Our critical issue is that we are at odds with most of the technologically advanced world due to the trade wars that President Donald Trump has launched on friend and foe alike. But the Administration should recognize that the threat posed by China also includes robotics, and therefore put aside its trade differences with allies to try to form a joint effort. To win this war, the U.S. must first establish a comprehensive federal robotics strategy, similar to China's approach, to coordinate efforts across the public and private sectors. This includes creating a dedicated federal office to oversee robotics innovation and adoption. Next is the financial commitment to this battle.

Fox News senior national correspondent Rich Edson has the latest on a Chinese pair charged with smuggling a'devastating' pathogen to the U.S. on'The Story.' By all appearances, the world is edging perilously close to the brink of a catastrophic global conflict. In just the past few days, five deeply troubling developments have emerged -- each significant on its own -- but taken together, they form a pattern too urgent to dismiss. Viewed in context, these events expose a rapidly deteriorating international order, where diplomacy is failing, deterrence is weakening, and the risk of multi-theater war is rising sharply. First, Ukraine's audacious drone strike deep inside Russian territory -- reportedly destroying or damaging a significant share of Russia's strategic bomber fleet -- bears the hallmarks of Western involvement.

Thousands of protesters have clashed with authorities as they took to the streets of Los Angeles for a third night in response to United States President Donald Trump's extraordinary deployment of the National Guard. Sunday's protests in Los Angeles, a sprawling city of 4 million people, were centred in several blocks of the city centre. It was the third and most intense day of demonstrations against Trump's immigration crackdown in the region, as the arrival of about 300 National Guard troops spurred anger and fear among many residents. The troops were deployed specifically to protect federal buildings, including the Metropolitan Detention Center where protesters concentrated. The crowds blocked a major highway and set fire to self-driving cars.

Three months after the Chinese artificial intelligence developer DeepSeek upended the tech world with a model that rivaled America's best, a 28-year-old AI executive named Alexandr Wang came to Capitol Hill to tell policymakers what they needed to do to maintain U.S. dominance. The U.S. needs to establish a "national AI data reserve," supply enough power for data centers and avoid an onerous patchwork of state-level rules, Wang said at the April hearing. "It's good to see you again here in Washington," Republican Representative Neal Dunn of Florida said. Wang, the chief executive officer of Scale AI, may not be a household name in the same way OpenAI's Sam Altman has become. But he and his company have gained significant influence in tech and policy circles in recent years.

In a wide-ranging report analysing the benefits and threats posed by AI to the UK's film, TV, video game and visual special effects industries, the BFI also raises fears that automation will eliminate the entry-level jobs that bring in the next generation of workers. It says the "primary issue" facing the 125bn industry is the use of intellectual property (IP) to train generative AI models without payment to, or permission from, rights holders. The UK creative industries want to see an "opt-in" regime, forcing AI companies to seek permission and strike licensing deals before they can use content, and the government is currently in the process of considering what legislation to put in place. "AI offers significant opportunities for the screen sector such as speeding up production workflows, democratising content creation and empowering new voices," said Rishi Coupland, director of research and innovation at the BFI. "However, it could also erode traditional business models, displace skilled workers, and undermine public trust in screen content."

As Los Angeles police struggled with another day of unrest in downtown L.A., several Waymo autonomous taxis were set on fire, sending black smoke billowing into the air. The dramatic images were captured during an afternoon of clashes between large groups who were protesting immigration raids by the Trump administration and L.A. police who were trying to maintain order. For some time, protesters blocked traffic on the 101 Freeway before California Highway Patrol officers slowly pushed them back. Police advised residents to avoid the the 101 Freeway through downtown L.A. Images of the Waymo cars on fire on Los Angeles Street were broadcast nationally as Los Angeles has become a flashpoint in the immigration debate. Tires were slashed, windows smashed, and anti-ICE messages spray-painted over the cars, which were parked in a row.

