Common modifications include:(i)tuning attack parameters (e.g., number ofsteps),(ii)replacing network components to simplify the attack (e.g., removing randomization or non-differentiable components), and(iii) replacing the loss function optimized by the attack.

In many scenarios, this failure can be attributed to obscuring the crucial interplay between the training algorithm and the underlying data distribution.

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.