Elon Musk's SpaceX is taking over his artificial intelligence (AI) start-up, as the billionaire continues to unify some of his many business interests. SpaceX confirmed the deal to acquire xAI, a smaller firm known for its Grok chatbot, posting a memo from Musk about the merger on its website. In the note, Musk said the combination would form an innovation engine putting AI, rockets, space-based internet, and media under one roof. Terms of the deal were not disclosed. However, a source familiar said it valued xAI at $125bn (£91bn) and SpaceX at $1tn, making it the most valuable private company ever.

The latest batch of Jeffrey Epstein files shed light on the convicted sex offender's ties to Silicon Valley--and Peter Thiel's exacting approach to food. Peter Thiel--the billionaire venture capitalist, PayPal, and Palantir cofounder, and outspoken commentator on all matters relating to the "Antichrist"--appears at least 2,200 times in the latest batch of files released by the Department of Justice related to convicted sex offender and disgraced financier Jeffrey Epstein . The tranche of records demonstrate how Epstein managed to cultivate an extensive network of wealthy and influential figures in Silicon Valley. A number of them, including Thiel, continued to interact with Epstein even after his 2008 guilty plea for solicitation of prostitution and of procurement of minors to engage in prostitution. The new files show that Thiel arranged to meet with Epstein several times between 2014 and 2017.

Barnsley has struggled with unemployment and deprivation since the coal pits closed. Barnsley has struggled with unemployment and deprivation since the coal pits closed. Barnsley rebranded UK's first'tech town' as US giants join AI push In 2002 Barnsley toyed with a redesign as a Tuscan hill village as it sought out a brighter post-industrial future. In 2021 it adopted the airily vague slogan "the place of possibilities". Now it is trying a different image: Britain's first "tech town".

We investigate the role of feature superposition in the emergence of power-law training dynamics using a teacher-student framework. We first derive an analytic theory for training without superposition, establishing that the power-law training exponent depends on both the input data statistics and channel importance. Remarkably, we discover that a superposition bottleneck induces a transition to a universal power-law exponent of $\sim 1$, independent of data and channel statistics. This one over time training with superposition represents an up to tenfold acceleration compared to the purely sequential learning that takes place in the absence of superposition. Our finding that superposition leads to rapid training with a data-independent power law exponent may have important implications for a wide range of neural networks that employ superposition, including production-scale large language models.

Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive implicit generative models such as diffusion and flow-based methods, these approaches are often data-hungry, computationally costly, and misaligned with the structured solution spaces frequently found in scientific problems. We demonstrate that Mixture Density Networks (MDNs) provide a principled yet largely overlooked alternative for multimodal uncertainty quantification in SciML. As explicit parametric density estimators, MDNs impose an inductive bias tailored to low-dimensional, multimodal physics, enabling direct global allocation of probability mass across distinct solution branches. This structure delivers strong data efficiency, allowing reliable recovery of separated modes in regimes where scientific data is scarce. We formalize these insights through a unified probabilistic framework contrasting explicit and implicit distribution networks, and demonstrate empirically that MDNs achieve superior generalization, interpretability, and sample efficiency across a range of inverse, multistable, and chaotic scientific regression tasks.

Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of machine learning methods in learning SDE dynamics, existing approaches either require expensive neural network training for score function estimation or lack the ability to handle continuous parameter dependence. We present a training-free conditional diffusion model framework for learning stochastic flow maps of parameter-dependent SDEs, where both drift and diffusion coefficients depend on physical parameters. The key technical innovation is a joint kernel-weighted Monte Carlo estimator that approximates the conditional score function using trajectory data sampled at discrete parameter values, enabling interpolation across both state space and the continuous parameter domain. Once trained, the resulting generative model produces sample trajectories for any parameter value within the training range without retraining, significantly accelerating parameter studies, uncertainty quantification, and real-time filtering applications. The performance of the proposed approach is demonstrated via three numerical examples of increasing complexity, showing accurate approximation of conditional distributions across varying parameter values.

It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning. However, beyond linear regression, the theoretical advantage of full-batch gradient descent (GD, which always reuses all the data) over one-pass stochastic gradient descent (online SGD, which uses each data point only once) remains unclear. In this work, we consider learning a $d$-dimensional single-index model with a quadratic activation, for which it is known that one-pass SGD requires $n\gtrsim d\log d$ samples to achieve weak recovery. We first show that this $\log d$ factor in the sample complexity persists for full-batch spherical GD on the correlation loss; however, by simply truncating the activation, full-batch GD exhibits a favorable optimization landscape at $n \simeq d$ samples, thereby outperforming one-pass SGD (with the same activation) in statistical efficiency. We complement this result with a trajectory analysis of full-batch GD on the squared loss from small initialization, showing that $n \gtrsim d$ samples and $T \gtrsim\log d$ gradient steps suffice to achieve strong (exact) recovery.

A new Fox News poll finds 60% of registered voters think artificial intelligence use is moving too quickly, while 63% lack confidence in federal government's AI regulation ability.

HHS Is Using AI Tools From Palantir to Target'DEI' and'Gender Ideology' in Grants Since March of 2025, the Trump Administration has used tools from Palantir and the startup Credal AI to weed out "DEI" and "gender ideology from child welfare programs. A view of the Palantir building is seen during the World Economic Forum Annual Meeting 2026 in Davos, Switzerland. Since last March, the Department of Health and Human Services has been using AI tools from Palantir to screen and audit grants, grant applications, and job descriptions for noncompliance with President Donald Trump's executive orders targeting "gender ideology" and anything related to diversity, equity, inclusion (DEI), according to a recently published inventory of all use cases HHS had for AI in 2025. Neither Palantir nor HHS has publicly announced that the company's software was being used for these purposes. During the first year of Trump's second term, Palantir earned more than $35 million in payments and obligations ...

Before the EPA, Utah saw 100 times more lead exposure. Breakthroughs, discoveries, and DIY tips sent six days a week. The evidence is clear--and in your hair. Americans were exposed to as much as 100 times more lead in their daily lives than they are today before the Environmental Protection Agency was established in 1970. In an effort to examine the dramatic reduction in toxic heavy metal exposure, researchers turned to human hair samples dating back a century.