The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam -- when treated as a function that maps initial conditions to optimized results -- is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.

We study the design of computationally efficient online learning algorithms under smoothed analysis. In this setting, at every step an adversary generates a sample from an adaptively chosen distribution whose density is upper bounded by 1/ times the uniform density. Given access to an offline optimization (ERM) oracle, we give the first computationally efficient online algorithms whose sublinear regret depends only on the pseudo/VC dimension dof the class and the smoothness parameter .

The long-awaited V4 is more efficient and a win for Chinese chipmakers. On Friday, Chinese AI firm DeepSeek released a preview of V4, its long-awaited new flagship model. Notably, the model can process much longer prompts than its last generation, thanks to a new design that helps it handle large amounts of text more efficiently. Like DeepSeek's previous models, V4 is open source, meaning it is available for anyone to download, use, and modify. V4 marks DeepSeek's most significant release since R1, the reasoning model it launched in January 2025. R1, which was trained on limited computing resources, stunned the global AI industry with its strong performance and efficiency, turning DeepSeek from a little-known research team into China's best-known AI company almost overnight.

Machine learning models can frequently produce systematic errors on critical subsets (or slices) of data that share common attributes. Discovering and explaining such model bugs is crucial for reliable model deployment. However, existing bug discovery and interpretation methods usually involve heavy human intervention and annotation, which can be cumbersome and have low bug coverage. In this paper, we propose HiBug, an automated framework for interpretable model debugging. Our approach utilizes large pre-trained models, such as chatGPT, to suggest human-understandable attributes that are related to the targeted computer vision tasks. By leveraging pre-trained vision-language models, we can efficiently identify common visual attributes of underperforming data slices using humanunderstandable terms. This enables us to uncover rare cases in the training data, identify spurious correlations in the model, and use the interpretable debug results to select or generate new training data for model improvement. Experimental results demonstrate the efficacy of the HiBug framework. Code is available at: https://github.com/cure-lab/HiBug.

Direct policy search serves as one of the workhorses in modern reinforcement learning (RL), and its applications in continuous control tasks have recently attracted increasing attention. In this work, we investigate the convergence theory of policy gradient (PG) methods for learning the linear risk-sensitive and robust controller. In particular, we develop PG methods that can be implemented in a derivative-free fashion by sampling system trajectories, and establish both global convergence and sample complexity results in the solutions of two fundamental settings in risk-sensitive and robust control: the finite-horizon linear exponential quadratic Gaussian, and the finite-horizon linear-quadratic disturbance attenuation problems. As a by-product, our results also provide the first sample complexity for the global convergence of PG methods on solving zero-sum linear-quadratic dynamic games, a nonconvex-nonconcave minimax optimization problem that serves as a baseline setting in multi-agent reinforcement learning (MARL) with continuous spaces. One feature of our algorithms is that during the learning phase, a certain level of robustness/risk-sensitivity of the controller is preserved, which we termed as the implicit regularization property, and is an essential requirement in safety-critical control systems.