Support journalism that doesn't flinch . Support journalism that doesn't flinch . Elon Musk leaves a meeting with House Republicans in the basement of the US Capitol building on March 5, 2025 in Washington, DC. Get your news from a source that's not owned and controlled by oligarchs. Tennessee teenagers are suing Elon Musk's company xAI over allegations that its artificial intelligence tool Grok undressed photos of them as minors--the latest challenge against the wealthiest living person's chatbot .

After the rise (and fall) of reservation scalping, DoorDash and a host of apps are fighting to book you a seat at the country's most exclusive restaurants. At The Eighty-Six in Manhattan, exclusivity is the point. The luxe, 11-table steakhouse is the sort of place that lavishes caviar and aged mimolette cheese on its potatoes, and crows that your market-price duck was raised by one Dr. Taylor Swift has reportedly dined there in a Miu Miu skirt. Reservations are a scarce commodity that the restaurant, and New York law forbids you from selling one. "Access is the main asset," wrote food writer Helen Rosner in a recent New Yorker review of The Eighty-Six. "The product is the door, and what a door!

Trump says he's'not afraid' of Vietnam-style ground combat in Iran Furious US troops erupt at CNN's $20m steak and lobster claims as grim photos expose reality Hollywood's top insider makes VERY catty observation about Kaitlan Collins Pam Bondi is formally subpoenaed by Congress as Trump's Epstein nightmare grows What the Jane Plan did to my body: The unfashionable retro diet's fans say it's life-changing, easy, better than fat jabs - and shifts weight fast. My husband tried a'cure' for his ALS... days later he went blind and couldn't move. The children screamed on video call as he died. Outrage after Pete Hegseth aide ousted for'leaks' lands new top secret intelligence job Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with SARAH VINE: How telling that Meghan's joined the ranks of those peddling wellness and fake lifestyles to the gullible My chilling conversations with the Unabomber and America's worst serial killers when I ran a Supermax prison, revealed in The Crime Desk newsletter Oscars afterparty snitches reveal cringing details of how stars stopped talking to him... a brutal message from Kylie's gloating ex... and her'humiliating' admission to friends Joe Burrow cements his place as the NFL's most eligible bachelor as he is spotted cozying up to Tate McRae and Alix Earle at glitzy Oscars afterparty Dark secret past of husband killer Kouri Richins' Iraq war veteran lover revealed... and their toe-curling sex texts that helped convict her Mystery as Communion bread and wine'miraculously' appear to turn into human tissue and blood READ MORE: Scientists stunned as 500-year-old'miracle' image of Virgin Mary reveals impossible microscopic reflection Catholics believe that during Communion, bread and wine become the body and blood of Jesus Christ, though they continue to appear unchanged to the human eye. But there have been a handful of rare and debated cases in which the sacred elements appeared to take on a far more literal, physical form.

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape. On the other hand, gradient descent with perturbations [Ge et al., 2015, Jin et al., 2017] is not slowed down by saddle points--it can find an approximate local minimizer in polynomial time. This result implies that GD is inherently slower than perturbed GD, and justifies the importance of adding perturbations for efficient non-convex optimization. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

We propose an alternative framework to existing setups for controlling false alarms when multiple A/B tests are run over time. This setup arises in many practical applications, e.g. when pharmaceutical companies test new treatment options against control pills for different diseases, or when internet companies test their default webpages versus various alternatives over time. Our framework proposes to replace a sequence of A/B tests by a sequence of best-arm MAB instances, which can be continuously monitored by the data scientist. When interleaving the MAB tests with an online false discovery rate (FDR) algorithm, we can obtain the best of both worlds: low sample complexity and any time online FDR control. Our main contributions are: (i) to propose reasonable definitions of a null hypothesis for MAB instances; (ii) to demonstrate how one can derive an always-valid sequential p-value that allows continuous monitoring of each MAB test; and (iii) to show that using rejection thresholds of online-FDR algorithms as the confidence levels for the MAB algorithms results in both sample-optimality, high power and low FDR at any point in time. We run extensive simulations to verify our claims, and also report results on real data collected from the New Yorker Cartoon Caption contest.

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How the US left Ukraine exposed to Russia's winter war Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? Starmer, Zelenskyy urge'focus' on Ukraine as Iran war diverts attention Ukrainian President Volodymyr Zelenskyy has met British Prime Minister Keir Starmer in London to sign a new defence pact as the unfolding US-Israeli war on Iran threatened to divert international attention away from Russia's attacks on Ukraine. Starmer welcomed Zelenskyy at his official Downing Street residence on Tuesday, reassuring the Ukrainian leader that "the focus must remain on Ukraine", days after the US partially rolled back sanctions against Moscow to cool oil prices sent soaring by its attacks on Iran. "There is obviously a conflict in Iran going on, in the Middle East, but we can't lose focus on what's going on in Ukraine and the need for our support there," said Starmer, who was meeting Zelenskyy to sign a defence partnership aimed at boosting "global defensive capability against the proliferation of low-cost, high-tech military hardware".

Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixed-percentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction \alpha of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c / (1 - \alpha) for each item, but it is not the optimal solution on maximizing the profit of the intermediary.

We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the trace of the conditional covariance operator. We prove various consistency results for this procedure, and also demonstrate that our method compares favorably with other state-of-the-art algorithms on a variety of synthetic and real data sets.

The BBC has obtained footage and interviews from the Iranian capital Tehran which evoke a city of strained nerves, of constant waiting for the next air strike and relentless fear of the state security apparatus. The identities of the people in this report have been protected. While independent journalists still try to gather testimony that offers a credible alternative view, they run the risk of arrest, torture and possibly worse. Displaced Palestinians were told to secure their tents to prevent them being blown away as a storm swept through the enclave. Video filmed by a witness and verified by the BBC shows a drone crashing close to the airport.