This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG .

Paxton trounces Cornyn in the Texas Senate Republican primary runoff; Trump waffles between a losing "peace deal" and a return to war in Iran; and congressional candidate Alex Bores makes the case for AI regulation. Please enable javascript to get your Slate Plus feeds. If you can't access your feeds, please contact customer support. Check your phone for a link to finish setting up your feed. Please enter a valid phone number.

Amazon is rolling out its ultra-fast delivery service, Amazon Now, in dozens of cities in the US, promising deliveries of groceries and household essentials in 30 minutes or less. Amazon says the service is also now widely available in Atlanta and Dallas-Fort Worth, and will rapidly expand into Austin, Houston, Minneapolis, Orlando, Phoenix, Denver, Oklahoma City and more throughout the rest of 2026. If Amazon Now is available in your area you'll see a 30-Minute Delivery option in the Amazon app or on the homepage when you're in a browser. Amazon Now offers will also be highlighted when you're browsing products. You can search by category, and as well as groceries and basic household items such as eggs, diary and laundry detergent, you can also order select electronics on the service, which Amazon says operates 24 hours a day in most places.

Roughly 500 labour groups across the United States have organised a widespread economic blackout calling for "no school, no work, no shopping" to mark May Day, also known as International Workers' Day. The events, organised as part of an initiative called May Day Strong, were inspired by economic boycotts following ramped-up immigration enforcement operations in Minneapolis, Minnesota, and the deaths of US citizens Renee Good and Alex Pretti in January. May Day Strong has a broad set of demands, including "tax the rich" and abolishing Immigration and Customs Enforcement (ICE) -- a call that comes as Republicans voted on Wednesday on a budgetary measure that would fund the agency under the Department of Homeland Security. It also calls for ending war and "expanding democracy", according to a statement from the group. While the tent is broad in nature, organisers stressed that it is a result of a wide set of challenges facing the US worker.

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG .

Diffusion models [1, 2, 3] have emerged as a powerful class of generative models, achieving state-of-the-art performance across a wide range of applications, including imaging [2] and scientific-data synthesis [4]. From a statistical perspective, they can be viewed as flexible nonparametric estimators of a (conditional) distribution via score estimation and reverse-time stochastic differential equations (SDEs) [5, 6]. Despite this expressive power, standard diffusion models are typically causality-agnostic: they learn a joint law without encoding the directional asymmetries required for causal interpretation. As a consequence, they do not, on their own, provide principled answers to interventional queries or support broader causal analyses, which are central to structural causal models (SCMs) [7]. When a causal ordering (or a directed acyclic graph) is available, it is natural to construct generative procedures that sample variables sequentially according to the causal factorisation. Such iterative, ordering-respecting approaches have been proposed using a variety of generative models, including generative adversarial networks [8], variational autoencoders [9], normalising flows [10], and diffusion-based constructions such as DDIM [11]. However, a rigorous statistical understandingof the advantages of exploitingsuch causalstructureand the inferential use of the resulting generator remain less developed.

Palantir Employees Are Starting to Wonder if They're the Bad Guys Interviews with current and former Palantir employees, along with internal Slack messages obtained by WIRED, suggest a workforce in turmoil. It took just a few months of President Donald Trump's second term for Palantir employees to question their company's commitments to civil liberties . Last fall, Palantir seemed to become the technological backbone of Trump's immigration enforcement machinery, providing software identifying, tracking, and helping deport immigrants on behalf of the Department of Homeland Security (DHS), when current and former employees started ringing the alarm. Right as they picked up the call, one of them asked, "Are you tracking Palantir's descent into fascism?" "That was their greeting," the other former employee says.

EVEN supervised learning is subject to the famous NoFree Lunch Theorems [1]-[3], which say that, in combinatorial optimization, there is no universal algorithm that works better than its competitors for every objective function [4]-[6]. Indeed, David Wolpert has recently proven that, on average, cross-validation performs as well as anti-crossvalidation (choosing among a set of candidate algorithms based on which has the worst out-of-sample behavior) for supervised learning. Still, he acknowledges that "it is hard to imagine any scientist who would not prefer to use [crossvalidation] to using anti-cross-validation" [7]. On the other hand, unsupervised learning has seldom been studied from the perspective of the NFLTs. This may be because the adjective "unsupervised" suggests that no human input is needed, which is misleading as many unsupervised tasks are combinatorial optimization problems that depend on the choice of the objective function. For instance, it is well known that, among the eigenvectors of the covariance matrix, Principal Components Analysis selects those with the largest variances [8]. However, mode-hunting techniques that rely on spectral manipulation aim at the opposite objective: selecting the eigenvectors of the covariance matrix with the smallest variances [9], [10]. Therefore, unlike in supervised learning, where it is difficult to identify reasons to optimize with respect to anti-cross-validation, in unsupervised learning there are strong reasons to reduce dimensionality for variance minimization. D. A. D ıaz-Pach on and T. Liu are with the Division of Biostatistics, University of Miami, Miami, FL, 33136 USA (e-mail: ddiaz3@miami.edu,

Despite the sustained popularity of Q-learning as a practical tool for policy determination, a majority of relevant theoretical literature deals with either constant ($η_{t}\equiv η$) or polynomially decaying ($η_{t} = ηt^{-α}$) learning schedules. However, it is well known that these choices suffer from either persistent bias or prohibitively slow convergence. In contrast, the recently proposed linear decay to zero (\texttt{LD2Z}: $η_{t,n}=η(1-t/n)$) schedule has shown appreciable empirical performance, but its theoretical and statistical properties remain largely unexplored, especially in the Q-learning setting. We address this gap in the literature by first considering a general class of power-law decay to zero (\texttt{PD2Z}-$ν$: $η_{t,n}=η(1-t/n)^ν$). Proceeding step-by-step, we present a sharp non-asymptotic error bound for Q-learning with \texttt{PD2Z}-$ν$ schedule, which then is used to derive a central limit theory for a new \textit{tail} Polyak-Ruppert averaging estimator. Finally, we also provide a novel time-uniform Gaussian approximation (also known as \textit{strong invariance principle}) for the partial sum process of Q-learning iterates, which facilitates bootstrap-based inference. All our theoretical results are complemented by extensive numerical experiments. Beyond being new theoretical and statistical contributions to the Q-learning literature, our results definitively establish that \texttt{LD2Z} and in general \texttt{PD2Z}-$ν$ achieve a best-of-both-worlds property: they inherit the rapid decay from initialization (characteristic of constant step-sizes) while retaining the asymptotic convergence guarantees (characteristic of polynomially decaying schedules). This dual advantage explains the empirical success of \texttt{LD2Z} while providing practical guidelines for inference through our results.

Self-supervised pre-training, where large corpora of unlabeled data are used to learn representations for downstream fine-tuning, has become a cornerstone of modern machine learning. While a growing body of theoretical work has begun to analyze this paradigm, existing bounds leave open the question of how sharp the current rates are, and whether they accurately capture the complex interaction between pre-training and fine-tuning. In this paper, we address this gap by developing an asymptotic theory of pre-training via two-stage M-estimation. A key challenge is that the pre-training estimator is often identifiable only up to a group symmetry, a feature common in representation learning that requires careful treatment. We address this issue using tools from Riemannian geometry to study the intrinsic parameters of the pre-training representation, which we link with the downstream predictor through a notion of orbit-invariance, precisely characterizing the limiting distribution of the downstream test risk. We apply our main result to several case studies, including spectral pre-training, factor models, and Gaussian mixture models, and obtain substantial improvements in problem-specific factors over prior art when applicable.