Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural electrophysiological experiments. Standard low-rank estimators impose a single global latent geometry, which can recover average structure but may smooth away subgroup-specific variation, especially when observations are unevenly distributed across groups. We introduce Group-Aware Matrix Estimation (GAME), a convex estimator for overlapping subgroup-wise low-rank matrix estimation. GAME regularizes category-specific submatrices through overlapping nuclear-norm penalties, allowing related groups to borrow information while preserving local latent structure in a shared coordinate system. We provide finite-sample guarantees for both reconstruction error and subgroup-specific subspace recovery, showing how performance depends on sampling density, subgroup rank, and overlap structure. Experiments on synthetic, recommendation, ecological, and neuroscience datasets show that GAME is most beneficial in structured missingness regimes, where subgroup-aware regularization improves both reconstruction accuracy and latent subspace fidelity. Across these benchmarks, GAME is competitive or best among global low-rank, side-information, and modern imputation baselines, with the largest gains when subgroups exhibit distinct low-rank structure.

Communication is a major bottleneck in distributed learning, especially in large-scale settings and in federated learning environments with slow links. Three standard ways to reduce this cost are communication compression, local training, and communication-computation overlap. Methods that combine these ingredients are used in practice and have been found to be effective for large-scale training, but there is little theory for methods that combine all three. We study a heterogeneous-compute setting in which different workers may take different numbers of local steps, and we propose LOSCAR-SGD, a Local SGD method that communicates only a sparse subset of model coordinates and continues optimizing while communication is in flight. A key ingredient is a delay-corrected merge rule that incorporates delayed synchronized information without discarding the progress made during the overlap phase. We give convergence guarantees for smooth non-convex objectives and show how sparsity, overlap, and worker heterogeneity affect the rate. To the best of our knowledge, this is the first theory for this combination of ingredients. Experiments further show that communication-computation overlap reduces training time and that the delay-corrected merge outperforms naive overwriting.

Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models, recasting predictive sampling as an ODE with closed-form Gaussian dynamics and a likelihood-dependent guidance term that admits a simple Monte Carlo approximation. In the linear-Gaussian setting, we recover standard GP conditioning exactly; beyond conjugacy, the same machinery handles any conditioning statement admitting point-wise likelihood evaluation -- including non-linear physics, and, for the first time, natural language via large language models. Whitening isolates the irreducible non-Gaussian dynamics, minimising Wasserstein-2 transport cost and eliminating numerical stiffness. The result is a general-purpose GP inference scheme requiring no bespoke derivations. Together, these results provide a general mechanism for incorporating the full richness of real-world knowledge as conditioning information, opening a new frontier for the probabilistic modelling of real-world problems.

Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In applications, however, the measures of interest are almost never known precisely, calling for a theory of optimal transport that accounts for statistical uncertainty. We construct such a framework, lifting the classical theory to the setting of random probability measures. We introduce the $L^2$ over Wasserstein space establishing that it inherits the formal Riemannian structure of the Wasserstein space by characterising distances and geodesic geometry. The structure induces random flows with Wasserstein gradient flow sample paths, making it the natural extension of the Wasserstein space which allows for random gradient flow dynamics. We ensemble statistical convergence results of the optimal transport machinery using the empirical measure within the $L^2$ over Wasserstein framework. Moreover, in the setting of Bayesian non-parametrics, we refine Schwartz's consistency theorem to the Wasserstein topology and deduce posterior convergence of the same machinery in the $L^2$ over Wasserstein space. We demonstrate that the growing theory of random token sampling for transformer models using self-attention flow paths can be embedded into the our framework. The results provide a unified treatment of random optimal transport and its consequences for principled inference and generative modelling under the statistical uncertainty of random sampling.

