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.

We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate distributions $μ$ and $ν$ to a rank histogram on $\{ 0, \ldots, K\}$ and measure its deviation from uniformity via a discrete $f$-divergence, yielding a rank-statistic divergence estimator. We prove that the resulting estimator of the divergence is monotone in $K$, is always a lower bound of the true $f$-divergence, and we establish quantitative convergence rates for $K\to\infty$ under mild regularity of the quantile-domain density ratio. To handle high-dimensional data, we define the sliced rank-statistic $f$-divergence by averaging the univariate construction over random projections, and we provide convergence results for the sliced limit as well. We also derive finite-sample deviation bounds along with asymptotic normality results for the estimator. Finally, we empirically validate the approach by benchmarking against neural baselines and illustrating its use as a learning objective in generative modelling experiments.

Self-supervised learning (SSL) -- a training paradigm in which models learn useful representations from unlabeled data by exploiting the data itself as a source of supervision -- has emerged as a foundational component of the recent success of transformer architectures. By avoiding the need for manual annotations, SSL retains many of the benefits traditionally associated with supervised learning while avoiding reliance on labeled data. Consequently, SSL is widely adopted as a pretraining paradigm for learning general-purpose representations that substantially accelerate the optimization of downstream tasks, especially in data-scarce settings. A canonical example of a self-supervised learning task is masked language modeling (MLM), in which a neural network is trained to predict masked tokens in text using the remaining tokens as contextual information (Devlin et al., 2019a; Howard and Ruder, 2018; Radford et al., 2018; Brown et al., 2020; OpenAI, 2024). For example, given the sentence "The capital of France is Paris", a typical MLM task would be to teach the model to infer that we are speaking about the capital of a country from the context "France" and "Paris" from the masked sentence "The [MASK] of France is Paris".

Twelve miners have been killed by a Russian drone strike in eastern Ukraine, the country's largest private energy firm has said. DTEK said a bus carrying workers after a shift in the Dnipropetrovsk region had been targeted in Sunday's attack. At least seven people were injured. Earlier, at least two others were killed and nine injured in separate Russian attacks overnight and on Sunday. The victims included six people hurt when a drone hit a maternity hospital in Zaporizhzhia.

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' At least 12 people have been killed in a Russian drone attack on a bus carrying miners in Ukraine's southeastern Dnipropetrovsk region, the country's energy minister said. "Today, the enemy carried out a cynical and targeted attack on energy sector workers in the Dnipro region," Minister of Energy Denys Shmyhal posted on Telegram on Sunday.

The country's Ministry of Communication and Digital Affairs said it will monitor xAI's newly implemented safety measures on an ongoing basis. Grok is once again available in Indonesia, after the country lifted its ban on the AI chatbot that was seen generating millions of sexualized deepfakes, thousands of which included children. The country's Ministry of Communication and Digital Affairs released a statement earlier today, which said X is allowed to resume service in Indonesia but will be subject to monitoring for any future violations. According to the Indonesian government agency, X provided a letter that detailed several implemented measures that prevent the misuse of its Grok chatbot. Alexander Sabar, the ministry's director general of digital space supervision, said in the statement that the agency will test the new measures on an ongoing basis and will ban Grok again if it's found spreading illegal content or violating the country's laws regarding children.

Melania Trump documentary sparks controversy with stark divide on Rotten Tomatoes as critics panned the documentary as "propaganda" despite it scoring 99% with the "verified audience."