Who will win the World Cup? Who will win the 2026 FIFA World Cup? Here's what AI predicts As the 2026 FIFA Men's World Cup enters its final stages, AJLabs asked nine leading AI models to predict the tournament's final podium based on all available data for each team, including: France emerged as the favourite to lift the trophy, receiving five (Gemini, Grock, DeepSeek, Le Chat and Qwen) of the nine champion votes. Argentina, the defending world champions, received the remaining four votes (ChatGPT, Claude, Copilot and Meta AI). Predictions for the runner-up were more divided: France and Argentina each received three votes, followed by England with two and Spain with one. Spain was the clear favourite to finish third, receiving six of the nine third-place predictions, while England and France each received fewer votes. The predictions reflect a broad AI consensus around the four remaining contenders, France, Argentina, Spain and England, but also highlight differences in how leading language models weigh recent performances, squad depth and tournament momentum.

The video assistant referee system, or VAR, has led to some controversial calls at the 2026 World Cup. The penultimate Round of 16 match at the 2026 World Cup between Argentina and Egypt was marked not just by exceptional goals, great saves, and fans devoted to their teams. The match also sparked one of the most widely discussed controversies surrounding the video assistant referee system, known as VAR, a technology designed to assist on-field officials in making fairer decisions, but whose use has been criticized for allegedly favoring certain teams. Egypt was eliminated from the tournament with a 3-2 loss to Argentina, after having held a two-goal lead. The Egyptian Football Association argued that "the failure to properly use VAR" had influenced several refereeing decisions that affected the final score.

Earlier today, Meta announced that it was testing a new Meta AI chatbot for Threads that would function a lot like Grok on X. Even though the early beta isn't available to most people on the platform yet, a number of Threads users have discovered its not possible to opt out of the feature or block chatbot's the account. While most people aren't able to interact with bot yet -- the initial testing is limited to Malaysia, Saudi Arabia, Mexico, Argentina and Singapore -- the public-facing @ meta.ai account is viewable to everyone on the platform. The account's initial post has been met with a flood of angry replies from users demanding to know why, unlike any other Threads account, there's no option to block it entirely. Some users have even said that they have reported the account for spam, which typically ends with the option to block, only to find out that the block didn't actually go into effect.

In many classification settings, the class of primary interest is underrepresented, leading to imbalanced data problems that arise in applications such as rare disease detection and fraud identification. In these contexts, identifying a potential positive instance typically triggers costly follow-up actions, such as medical imaging or detailed transaction inspection, which are subject to limited operational capacity. Motivated by this setting, we consider classification problems where data may arrive sequentially and decisions must be made under constraints on the number of instances that can be selected for further analysis. We propose a classification framework that explicitly controls the rate of positive predictions, enforcing a user-defined bound on the proportion of observations classified as belonging to the minority class while maximizing detection performance. The approach can be implemented using standard learning methods and naturally extends to online settings, where decisions are taken in real time. We show that incorporating capacity constraints leads to substantial improvements over classical approaches, including resampling techniques such as SMOTE, which do not directly control the selection rate.

Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect to be corrected immediately. In this article, we adopt a different point of view: part of the nonreciprocity may reflect a genuine variation in the evaluation scale, while another part is due to random perturbations. We introduce an additive model in which the unknown underlying comparison matrix is consistent but not necessarily reciprocal. The reciprocal component carries the global ranking information, whereas the symmetric component describes possible scale variation. Around this structured matrix, we add a random perturbation and show how to estimate the noise level, assess whether the scale variation remains moderate, and assign probabilities to admissible ranking regions in the sense of strict ranking by pairwise comparisons. We also compare this approach with the brutal projection onto reciprocal matrices, which suppresses all symmetric information at once. The Gaussian perturbation model is used here not because human decisions are exactly Gaussian, but because observed judgment errors often result from the accumulation of many small effects. In such a context, the central limit principle provides a natural heuristic justification for Gaussian noise. This makes it possible to derive explicit estimators and probability assessments while keeping the model interpretable for decision problems.

The natural gradient method is widely used in statistical optimization, but its standard formulation assumes a Euclidean parameter space. This paper proposes an inversion-free stochastic natural gradient method for probability distributions whose parameters lie on a Riemannian manifold. The manifold setting offers several advantages: one can implicitly enforce parameter constraints such as positive definiteness and orthogonality, ensure parameters are identifiable, or guarantee regularity properties of the objective like geodesic convexity. Building on an intrinsic formulation of the Fisher information matrix (FIM) on a manifold, our method maintains an online approximation of the inverse FIM, which is efficiently updated at quadratic cost using score vectors sampled at successive iterates. In the Riemannian setting, these score vectors belong to different tangent spaces and must be combined using transport operations. We prove almost-sure convergence rates of $O(\log{s}/s^α)$ for the squared distance to the minimizer when the step size exponent $α>2/3$. We also establish almost-sure rates for the approximate FIM, which now accumulates transport-based errors. A limited-memory variant of the algorithm with sub-quadratic storage complexity is proposed. Finally, we demonstrate the effectiveness of our method relative to its Euclidean counterparts on variational Bayes with Gaussian approximations and normalizing flows.

Transformer architectures have achieved remarkable empirical success in modeling contextual relationships in natural language, yet a precise mathematical characterization of their expressive power remains incomplete. In this work, we introduce a measure-theoretic framework for contextual representations in which texts are modeled as probability measures over a semantic embedding space, and contextual relations between words, are represented as coupling measures between them. Within this setting, we introduce Sinkhorn Transformer, a transformer-like architecture. Our main result is a universal approximation theorem: any continuous coupling function between probability measures, that encodes the semantic relation coupling measure, can be uniformly approximated by a Sinkhorn Transformer with appropriate parameters.

Panel data methods are widely used in empirical analysis to address unobserved heterogeneity, but causal inference remains challenging when treatments are endogenous and confounding variables high-dimensional and potentially nonlinear. Standard instrumental variables (IV) estimators, such as two-stage least squares (2SLS), become unreliable when instrument validity requires flexibly conditioning on many covariates with potentially non-linear effects. This paper develops a Double Machine Learning estimator for static panel models with endogenous treatments (panel IV DML), and introduces weak-identification diagnostics for it. We revisit three influential migration studies that use shift-share instruments. In these settings, instrument validity depends on a rich covariate adjustment. In one application, panel IV DML strengthens the predictive power of the instrument and broadly confirms 2SLS results. In the other cases, flexible adjustment makes the instruments weak, leading to substantially more cautious causal inference than conventional 2SLS. Monte Carlo evidence supports these findings, showing that panel IV DML improves estimation accuracy under strong instruments and delivers more reliable inference under weak identification.

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