Things to Do in L.A. Tap to enable a layout that focuses on the article. Self-driving vehicles charge at the Waymo station in Santa Monica. This is read by an automated voice. Please report any issues or inconsistencies here . Waymo is taking the city of Santa Monica to court after the city ordered the company to cease charging its autonomous vehicles at two facilities overnight, claiming the lights and beeping at the lots were a nuisance to residents.

They work 24/7 at high speeds and get searingly hot - but data centre computer chips get plenty of pampering. Some of them basically live at the spa. We'll have fluid that comes up and [then] shower down, or trickle down, onto a component, says Jonathan Ballon, chief executive at liquid cooling firm Iceotope. Some things will get sprayed. In other cases, the industrious gizmos recline in circulating baths of fluid, which ferries away the heat they generate, enabling them to function at very high speeds, known as overclocking.

The search for primordial gravitational waves is a central goal of cosmic microwave background (CMB) surveys. Isolating the characteristic $B$-mode polarization signal sourced by primordial gravitational waves is challenging for several reasons: the amplitude of the signal is inherently small; astrophysical foregrounds produce $B$-mode polarization contaminating the signal; and secondary $B$-mode polarization fluctuations are produced via the conversion of $E$ modes. Current and future low-noise, multi-frequency observations enable sufficient precision to address the first two of these challenges such that secondary $B$ modes will become the bottleneck for improved constraints on the amplitude of primordial gravitational waves. The dominant source of secondary $B$-mode polarization is gravitational lensing by large scale structure. Various strategies have been developed to estimate the lensing deflection and to reverse its effects the CMB, thus reducing confusion from lensing $B$ modes in the search for primordial gravitational waves. However, a few complications remain. First, there may be additional sources of secondary $B$-mode polarization, for example from patchy reionization or from cosmic polarization rotation. Second, the statistics of delensed CMB maps can become complicated and non-Gaussian, especially when advanced lensing reconstruction techniques are applied. We previously demonstrated how a deep learning network, ResUNet-CMB, can provide nearly optimal simultaneous estimates of multiple sources of secondary $B$-mode polarization. In this paper, we show how deep learning can be applied to estimate and remove multiple sources of secondary $B$-mode polarization, and we further show how this technique can be used in a likelihood analysis to produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity on real-world data. Kernel methods using the partial covariance operator offer a more principled approach but suffer from limited adaptivity, slow convergence, and poor scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of the partial covariance operator and use them to construct a simple test statistic, reminiscent of the Hilbert-Schmidt Independence Criterion (HSIC). We also introduce a practical bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Preliminary experiments suggest that this approach offers a practical and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

Explainable machine learning aims to strike a balance between prediction accuracy and model transparency, particularly in settings where black-box predictive models, such as deep neural networks or kernel-based methods, achieve strong empirical performance but remain difficult to interpret. This work introduces a mixture of generalized additive models (GAMs) in which random Fourier feature (RFF) representations are leveraged to uncover locally adaptive structure in the data. In the proposed method, an RFF-based embedding is first learned and then compressed via principal component analysis. The resulting low-dimensional representations are used to perform soft clustering of the data through a Gaussian mixture model. These cluster assignments are then applied to construct a mixture-of-GAMs framework, where each local GAM captures nonlinear effects through interpretable univariate smooth functions. Numerical experiments on real-world regression benchmarks, including the California Housing, NASA Airfoil Self-Noise, and Bike Sharing datasets, demonstrate improved predictive performance relative to classical interpretable models. Overall, this construction provides a principled approach for integrating representation learning with transparent statistical modeling.

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{á}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions obtained as level sets of a real-valued function. This loss function allows optimal trade-offs between conditional probabilistic coverage and the ''size'' of the set, measured by a non-decreasing submodular function. We also propose several extensions that mimic loss functions and criteria for binary classification with asymmetric losses, and show how to naturally obtain sets with optimized conditional coverage. We derive efficient optimization algorithms, either based on stochastic gradient descent or reweighted least-squares formulations, and illustrate our findings with a series of experiments on synthetic datasets for classification and regression tasks, showing improvements over approaches that aim for marginal coverage.

Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying lower dimensional structures, either at the population level or at the sample level. We tackle this issue by proposing a new method, generative sufficient dimension reduction (GenSDR), which leverages modern generative models. We show that GenSDR is able to fully recover the information contained in the central $σ$-field at both the population and sample levels. In particular, at the sample level, we establish a consistency property for the GenSDR estimator from the perspective of conditional distributions, capitalizing on the distributional learning capabilities of deep generative models. Moreover, by incorporating an ensemble technique, we extend GenSDR to accommodate scenarios with non-Euclidean responses, thereby substantially broadening its applicability. Extensive numerical results demonstrate the outstanding empirical performance of GenSDR and highlight its strong potential for addressing a wide range of complex, real-world tasks.

This paper considers the problem of testing for latent structure in large symmetric data matrices. The goal here is to develop statistically principled methodology that is flexible in its applicability, computationally efficient, and insensitive to extreme data variation, thereby overcoming limitations facing existing approaches. To do so, we introduce and systematically study certain symmetric matrices, called Wilcoxon--Wigner random matrices, whose entries are normalized rank statistics derived from an underlying independent and identically distributed sample of absolutely continuous random variables. These matrices naturally arise as the matricization of one-sample problems in statistics and conceptually lie at the interface of nonparametrics, multivariate analysis, and data reduction. Among our results, we establish that the leading eigenvalue and corresponding eigenvector of Wilcoxon--Wigner random matrices admit asymptotically Gaussian fluctuations with explicit centering and scaling terms. These asymptotic results enable rigorous parameter-free and distribution-free spectral methodology for addressing two hypothesis testing problems, namely community detection and principal submatrix detection. Numerical examples illustrate the performance of the proposed approach. Throughout, our findings are juxtaposed with existing results based on the spectral properties of independent entry symmetric random matrices in signal-plus-noise data settings.

Concept learning becomes possible only when existing representations fail to account for experience. Most models of learning and inference, however, presuppose a fixed representational basis within which belief updating occurs. In this paper, I address a prior question: under what structural conditions can the representational basis itself expand in a principled and selective way? I propose a geometric framework in which conceptual growth is modeled as admissible basis extension evaluated under a Minimum Description Length (MDL) criterion. Experience, whether externally observed or internally simulated, is represented as vectors relative to a current conceptual subspace. Residual components capture systematic representational failure, and candidate conceptual extensions are restricted to low-rank, admissible transformations. I show that any MDL-accepted extension can be chosen so that its novel directions lie entirely within the residual span induced by experience, while extensions orthogonal to this span strictly increase description length and are therefore rejected. This yields a conservative account of imagination and conceptual innovation. Internally generated counterfactual representations contribute to learning only insofar as they expose or amplify structured residual error, and cannot introduce arbitrary novelty. I further distinguish representational counterfactuals--counterfactuals over an agent's conceptual basis--from causal or value-level counterfactuals, and show how MDL provides a normative selection principle governing representational change. Overall, the framework characterizes conceptual development as an error-driven, geometry-constrained process of basis extension, clarifying both the role and the limits of imagination in learning and theory change.

Effective feature selection is essential for high-dimensional data analysis and machine learning. Unsupervised feature selection (UFS) aims to simultaneously cluster data and identify the most discriminative features. Most existing UFS methods linearly project features into a pseudo-label space for clustering, but they suffer from two critical limitations: (1) an oversimplified linear mapping that fails to capture complex feature relationships, and (2) an assumption of uniform cluster distributions, ignoring outliers prevalent in real-world data. To address these issues, we propose the Robust Autoencoder-based Unsupervised Feature Selection (RAEUFS) model, which leverages a deep autoencoder to learn nonlinear feature representations while inherently improving robustness to outliers. We further develop an efficient optimization algorithm for RAEUFS. Extensive experiments demonstrate that our method outperforms state-of-the-art UFS approaches in both clean and outlier-contaminated data settings.