Zeroth-order methods are extensively used in machine learning applications where gradients are infeasible or expensive to compute, such as black-box attacks, reinforcement learning, and language model fine-tuning. Existing optimization theory focuses on convergence to an arbitrary stationary point, but less is known on the implicit regularization that provides a fine-grained characterization on which particular solutions are finally reached. We show that zeroth-order optimization with the standard two-point estimator favors solutions with small trace of Hessian, which is widely used in previous work to distinguish between sharp and flat minima. We further provide convergence rates of zeroth-order optimization to approximate flat minima for convex and sufficiently smooth functions, where flat minima are defined as the minimizers that achieve the smallest trace of Hessian among all optimal solutions. Experiments on binary classification tasks with convex losses and language model fine-tuning support our theoretical findings.

Physics has been transforming our view of nature for centuries. While combining physical knowledge with computational approaches has enabled detailed modeling of physical systems' evolution, understanding the emergence of patterns and structures remains limited. Correlations between quantities are the most reliable approach to describe relationships between different variables. However, for complex patterns, directly searching for correlations is often impractical, as complexity and spatial inhomogeneity can obscure correlations. We discovered that the key is to search for correlations in local regions and developed a new method, adjacent correlation analysis, to extract such correlations and represent them in phase space. When multiple observations are available, a useful way to study a system is to analyze distributions in phase space using the Probability Density Function (PDF). Adjacent correlation analysis evaluates vectors representing local correlations, which can be overlaid on the PDF plot to form the adjacent correlation plot. These correlation vectors often exhibit remarkably regular patterns and may lead to the discovery of new laws. The vectors we derive are equivalent to the vector field in dynamical systems on the attracting manifold. By efficiently representing spatial patterns as correlation vectors in phase space, our approach opens avenues for classification, prediction, parameter fitting, and forecasting.

We propose $\textbf{MGCL}$, a model-driven graph contrastive learning (GCL) framework that leverages graphons (probabilistic generative models for graphs) to guide contrastive learning by accounting for the data's underlying generative process. GCL has emerged as a powerful self-supervised framework for learning expressive node or graph representations without relying on annotated labels, which are often scarce in real-world data. By contrasting augmented views of graph data, GCL has demonstrated strong performance across various downstream tasks, such as node and graph classification. However, existing methods typically rely on manually designed or heuristic augmentation strategies that are not tailored to the underlying data distribution and operate at the individual graph level, ignoring similarities among graphs generated from the same model. Conversely, in our proposed approach, MGCL first estimates the graphon associated with the observed data and then defines a graphon-informed augmentation process, enabling data-adaptive and principled augmentations. Additionally, for graph-level tasks, MGCL clusters the dataset and estimates a graphon per group, enabling contrastive pairs to reflect shared semantics and structure. Extensive experiments on benchmark datasets demonstrate that MGCL achieves state-of-the-art performance, highlighting the advantages of incorporating generative models into GCL.

A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation, successful application in several domains, and experimental validation, a formal complete convergence analysis remains elusive. Building on this framework, we consider and analyze a continuous-time neural network, the \emph{similarity matching network}, for principal subspace projection. Derived from a min-max-min objective, this biologically-plausible network consists of three coupled dynamics evolving at different time scales: neural dynamics, lateral synaptic dynamics, and feedforward synaptic dynamics at the fast, intermediate, and slow time scales, respectively. The feedforward and lateral synaptic dynamics consist of Hebbian and anti-Hebbian learning rules, respectively. By leveraging a multilevel optimization framework, we prove convergence of the dynamics in the offline setting. Specifically, at the first level (fast time scale), we show strong convexity of the cost function and global exponential convergence of the corresponding gradient-flow dynamics. At the second level (intermediate time scale), we prove strong concavity of the cost function and exponential convergence of the corresponding gradient-flow dynamics within the space of positive definite matrices. At the third and final level (slow time scale), we study a non-convex and non-smooth cost function, provide explicit expressions for its global minima, and prove almost sure convergence of the corresponding gradient-flow dynamics to the global minima. These results rely on two empirically motivated conjectures that are supported by thorough numerical experiments. Finally, we validate the effectiveness of our approach via a numerical example.