Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' A Russian drone strike on a bus carrying miners in Ukraine's Dnipropetrovsk region killed at least 12 people, according to officials. Ukrainian Deputy Prime Minister Denys Shmyhal denounced the strike as a "cynical and targeted" attack on energy workers.

The Kennedy Center in Washington DC will be closed for a two-year renovation beginning in July, President Donald Trump has announced. In a post on Truth Social on Sunday, Trump said the centre would close on 4 July this year in honor of the 250th Anniversary of our Country. The move follows several artists cancelling performances at the storied institution after it was recently renamed as the Trump Kennedy Center. Shortly after taking office, the president fired several of the board members at the centre and replaced them with allies, who then voted to make Trump chairman of the board. The new board renamed the institution the Donald J Trump and the John F Kennedy Memorial Center for the Performing Arts in December.

Three West African juntas have turned to Russia. The US has declared a stark policy shift towards three West African countries which are battling Islamist insurgents and whose military governments have broken defence ties with France and turned towards Russia. The state department announced that Nick Checker, head of its Bureau of African Affairs, would visit Mali's capital Bamako to convey the United States' respect for Mali's sovereignty and chart a new course in relations, moving past policy missteps. It adds that the US also looks forward to co-operating with Mali's allies, neighbouring Burkina Faso and Niger, on shared security and economic interests. Absent from the agenda is the longstanding American concern for democracy and human rights.

Americans pulling into a Starbucks drive thru might think they are being served by a friendly staff member. But at some locations, the voice listening to the order is actually an AI robot. Behind the counter inside the store, baristas can lean on a virtual personal assistant to recall recipes or manage schedules. In the back of the shop, a scanning tool has taken on the painstaking process of counting the inventory, relieving staff of one of retail's most tedious chores, in a bid to fix the out-of-stock gaps that have frustrated the firm. The new technology is part of the hundreds of millions of dollars the 55-year-old coffee giant has been investing as it tries to win back customers after several years of struggling sales.

Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a mathematical framework for LLMs by describing the encoding of text sequences into sequences of tokens, defining the architecture for next-token prediction models, explaining how these models are learned from data, and demonstrating how they are deployed to address a variety of tasks. The mathematical sophistication required to understand this material is not high, and relies on straightforward ideas from information theory, probability and optimization. Nonetheless, the combination of ideas resting on these different components from the mathematical sciences yields a complex algorithmic structure; and this algorithmic structure has demonstrated remarkable empirical successes. The mathematical framework established here provides a platform from which it is possible to formulate and address questions concerning the accuracy, efficiency and robustness of the algorithms that constitute LLMs. The framework also suggests directions for development of modified and new methodologies.

Overparameterized models have recently challenged conventional learning theory by exhibiting improved generalization beyond the interpolation limit, a phenomenon known as benign overfitting. This work introduces Adaptive Benign Overfitting (ABO), extending the recursive least-squares (RLS) framework to this regime through a numerically stable formulation based on orthogonal-triangular updates. A QR-based exponentially weighted RLS (QR-EWRLS) algorithm is introduced, combining random Fourier feature mappings with forgetting-factor regularization to enable online adaptation under non-stationary conditions. The orthogonal decomposition prevents the numerical divergence associated with covariance-form RLS while retaining adaptability to evolving data distributions. Experiments on nonlinear synthetic time series confirm that the proposed approach maintains bounded residuals and stable condition numbers while reproducing the double-descent behavior characteristic of overparameterized models. Applications to forecasting foreign exchange and electricity demand show that ABO is highly accurate (comparable to baseline kernel methods) while achieving speed improvements of between 20 and 40 percent. The results provide a unified view linking adaptive filtering, kernel approximation, and benign overfitting within a stable online learning framework.

We study offline imitation learning (IL) when part of the decision-relevant state is observed only through noisy measurements and the distribution may change between training and deployment. Such settings induce spurious state-action correlations, so standard behavioral cloning (BC) -- whether conditioning on raw measurements or ignoring them -- can converge to systematically biased policies under distribution shift. We propose a general framework for IL under measurement error, inspired by explicitly modeling the causal relationships among the variables, yielding a target that retains a causal interpretation and is robust to distribution shift. Building on ideas from proximal causal inference, we introduce \texttt{CausIL}, which treats noisy state observations as proxy variables, and we provide identification conditions under which the target policy is recoverable from demonstrations without rewards or interactive expert queries. We develop estimators for both discrete and continuous state spaces; for continuous settings, we use an adversarial procedure over RKHS function classes to learn the required parameters. We evaluate \texttt{CausIL} on semi-simulated longitudinal data from the PhysioNet/Computing in Cardiology Challenge 2019 cohort and demonstrate improved robustness to distribution shift compared to BC baselines.

We study continual mean estimation, where data vectors arrive sequentially and the goal is to maintain accurate estimates of the running mean. We address this problem under user-level differential privacy, which protects each user's entire dataset even when they contribute multiple data points. Previous work on this problem has focused on pure differential privacy. While important, this approach limits applicability, as it leads to overly noisy estimates. In contrast, we analyze the problem under approximate differential privacy, adopting recent advances in the Matrix Factorization mechanism. We introduce a novel mean estimation specific factorization, which is both efficient and accurate, achieving asymptotically lower mean-squared error bounds in continual mean estimation under user-level differential privacy.

We introduce the Thresholding Monte Carlo Tree Search problem, in which, given a tree $\mathcal{T}$ and a threshold $θ$, a player must answer whether the root node value of $\mathcal{T}$ is at least $θ$ or not. In the given tree, `MAX' or `MIN' is labeled on each internal node, and the value of a `MAX'-labeled (`MIN'-labeled) internal node is the maximum (minimum) of its child values. The value of a leaf node is the mean reward of an unknown distribution, from which the player can sample rewards. For this problem, we develop a $δ$-correct sequential sampling algorithm based on the Track-and-Stop strategy that has asymptotically optimal sample complexity. We show that a ratio-based modification of the D-Tracking arm-pulling strategy leads to a substantial improvement in empirical sample complexity, as well as reducing the per-round computational cost from linear to logarithmic in the number of arms.

Large-scale AI evaluation increasingly relies on aggregating binary judgments from $K$ annotators, including LLMs used as judges. Most classical methods, e.g., Dawid-Skene or (weighted) majority voting, assume annotators are conditionally independent given the true label $Y\in\{0,1\}$, an assumption often violated by LLM judges due to shared data, architectures, prompts, and failure modes. Ignoring such dependencies can yield miscalibrated posteriors and even confidently incorrect predictions. We study label aggregation through a hierarchy of dependence-aware models based on Ising graphical models and latent factors. For class-dependent Ising models, the Bayes log-odds is generally quadratic in votes; for class-independent couplings, it reduces to a linear weighted vote with correlation-adjusted parameters. We present finite-$K$ examples showing that methods based on conditional independence can flip the Bayes label despite matching per-annotator marginals. We prove separation results demonstrating that these methods remain strictly suboptimal as the number of judges grows, incurring nonvanishing excess risk under latent factors. Finally, we evaluate the proposed method on three real-world datasets, demonstrating improved performance over the classical baselines.