Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Astronomers watch the birth of one of the universe's most extreme objects for the first time Astronomers have watched the birth of one of the universe's most extreme objects for the very first time - a magnetar comprising the mass of 500,000 Earths inside a sphere measuring just 12 miles across. Magnetars are a type of neutron star, an incredibly dense object mainly made up of tightly packed neutron, which forms from the collapsed core of a massive star during a supernova. What sets magnetars apart from other neutron stars is that they also have the most powerful known magnetic fields in the universe.

Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' You might have thought AI was going to make your job easier. But a new survey suggests it's actually making us do more work. One in four UK employees claim tools like ChatGPT have in fact piled on more pressure - and made bosses expect them to do more.

Science Space Deep Space Black Holes For the first time, astronomers witnessed the birth of a'magnetar' These fast spinning, magnetic neutron stars may power some of the brightest supernovae in the cosmos. Artist's conception of a magnetar surrounded by an accretion disk that is wobbling, or precessing, because of the effects of general relativity. Some models of magnetars suggest that high-speed jets of charged particles emanate from the magnetar along its rotation axis. Breakthroughs, discoveries, and DIY tips sent six days a week. In December 2024, astronomers watched a star around 25 times the mass of our sun die in a blaze of glory.

'I wish I could push ChatGPT off a cliff': professors scramble to save critical thinking in an age of AI Lea Pao, a professor of literature at Stanford University, has been experimenting with ways to get her students to learn offline. She has them memorize poems, perform at recitation events, look at art in the real world. It's an effort to reconnect them to the bodily experience of learning, she said, and to keep them from turning to artificial intelligence to do the work for them. "There's no AI-proof anything," Pao said. "Rather than policing it, I hope that their overall experiences in this class will show them that there's a way out."

The speed at which artificial intelligence is gaining in mathematical ability has taken many by surprise. Are the days of handwritten mathematics coming to an end? In March 2025, mathematician Daniel Litt made a bet. Despite the march of progress of artificial intelligence in many fields, he believed his subject was safe, wagering with a colleague that there was only a 25 per cent chance an AI could write a mathematical paper at the level of the best human mathematicians by 2030. Only a year later, he thinks he was wrong.

We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte Carlo error from a covariance floor that persists under infinite aggregation. The floor arises through two mechanisms: observation reuse, where the same training outcomes receive weight across multiple trees, and partition alignment, where independently generated trees discover similar conditional prediction rules. We prove the floor is strictly positive under minimal conditions and show that alignment persists even when sample splitting eliminates observation overlap entirely. We introduce procedure-aligned synthetic resampling (PASR) to estimate the covariance floor, decomposing the total prediction uncertainty of a deployed forest into interpretable components. For continuous outcomes, resulting prediction intervals achieve nominal coverage with a theoretically guaranteed conservative bias direction. For classification forests, the PASR estimator is asymptotically unbiased, providing the first pointwise confidence intervals for predicted conditional probabilities from a deployed forest. Nominal coverage is maintained across a range of design configurations for both outcome types, including high-dimensional settings. The underlying theory extends to any tree-based ensemble with an exchangeable tree-generating mechanism.

Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning theory, such as the VC theorem and Littlestone's characterization of online learnability, establish conditions on the hypothesis class that allow for learning under independent data and adversarial data, respectively. Building upon recent work bridging these extremes, we study sequential decision making under distributional adversaries that can adaptively choose data-generating distributions from a fixed family $U$ and ask when such problems are learnable with sample complexity that behaves like the favorable independent case. We provide a near complete characterization of families $U$ that admit learnability in terms of a notion known as generalized smoothness i.e. a distribution family admits VC-dimension-dependent regret bounds for every finite-VC hypothesis class if and only if it is generalized smooth. Further, we give universal algorithms that achieve low regret under any generalized smooth adversary without explicit knowledge of $U$. Finally, when $U$ is known, we provide refined bounds in terms of a combinatorial parameter, the fragmentation number, that captures how many disjoint regions can carry nontrivial mass under $U$. These results provide a nearly complete understanding of learnability under distributional adversaries. In addition, building upon the surprising connection between online learning and differential privacy, we show that the generalized smoothness also characterizes private learnability under distributional constraints.

From left: India's prime minister, Narendra Modi, with the chief executives of OpenAI, Sam Altman, and Anthropic, Dario Amodei, at the AI Impact summit in Delhi. From left: India's prime minister, Narendra Modi, with the chief executives of OpenAI, Sam Altman, and Anthropic, Dario Amodei, at the AI Impact summit in Delhi. AI hit: India hungry to harness US tech giants' technology at Delhi summit Narendra Modi's thirst to supercharge economic growth is matched by US desire to inject AI into world's biggest democracy I ndia celebrates 80 years of independence from the UK in August 2027. At about that same moment, "early versions of true super intelligence" could emerge, Sam Altman, the co-founder of OpenAI, said this week. It's a looming coincidence that raised a charged question at the AI Impact summit in Delhi, hosted by India's prime minister, Narendra Modi: can India avoid returning to the status of a vassal state when it imports AI to raise the prospects of its 1.4 billion people? Modi's hunger to harness AI's capability is great.

The proliferation of Large Language Models (LLMs) necessitates efficient mechanisms to distinguish machine-generated content from human text. While statistical watermarking has emerged as a promising solution, existing methods suffer from two critical limitations: the lack of a principled approach for selecting sampling distributions and the reliance on fixed-horizon hypothesis testing, which precludes valid early stopping. In this paper, we bridge this gap by developing the first e-value-based watermarking framework, Anchored E-Watermarking, that unifies optimal sampling with anytime-valid inference. Unlike traditional approaches where optional stopping invalidates Type-I error guarantees, our framework enables valid, anytime-inference by constructing a test supermartingale for the detection process. By leveraging an anchor distribution to approximate the target model, we characterize the optimal e-value with respect to the worst-case log-growth rate and derive the optimal expected stopping time. Our theoretical claims are substantiated by simulations and evaluations on established benchmarks, showing that our framework can significantly enhance sample efficiency, reducing the average token budget required for detection by 13-15% relative to state-of-the-art baselines.

All models discussed in the paper use ReLU non-linearity.