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The world's oceans are under heat stress, with average sea surface temperatures hitting 21 C, surpassing the record highs of 2023 and 2024. They're expected to rise further as El Niño, a natural climate pattern that warms the tropical Pacific for months, develops. How AI is being weaponised against India's Muslim women

We develop a framework for analyzing the learning dynamics of $\ell_2$-adversarial training of single-index models on Gaussian mixtures in the high-dimensional limit under streaming stochastic gradient descent (SGD). We derive deterministic equivalents for a broad class of statistics of the SGD iterates, including the adversarial risk and distance to adversarial optimality, in terms of the solution to a system of ODEs. We use them to study two idealized learning rate schedules: the Polyak stepsize and exact line search. In the case of $\ell_2$-adversarial least squares with a single class, we show that, unlike noiseless standard least squares, no constant learning rate guarantees monotone descent of SGD towards a minimizer of the adversarial risk. We identify anisotropic covariance and a mismatch in ridge parameters as the main sources of suboptimality of exact line search relative to the Polyak stepsize. We also introduce a stochastic differential equation (SDE), called adversarial homogenized SGD, that captures the evolution of statistics of the iterates of SGD. For $\ell_2$-adversarial least squares, using this SDE, we show the evolution of the risk is equivalent, up to dimension-free constants, to that of SGD on standard least squares with an adaptive learning rate and adaptive $\ell_2$-regularization. When the dynamics converge, the limiting adversarial risk and SGD iterate are determined by a fixed-point equation, with the limiting iterate being equivalent to the solution of a ridge regression problem whose regularization parameter is the limiting effective regularization of SGD.

People participate in a march to protest against the opening of AI datacentres in Vancouver, Canada, on 27 June 2026. People participate in a march to protest against the opening of AI datacentres in Vancouver, Canada, on 27 June 2026. We can live without AI, but can we live without clean water? Readers respond to an article about Erin Brockovich's battle against datacentres and voice their fears for the environment What are the benefits obtained from AI's massive use of electricity and water ( 'We're up against forces that have all the money in the world': Erin Brockovich on her battle against AI datacentres, 29 June)? Analysis shows that the top four uses of AI are "therapy/companionship", "technical assistance and troubleshooting", "fun and nonsense", and "fan fiction and storytelling". AI use for therapy, and due to loneliness, appears not to reduce loneliness.

Gojek co-founder and former Education Minister Nadiem Makarim has been sentenced to 10 years in prison after being convicted of corruption. Makarim, a former billionaire and symbol of Indonesia's tech boom, says the verdict is politically motivated and plans to appeal. Why is MAGA in meltdown over the Supreme Court birthright ruling? Supreme Court's divided ruling on birthright citizenship may be revisited Iran says it couldn't export a'single barrel of oil' during US blockade Mexican fans keep Ecuador's team awake before World Cup showdown

The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections. Standard estimators of the SW distance rely on Monte Carlo averages of one-dimensional Wasserstein distances computed via quantile functions, which require sorting projected samples and access to full datasets. In this work, we introduce a new class of estimators for the Sliced Wasserstein distance based on cumulative distribution functions (CDFs) of projected measures, that avoid sorting and scale via massive dataset parallelism. This class includes several estimators, some of them being indexed by hyperparameters controlling their variance or smoothness. We show that they are especially well suited to scenarios in which CDFs are more tractable than quantile functions, such as mixtures of Gaussians, and moreover that they are also naturally compatible with federated learning, since CDFs of projected data can be computed and aggregated locally without requiring the exchange of raw samples.

Speculative decoding accelerates language model inference by using a fast drafter to propose candidate tokens that are then verified by a larger target model. Existing theory largely studies the stochastic, distribution-preserving setting, where the goal is to exactly sample from the target distribution. In contrast, many practical systems use greedy decoding, relaxed acceptance rules, or tree-based candidate sets, where success is governed by local ranking and threshold events rather than exact distributional equality. We develop a theory for these regimes. We identify that many common acceptance criteria have rejection regions that can be characterized as lower level sets of the target distribution. For these, we characterize the exact KL divergence required for rejection yielding exact certificates and sharp margin-based bounds for strict greedy decoding, additive and multiplicative relaxed acceptance, top-(m) relaxed criteria, and entropy-thresholded acceptance. We then extend the framework to greedy tree decoding, deriving exact and margin-only certificates for when the target greedy token remains covered by the drafter's top-(m) candidates. Finally, we evaluate the resulting certificates on Qwen3 models, showing that relaxed and tree-based criteria substantially enlarge the region of certified acceptance, especially on decoding steps with low target model distribution margin. These results complement existing distribution-preserving analyses of speculative decoding by characterizing the deterministic local acceptance events common in practical inference systems.

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We study PAC-Bayes derandomization for smooth loss functions. Our goal is to obtain generalization bounds that hold with high probability for deterministic predictors by exploiting smoothness properties of both the loss and the predictor class. We show that passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost, given by the generalization gap of the Jensen gap class. We control this class through its Rademacher complexity, leading to bounds for deterministic predictors that involve flatness quantities expressed in terms of parameter Jacobians and Hessians of the score map. The framework applies to both bounded and unbounded smooth loss functions, and we specialize the results to linear predictors and smooth neural networks. Finally, the Jacobian and Hessian quantities appearing in the theory motivate a practical regularizer. For BatchNorm networks, we compute this regularizer with respect to effective BatchNorm weights obtained by folding the BatchNorm transformation into the adjacent affine weights. Experiments on CIFAR-10 illustrate the behavior of this regularizer under different batch sizes.

It's a rare chance to save on the outdoor-coded Canadian company's understated and stylish performance clothing. Now that Amazon Prime Day is over, it's time to start gearing up for Fourth of July sales. Most large retailers pivoted their summer-sale timing to compete head-on with Amazon's accelerated schedule, but you can still snag great deals this July 4th, particularly in active and outdoorsy categories. REI has the hottest sale of the weekend as far as the WIRED Reviews team is concerned, but there are notable midsummer sales on other sites we shop, like Backcountry, Home Depot, and Lululemon . Also, make sure you don't sleep on Duer.