Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings. While Nesterov acceleration is well understood for full-gradient and coordinate-based methods, obtaining accelerated methods for general subspace sketches that use only projected-gradient information and can improve over full-dimensional Nesterov acceleration in oracle complexity is technically nontrivial. We develop randomized-subspace Nesterov accelerated gradient methods for smooth convex and smooth strongly convex optimization under matrix smoothness and generic sketch moment assumptions. The key technical ingredient is a three-sequence formulation tailored to matrix smoothness, which recovers the corresponding classical Nesterov methods in the full-dimensional case. The resulting theory establishes accelerated oracle-complexity guarantees and makes explicit how matrix smoothness and the sketch distribution enter the complexity. It also provides a unified basis for comparing sketch families and identifying when randomized-subspace acceleration improves over full-dimensional Nesterov acceleration in oracle complexity.

The UAE says it will integrate agentic AI across half of its government operations within two years, making one of the most aggressive moves in the global AI race.

How does live facial recognition work and how many police forces use it? Britain's biometrics watchdogs have warned that national oversight of AI-powered face scanning to catch criminals is lagging far behind the technology's rapid growth. With the Metropolitan police almost doubling the number of faces they scan in London over the past 12 months and a rising use of the technology by retailers in the UK, Prof William Webster, the biometrics commissioner for England and Wales, said the "slow pace of legislation was trying to catch up with the real world" and "the horse had gone before the cart". Dr Brian Plastow, who holds the same role in Scotland, warned the technology was "nowhere near as effective as the police claim it is" and said there was a "patchwork legal framework" throughout the UK. He said in England and Wales, police were "really just marking their own homework".

Varun Chandra advises Keir Starmer on trade negotiations including AI investment. Varun Chandra advises Keir Starmer on trade negotiations including AI investment. Exclusive: Varun Chandra's talks with Google, Meta, Apple and others raise fears of'lobbying behind closed doors' An influential government adviser close to Keir Starmer and Rachel Reeves held 16 undisclosed meetings with top US tech executives, the Guardian can reveal. The No 10 business aide Varun Chandra discussed regulatory changes, AI and Donald Trump's second administration with tech corporations during confidential meetings between October 2024 and October 2025. In one meeting he offered to help a top executive meet the prime minister directly.

Things to Do in L.A. Tap to enable a layout that focuses on the article. Cole Allen's journey from young athlete and Caltech grad to accused gunman in D.C. attack Cole Tomas Allen selfie before the attack in Washington, D.C., according to a pretrial detention memo filed by prosecutors Wednesday. This is read by an automated voice. Please report any issues or inconsistencies here . A quiet, respected tutor and engineer from Southern California with a "godly" upbringing allegedly attempted to assassinate President Trump at the White House correspondents' dinner, shocking those who knew him. Allen's social media accounts under the handle "coldForce" show years of posts criticizing Trump and supporting Ukraine, but contain no indication of violent intent despite the alleged assassination plot.

OpenAI's Sam Altman, left, is a backer of Rain Neuromophics, one of the companies that received funds from the UK's Aria, the brainchild of Dominic Cummings, right OpenAI's Sam Altman, left, is a backer of Rain Neuromophics, one of the companies that received funds from the UK's Aria, the brainchild of Dominic Cummings, right Exclusive: Brainchild of Dominic Cummings, Aria is aimed at funding'crazy' scientific projects to benefit the UK Britain's "invention agency" has pledged £50m of UK taxpayer money to US tech companies and venture capital projects. Dreamed up by Dominic Cummings to fund "crazy" ideas, the Advanced Research and Invention Agency (Aria) is meant to " restore Britain's place as a scientific superpower ". But a joint investigation by the Guardian and Democracy for Sale, an investigative website, has established that more than an eighth of the agency's £400m in research and development funding over the past two years has gone to 14 US tech companies and venture capital groups, in some cases, with no clear return for the UK or Aria. One of these companies, Rain Neuromorphics, is also backed by the OpenAI chief executive, Sam Altman, and was reported to be near collapse last year, shortly after winning Aria money. It did not respond to a request for comment; two of its founders appear to have left the company.

Detail from Holbein's sketch of an unidentified woman, which it is claimed may depict Anne Boleyn. Detail from Holbein's sketch of an unidentified woman, which it is claimed may depict Anne Boleyn. They are two small sketches by the Renaissance master Hans Holbein: one has long been considered to be a portrait of Henry VIII's doomed second wife, Anne Boleyn, and the other is of an unknown woman whose name was lost to time. Now researchers using AI have discovered that the unnamed woman might be the tragic queen after all, while the other figure could in fact be Boleyn's mother. The works, which belong to the royal collection and are known as the Windsor sketch and the Unidentified Woman respectively, were analysed by a team at the University of Bradford, who found that they might have been incorrectly inscribed in the 1700s, leading to a misunderstanding that has lasted centuries.

Game Theory: Who gets to go to the 2026 World Cup? Who actually gets to go to the World Cup? With US President Donald Trump's strict immigration policies, some fans may never make it past the American border. Because while teams qualify on merit, passports don't. Al Jazeera's Samantha Johnson explains. The Masters: Golf's segregated past Are Iran's athletes political pawns?

When you purchase through links in our articles, we may earn a small commission. Microsoft 365 is down to $69.99 for a full year, giving you premium Office apps, 1TB storage, and built-in AI tools across your devices. If you're already using Word, Excel, or PowerPoint --even occasionally--this is one of those upgrades that just makes your setup smoother across the board. Microsoft 365 is currently $69.99 for a 1-year subscription (MSRP $99.99), and it bundles together the apps you actually use with features that go beyond basic document editing. That means your files are accessible across devices, backed up, and easy to share without emailing attachments back and forth. One of the bigger upgrades here is the built-in AI assistant, Copilot .

Trump reveals'absolutely pathetic' first words he says Bill Maher uttered at fabled White House visit Charles had late-stage ALS and couldn't speak or move. Bigamist pastor's'marriage scam': Five-times-wed author told women God wanted them to be together for twisted ulterior motive, wives say The rat'apocalypse' forcing residents in a northwestern state to catch vermin with their bare hands Kylie Jenner's BFF Stassie reveals dramatic butt reduction in skimpy bikini after cosmetic surgery'regrets' I had agonising acid reflux every day - but then overnight it stopped thanks to something you can buy in any supermarket. With 39 bedrooms, 59 bathrooms and its own X-ray machine, America's most expensive home hits the market for $400million - but will anyone afford to buy it? 'Dog Whisperer' Cesar Millan reveals price of the world's'safest' collar - and it TALKS to your pet Moment'disgruntled former employee' smashed car full of explosives into Portland athletics club caught on camera'She's spiralling badly': How Meghan and Harry have burned ALL their bridges as insiders reveal spectacular fallout with Anna Wintour and Kardashians, money woes - and'problems' that are worse than anyone realises Former FBI deputy director Dan Bongino'living in fear' as he issues astonishing warning after mysteriously leaving intel agency Whether it's a celebration or a bottomless brunch, nothing hits the spot quite like a glass of fizz. But it turns out you've probably been drinking prosecco wrong this entire time.