Meet the UK's very own LeBron James... but not as you know it Look out LeBron James and Michael Jordan, there's a new basketball champ around. But it was made in Lisburn rather than Los Angeles or Chicago. The name 25416 may not appear on many replica vests, but it can shoot hoops like no-one else. And the basketball-playing robot won a school in Lisburn first prize at the UK-wide First Tech Challenge robotics competition. The team of sixth-formers from Friends' School came top of 48 schools from across the UK at the competition held in London's Copper Box Arena. Going down and working on it with my friends is honestly one of the highlights of my last year in school, he said.

Wall Street's AI winner hunt leads to seasoning maker in Japan Ajinomoto, known more as a seasonings and foods maker, holds more than 95% of global market share for insulating materials used in personal computers and data center servers. The beneficiaries of the artificial intelligence buildout are spreading far beyond technology high-flyers. Laura Lau found one in seasoning maker Ajinomoto. The Tokyo-based company is best known for making monosodium glutamate, or MSG, a flavor enhancer used in soups and vegetables. Its lesser-known business, called Build-Up Film, or ABF, makes insulating film used to package high-performance semiconductors.

People visit an Alibaba booth during the World Artificial Intelligence Conference in Shanghai on July 26, 2025. China is restricting overseas travel for top AI professionals in private firms such as Alibaba Group and DeepSeek, suggesting an escalation in measures intended to safeguard its technology and catch up to the U.S. in a pivotal sphere. Government agencies have begun imposing restrictions on individuals involved in advanced AI work and considered strategically important to the country, people familiar with the matter said. That means they need approval from relevant authorities before embarking on overseas travel, the people said, asking for anonymity to discuss a sensitive issue. Beijing has for years imposed travel restrictions on key personnel from prominent college researchers to nuclear scientists and executives at state firms.

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An ethical hacker who just won major prizes at a prestigious international competition says her days of competing could be numbered due to the rise of AI tools like Claude Mythos. Valentina Palmiotti - better known as Chompie - was the most successful individual at the annual Pwn2Own hacking competition in Berlin. She told BBC News that, for now, AI tools were helping her to win bug bounties - money given to hackers who spot vulnerabilities in online systems before they can be exploited by cyber-criminals. But she said systems like Mythos were so powerful that even champion hackers like her would soon struggle to compete with them. AI has shaken the cyber-security world, with concerns focussing on Mythos in particular.

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Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the coupling constraints, LR enables parallel subproblem solving and often yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical work has shown promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of $\mathcal{O}(s^{1.5}/\sqrt{N})$ for the learned multipliers, where $s$ is the number of coupling constraints and $N$ is the sample size. Second, we provide a minimax lower-bound of $Ω(s/\sqrt{N})$, proving that a linear dependency is unavoidable. Third, we constructively close this theoretical gap by proving that Stochastic Gradient Ascent (SGA) with averaging achieves the minimax optimal rate $Θ(s/\sqrt{N})$. Finally, we extend our framework to the learning-to-warm-start setting, proving that it achieves a fast, minimax-optimal rate of $Θ(s/N)$ and establishing a theoretical advantage over direct multiplier prediction.

Selecting a finite dictionary of observables whose span is Koopman-invariant is a central challenge in data-driven Koopman operator approximation. We address this problem by exploiting zero-block structure in Extended Dynamic Mode Decomposition (EDMD) matrices. We show that any sub-dictionary whose span is Koopman-invariant induces an exact zero block in the EDMD matrix, even for finite data. We then show that such blocks can be detected by applying PageRank to a row-normalized EDMD matrix constructed from a large initial dictionary. The theory extends to approximately invariant subspaces and yields stronger guarantees for personalized PageRank (PPR) when the seed observables lie inside the target block and reach all observables in that block. Combining EDMD concentration bounds with PageRank perturbation theory gives end-to-end detection guarantees with $O(1/\sqrt{M})$ finite-sample scaling and explicit constants. More generally, without assuming an invariant subspace exists, high PPR mass on a sub-dictionary controls discounted multi-step leakage from the seed observables. Numerical experiments on the Duffing oscillator, Van der Pol oscillator, Lorenz system, and a three-well Ramachandran potential suggest that the method identifies compact, interpretable dictionaries with accurate predictions.

We study the problem of multiclass PAC learning with bandit feedback in the realizable setting. In this framework, there is an unknown data distribution over an instance space $\mathcal{X}$ and a label space $\mathcal{Y}$, as in classical multiclass PAC learning, but the learner does not observe the labels of the i.i.d. training examples. Instead, in each round, it receives an unlabeled instance, predicts its label, and receives bandit feedback indicating only whether the prediction is correct. Despite this restriction, the goal remains the same as in classical PAC learning. We provide a general characterization of the optimal sample complexity of this problem, sharp for every concept class up to logarithmic factors. Our characterization is based on a new combinatorial dimension, termed the bandit $\mathrm{DS}$ dimension, defined via generalized combinatorial structures we call pseudo-boxes. These extend the pseudo-cubes underlying the $\mathrm{DS}$ dimension by allowing a different number of neighbors in each coordinate. In contrast to the $\mathrm{DS}$ dimension, which governs the full-information setting by counting the number of coordinates in the pseudo-cube, the bandit $\mathrm{DS}$ dimension aggregates the number of neighbors across coordinates, leading to a characterization in which the sample complexity scales with the total number of neighbors. We also propose a general learning algorithm achieving the upper bound, based on an algorithmic principle called ListCascade, which connects bandit learning to list learning and may be of independent interest.

Understanding the relationship between generalization and privacy remains a central challenge in modern machine learning theory, particularly for deep networks trained by variants of differentially private stochastic gradient descent (DP-SGD). In this work we make progress on this persistent open problem by proving a finite-sample bound on the approximate max-information of DP-SGD that exhibits scaling properties comparable with (Dwork et al, 2015)'s classic result for $ε$-differentially private algorithms, namely at most linear in the dataset size. From our result we obtain a general-purpose PAC-Bayes generalization bound in which the necessary prior distribution can be learned by DP-SGD, as well as a generalization bound for DP-SGD-trained models themselves, with a complexity term that is fully explicit and controlled by the optimization hyperparameters.