Earthquake forecasting is a critical task for natural risk management, infrastructure resilience planning, and emergency response operations. For Central Asia, and the Tian Shan mountain system in particular, this problem carries heightened importance due to high tectonic activity, complex geodynamics, and pronounced spatiotemporal heterogeneity of seismic processes. In the applied setting, the goal is not a deterministic forecast of individual events, but a macroscopic forecast of seismicity intensity: estimating the expected number of earthquakes with magnitude M 3.0 on a spatial grid at a weekly horizon. Historically, count data forecasting in fixed spatiotemporal cells has been formulated within the Poisson framework. However, its key assumption--equality of the conditional mean and conditional variance--is systematically violated in real seismological data. Earthquakes exhibit pronounced clustering associated with swarm activity, foreshock-aftershock sequences, and episodes of anomalous activity, resulting in overdispersion in which the variance substantially exceeds the mean. Under these conditions, uncritical application of the Poisson distribution leads to biased uncertainty estimates and, consequently, to underestimation of the risk of extreme scenarios. Despite the widespread adoption of machine learning methods in seismological problems, a substantial portion of existing work remains methodologically vulnerable. On one hand, several approaches apply continuous regression loss functions and metrics (e.g., MSE), ignoring the

Elon Musk's SpaceX has revealed its plans to go public in the US, allowing people to trade shares in the firm on the stock market. SpaceX makes rockets, offers a satellite internet service called Starlink, and also owns Musk's controversial artificial intelligence (AI) firm xAI. The initial public offering (IPO) on the US stock market is set to be the largest in Wall Street history and could start next month under the ticker symbol SPCX. Because of the shares he will own in SpaceX, the IPO could make billionaire Musk, who is already the world's richest person, a trillionaire. SpaceX values itself at $1.25tn, and Musk's majority ownership of the company means his share could be worth more than $600bn.

One line tucked into a federal highway bill would strip funds from cities and states unless they kill their automated plate tracking programs--effectively banning the tech for all but toll collection. US lawmakers plan to introduce an amendment Thursday at a House committee markup hearing that would prohibit any recipient of federal highway funding from using automated license plate readers for any purpose other than tolling--a sweeping restriction that, if adopted, would bring an immediate end to state and local ALPR programs across the United States. The amendment, obtained first by WIRED, is sponsored by Representative Scott Perry, a Pennsylvania Republican and Freedom Caucus member, and Representative Jesús "Chuy" García, an Illinois progressive whose state has become a flash point in the national fight over ALPR misuse. The House Transportation and Infrastructure Committee will mark up the underlying bill--a $580 billion, five-year reauthorization of federal surface transportation programs--at 10 am ET on Thursday. Neither Perry nor García's offices immediately responded to WIRED's request for comment. The amendment runs a single sentence: "A recipient of assistance under Title 23, United States Code, may not use automated license plate readers for any purpose other than tolling."

Finally, the Google I/O announcement you've been waiting for. With Google transforming search into an AI-driven experience, it was only a matter of time before AI ads entered the fray. As part of its Google I/O week announcements, the company previewed how Gemini-powered, conversational ads will start appearing in search results. Fortunately, all of the new AI-generated ad formats will be labeled as sponsored. Google is testing two new ad types in AI Mode, both powered by an independent AI explainer.

PCWorld reports Google's new Gemini-powered smart glasses prototype represents a refined approach to smart eyewear, manufactured by Samsung with discreet camera and touch controls. The lightweight glasses integrate Google's AI assistant for real-world navigation, search functions, and phone replacement capabilities while maintaining a normal sunglasses appearance. Despite improved public acceptance and seamless design, limitations include basic heads-up display, battery concerns, and sometimes forced AI features. A decade after Google launched Google Glass to spectacular failure, it's trying again. And I think that the world (and I) will be more receptive to what Google's online AI interpreter, Gemini, can do when plugged into your ear.

AS A sci-fi fan, you learn not to dwell on the films that could have been. Whether it's Alejandro Jodorowsky's unmade Dune, Guillermo del Toro's cancelled take on At the Mountains of Madness, or the versions of Return of the Jedi that Davids Lynch and Cronenberg could have made, it's best not to torture yourself over cinematic what-ifs. That's why I had given up hope of there being a new instalment of the most underrated sci-fi film franchise of the 21st century so far. Though well received by critics and audiences alike, none of the four films have won Oscars or seem to have made much of an impact on pop culture. But then, earlier this month, we got confirmation that a fifth movie was on the way.