Pots, quadrants, confederation constraints, group position grids... the 2026 World Cup finals draw on Friday is not going to be a straightforward affair. There's a lot to unpack so we're going to explain it as simply as we can. Luckily, Fifa will have a computer to do most of the heavy lifting and make sure everything runs smoothly. Though as Uefa found out in 2021, sometimes technology does go wrong. Let's hope there will be no gremlins in Washington once the draw ceremony kicks off.

What is a Palestinian without olives? In Gaza, the world has seen the cost of a diplomacy that claims to uphold a rules-based order but applies it selectively. The United States intervened late, and only to defend an occupation the International Court of Justice (ICJ) has ruled illegal. Alongside other Western nations that built multilateral institutions, the US increasingly pursues nationalist agendas that undermine them. The hypocrisy is stark: one set of rules for Ukraine, another for Gaza.

Police accused of'homophobic assumptions' over victims of blackmail on Grindr Police failed to properly investigate allegations that a gang was blackmailing men on the gay dating app Grindr, the BBC can reveal. Our investigation has learned of five cases of suspected blackmail involving victims targeted on Grindr in one area, with at least four of them connected to the same gang, which remains at large. In one instance, a suspected victim killed himself 24 hours after a group of men turned up at his home demanding he hand over his new Range Rover. The Independent Office for Police Conduct (IOPC) watchdog has told Hertfordshire Police - the investigating force - to examine whether homophobic assumptions could have contributed to failures in the investigation. Hertfordshire Police said it was unable to discuss specific points about the case, which has now been reopened, but said it is committed to building and maintaining good working relationships with the LGBTQ+ communities.

Facial recognition technology could be used more often by UK police forces, according to new plans announced by the Home Office. Policing and crime minister Sarah Jones said a widespread rollout of the equipment could mark the biggest breakthrough in catching criminals since DNA matching. People are being asked for their views on its use, as part of a 10-week consultation launched on Thursday, possibly paving the way for new laws. Jones credited the technology for helping to arrest thousands of criminals, but campaign group Big Brother Watch said increased use would make George Orwell roll in his grave. Facial recognition is used to locate wanted suspects and find vulnerable people.

Cross-entropy (CE) training loss dominates deep learning practice, yet existing theory often relies on simplifications, either replacing it with squared loss or restricting to convex models, that miss essential behavior. CE and squared loss generate fundamentally different dynamics, and convex linear models cannot capture the complexities of non-convex optimization. We provide an in-depth characterization of multi-class CE optimization dynamics beyond the convex regime by analyzing a canonical two-layer linear neural network with standard-basis vectors as inputs: the simplest non-convex extension for which the implicit bias remained unknown. This model coincides with the unconstrained features model used to study neural collapse, making our work the first to prove that gradient flow on CE converges to the neural collapse geometry. We construct an explicit Lyapunov function that establishes global convergence, despite the presence of spurious critical points in the non-convex landscape. A key insight underlying our analysis is an inconspicuous finding: Hadamard Initialization diagonalizes the softmax operator, freezing the singular vectors of the weight matrices and reducing the dynamics entirely to their singular values. This technique opens a pathway for analyzing CE training dynamics well beyond our specific setting considered here.

Federated Learning (FL) is plagued by two key challenges: high communication overhead and performance collapse on heterogeneous (non-IID) data. Analytic FL (AFL) provides a single-round, data distribution invariant solution, but is limited to linear models. Subsequent non-linear approaches, like DeepAFL, regain accuracy but sacrifice the single-round benefit. In this work, we break this tradeoff. W e propose SAFLe, a framework that achieves scalable non-linear expressivity by introducing a structured head of bucketed features and sparse, grouped embeddings. W e prove this non-linear architecture is mathematically equivalent to a high-dimensional linear regression. This key equivalence allows SAFLe to be solved with AFL's single-shot, invariant aggregation law. Empirically, SAFLe establishes a new state-of-the-art for analytic FL, significantly outperforming both linear AFL and multi-round DeepAFL in accuracy across all benchmarks, demonstrating a highly efficient and scalable solution for federated vision.

