunnel that's open to visitors for the first time. Breakthroughs, discoveries, and DIY tips sent six days a week. They say all roads lead to Rome . But in the Eternal City, all of the major roads were thought to lead somewhere very specific--a single column called the Milliarium Auereum, or the golden milestone.

Leveraging this flexibility, we implement 47 novel MCBO algorithms and benchmark them against seven existing MCBO solvers and five standard black-box optimization algorithms on ten tasks, conducting over 4000 experiments.

It is more memory-efficient than Adam as it only keeps track of the momentum. Different from adaptive optimizers, its update has the same magnitude for each parameter calculated through the sign operation. We compare Lion with widely used optimizers, such as Adam and Adafactor, for training a variety of models on different tasks. On image classification, Lion boosts the accuracy of ViT by up to 2% on ImageNet and saves up to 5x the pre-training compute on JFT.

Hyperparameter optimization is an important subfield of machine learning that focuses on tuning the hyperparameters of a chosen algorithm to achieve peak performance. Recently, there has been a stream of methods that tackle the issue of hyperparameter optimization, however, most of the methods do not exploit the dominant power law nature of learning curves for Bayesian optimization. In this work, we propose Deep Power Laws (DPL), an ensemble of neural network models conditioned to yield predictions that follow a power-law scaling pattern. Our method dynamically decides which configurations to pause and train incre-mentally by making use of gray-box evaluations.

In general, this has a cubic cost in dataset size and is sensitive to conditioning.

Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities.

By now Bayesian methods are routinely used in practice for solving inverse problems.