The FIFA Club World Cup has undergone a revamp since it was last competed in December 2023 in Saudi Arabia. The number of participating clubs has increased fourfold to 32, the frequency of the competition has gone from annual to quadrennial and the champion's prize money – previously 5m – has gone up by a whopping 35m. It's not just the numbers that have changed in the tournament. FIFA is also looking to introduce new technology, including artificial intelligence to help the referees, and it is getting stricter on goalkeepers who waste time while holding the ball. Here's a look at the three big changes to be implemented at the monthlong tournament, which will get under way on Saturday in the United States: Small cameras, protruding from the referees' ears, will capture the live action unfolding in front of them.

On Friday, Elon Musk once again pledged to depart his role at DOGE, taking with him his bad personality, weird public behavior, complicated family life, troubled businesses, alleged regular illegal drug use, compulsive social media habits, exploding rockets, messianic conviction that he control all of earth's resources so as to colonize Mars, and a remarkably poor track record in his brief life as a quasi-public servant. He leaves behind the incredible destruction DOGE has wrought, and of course, DOGE itself, which will continue its work, as Project 2025 architect and Office of Management and Budget director Russell Vought reportedly floats making its cuts permanent without the approval of Congress. Even Trump says Musk is "really not leaving." But it would be a mistake to think that Musk's grip on the government is lessening; beyond his continued relationship with the Trump administration, Musk's companies will still have billions in lucrative and influential federal contracts. And as his recent travel shows, there are clear signs that Musk is also using his relationship with President Trump to pursue business, especially in the Middle East.

Current state-of-the-art synchrony-based models encode object bindings with complex-valued activations and compute with real-valued weights in feedforward architectures. We argue for the computational advantages of a recurrent architecture with complex-valued weights. We propose a fully convolutional autoencoder, SynCx, that performs iterative constraint satisfaction: at each iteration, a hidden layer bottleneck encodes statistically regular configurations of features in particular phase relationships; over iterations, local constraints propagate and the model converges to a globally consistent configuration of phase assignments. Binding is achieved simply by the matrix-vector product operation between complex-valued weights and activations, without the need for additional mechanisms that have been incorporated into current synchrony-based models. SynCx outperforms or is strongly competitive with current models for unsupervised object discovery. SynCx also avoids certain systematic grouping errors of current models, such as the inability to separate similarly colored objects without additional supervision.

We consider the decentralized stochastic asynchronous optimization setup, where many workers asynchronously calculate stochastic gradients and asynchronously communicate with each other using edges in a multigraph. For both homogeneous and heterogeneous setups, we prove new time complexity lower bounds under the assumption that computation and communication speeds are bounded.

Solving nonlinear partial differential equations (PDEs) with multiple solutions is essential in various fields, including physics, biology, and engineering.

Inspired by a recent breakthrough of Mishchenko et al. [2022], who for the first time showed that local gradient steps can lead to provable communication acceleration, we propose an alternative algorithm which obtains the same communication acceleration as their method (ProxSkip). Our approach is very different, however: it is based on the celebrated method of Chambolle and Pock [2011], with several nontrivial modifications: i) we allow for an inexact computation of the prox operator of a certain smooth strongly convex function via a suitable gradient-based method (e.g., GD, Fast GD or FSFOM), ii) we perform a careful modification of the dual update step in order to retain linear convergence. Our general results offer the new state-of-the-art rates for the class of strongly convex-concave saddle-point problems with bilinear coupling characterized by the absence of smoothness in the dual function.

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication rounds required to achieve ε accuracy have recently been proven. We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. We show that our first method is optimal both in terms of the number of communication rounds and in terms of the number of gradient computations. Unlike existing optimal algorithms, our algorithm does not rely on the expensive evaluation of dual gradients. Our second algorithm is optimal in terms of the number of communication rounds, without a logarithmic factor. Our approach relies on viewing the two proposed algorithms as accelerated variants of the Forward Backward algorithm to solve monotone inclusions associated with the decentralized optimization problem. We also verify the efficacy of our methods against state-of-the-art algorithms through numerical experiments.

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication rounds required to achieve ε accuracy have recently been proven. We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. We show that our first method is optimal both in terms of the number of communication rounds and in terms of the number of gradient computations. Unlike existing optimal algorithms, our algorithm does not rely on the expensive evaluation of dual gradients. Our second algorithm is optimal in terms of the number of communication rounds, without a logarithmic factor. Our approach relies on viewing the two proposed algorithms as accelerated variants of the Forward Backward algorithm to solve monotone inclusions associated with the decentralized optimization problem. We also verify the efficacy of our methods against state-of-the-art algorithms through numerical experiments.

We propose a new algorithm--Stochastic Proximal Langevin Algorithm (SPLA)--for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting technique only requires access to a stochastic gradient of the smooth term and a stochastic proximal operator for each of the nonsmooth terms. We establish nonasymptotic sublinear and linear convergence rates under convexity and strong convexity of the smooth term, respectively, expressed in terms of the KL divergence and Wasserstein distance. We illustrate the efficiency of our sampling technique through numerical simulations on a Bayesian learning task.