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.

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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".

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.

With the goal of making high-resolution forecasts of regional rainfall, precipitation nowcasting has become an important and fundamental technology underlying various public services ranging from rainstorm warnings to flight safety. Recently, the Convolutional LSTM (ConvLSTM) model has been shown to outperform traditional optical flow based methods for precipitation nowcasting, suggesting that deep learning models have a huge potential for solving the problem. However, the convolutional recurrence structure in ConvLSTM-based models is location-invariant while natural motion and transformation (e.g., rotation) are location-variant in general. Furthermore, since deep-learning-based precipitation nowcasting is a newly emerging area, clear evaluation protocols have not yet been established. To address these problems, we propose both a new model and a benchmark for precipitation nowcasting. Specifically, we go beyond ConvLSTM and propose the Trajectory GRU (TrajGRU) model that can actively learn the location-variant structure for recurrent connections. Besides, we provide a benchmark that includes a real-world large-scale dataset from the Hong Kong Observatory, a new training loss, and a comprehensive evaluation protocol to facilitate future research and gauge the state of the art.

You can now buy a humanoid robot housekeeper for less than the price of a second-hand car. But before splashing out, there's something you need to know Science fiction is strewn with humanoid robots, from bad-tempered Bender in to cunning Ava in . And it has long seemed like that's the natural home for such robots - on the screen and in books. The idea of a walking, talking, functioning robot with two arms and two legs has appeared to be a distant dream. Last year, machines ran, boxed and even played football at China's World Humanoid Robot Games, albeit sometimes falling over in the process . Meanwhile, companies have been readying their own range of humanoids that promise to do something a bit more useful: help around the house .

We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods, for the smooth nonconvex finite-sum optimization problem. Only assuming the smoothness of each component, the complexity of SCSG to reach a stationary point with $E \|\nabla f(x)\|^{2}\le \epsilon$ is $O(\min\{\epsilon^{-5/3}, \epsilon^{-1}n^{2/3}\})$, which strictly outperforms the stochastic gradient descent. Moreover, SCSG is never worse than the state-of-the-art methods based on variance reduction and it significantly outperforms them when the target accuracy is low. A similar acceleration is also achieved when the functions satisfy the Polyak-Lojasiewicz condition. Empirical experiments demonstrate that SCSG outperforms stochastic gradient methods on training multi-layers neural networks in terms of both training and validation loss.

In the online multiple testing problem, p-values corresponding to different null hypotheses are presented one by one, and the decision of whether to reject a hypothesis must be made immediately, after which the next p-value is presented. Alpha-investing algorithms to control the false discovery rate were first formulated by Foster and Stine and have since been generalized and applied to various settings, varying from quality-preserving databases for science to multiple A/B tests for internet commerce. This paper improves the class of generalized alpha-investing algorithms (GAI) in four ways: (a) we show how to uniformly improve the power of the entire class of GAI procedures under independence by awarding more alpha-wealth for each rejection, giving a near win-win resolution to a dilemma raised by Javanmard and Montanari, (b) we demonstrate how to incorporate prior weights to indicate domain knowledge of which hypotheses are likely to be null or non-null, (c) we allow for differing penalties for false discoveries to indicate that some hypotheses may be more meaningful/important than others, (d) we define a new quantity called the \emph{decaying memory false discovery rate, or $\memfdr$} that may be more meaningful for applications with an explicit time component, using a discount factor to incrementally forget past decisions and alleviate some potential problems that we describe and name ``piggybacking'' and ``alpha-death''. Our GAI++ algorithms incorporate all four generalizations (a, b, c, d) simulatenously, and reduce to more powerful variants of earlier algorithms when the weights and decay are all set to unity.