High quality data is needed to unlock the full potential of AI for end users. However finding new sources of such data is getting harder: most publicly-available human generated data will soon have been used. Additionally, publicly available data often is not representative of users of a particular system -- for example, a research speech dataset of contractors interacting with an AI assistant will likely be more homogeneous, well articulated and self-censored than real world commands that end users will issue. Therefore unlocking high-quality data grounded in real user interactions is of vital interest. However, the direct use of user data comes with significant privacy risks. Differential Privacy (DP) is a well established framework for reasoning about and limiting information leakage, and is a gold standard for protecting user privacy. The focus of this work, \emph{Differentially Private Synthetic data}, refers to synthetic data that preserves the overall trends of source data,, while providing strong privacy guarantees to individuals that contributed to the source dataset. DP synthetic data can unlock the value of datasets that have previously been inaccessible due to privacy concerns and can replace the use of sensitive datasets that previously have only had rudimentary protections like ad-hoc rule-based anonymization. In this paper we explore the full suite of techniques surrounding DP synthetic data, the types of privacy protections they offer and the state-of-the-art for various modalities (image, tabular, text and decentralized). We outline all the components needed in a system that generates DP synthetic data, from sensitive data handling and preparation, to tracking the use and empirical privacy testing. We hope that work will result in increased adoption of DP synthetic data, spur additional research and increase trust in DP synthetic data approaches.

Agentic AI systems execute a sequence of actions, such as reasoning steps or tool calls, in response to a user prompt. To evaluate the success of their trajectories, researchers have developed verifiers, such as LLM judges and process-reward models, to score the quality of each action in an agent's trajectory. Although these heuristic scores can be informative, there are no guarantees of correctness when used to decide whether an agent will yield a successful output. Here, we introduce e-valuator, a method to convert any black-box verifier score into a decision rule with provable control of false alarm rates. We frame the problem of distinguishing successful trajectories (that is, a sequence of actions that will lead to a correct response to the user's prompt) and unsuccessful trajectories as a sequential hypothesis testing problem. E-valuator builds on tools from e-processes to develop a sequential hypothesis test that remains statistically valid at every step of an agent's trajectory, enabling online monitoring of agents over arbitrarily long sequences of actions. Empirically, we demonstrate that e-valuator provides greater statistical power and better false alarm rate control than other strategies across six datasets and three agents. We additionally show that e-valuator can be used for to quickly terminate problematic trajectories and save tokens. Together, e-valuator provides a lightweight, model-agnostic framework that converts verifier heuristics into decisions rules with statistical guarantees, enabling the deployment of more reliable agentic systems.

In the vision domain, dataset distillation arises as a technique to condense a large dataset into a smaller synthetic one that exhibits a similar result in the training process. While image data presents an extensive literature of distillation methods, text dataset distillation has fewer works in comparison. Text dataset distillation initially grew as an adaptation of efforts from the vision universe, as the particularities of the modality became clear obstacles, it rose into a separate branch of research. Several milestones mark the development of this area, such as the introduction of methods that use transformer models, the generation of discrete synthetic text, and the scaling to decoder-only models with over 1B parameters. Despite major advances in modern approaches, the field remains in a maturing phase, with room for improvement on benchmarking standardization, approaches to overcome the discrete nature of text, handling complex tasks, and providing explicit examples of real-world applications. In this report, we review past and recent advances in dataset distillation for text, highlighting different distillation strategies, key contributions, and general challenges.

This study presents an LLM-assisted annotation pipeline for the sociolinguistic and topical analysis of bilingual discourse in two typologically distinct contexts: Spanish-English and Spanish-Guaraní. Using large language models, we automatically labeled topic, genre, and discourse-pragmatic functions across a total of 3,691 code-switched sentences, integrated demographic metadata from the Miami Bilingual Corpus, and enriched the Spanish-Guaraní dataset with new topic annotations. The resulting distributions reveal systematic links between gender, language dominance, and discourse function in the Miami data, and a clear diglossic division between formal Guaraní and informal Spanish in Paraguayan texts. These findings replicate and extend earlier interactional and sociolinguistic observations with corpus-scale quantitative evidence. The study demonstrates that large language models can reliably recover interpretable sociolinguistic patterns traditionally accessible only through manual annotation, advancing computational methods for cross-linguistic and low-resource bilingual research.