When you purchase through links in our articles, we may earn a small commission. It's not perfect, but it definitely surprised me The Mammotion Luba 3 AWD turns out to be a lot more capable than expected, handling a rough, awkward yard surprisingly well, even if the app and setup aren't always smooth. Before testing, I never gave robot lawn mowers the time of day. They just seemed like expensive gadgets for people who didn't want to deal with mowing. After a few weeks with the Mammotion Luba 3 AWD, that assumption didn't really hold up.

Karmelo Anthony's sobbing mother pleads with jurors to show'mercy' for her son as they prepare to sentence him for murder of Austin Metcalf, 17, that shocked America Caitlyn Jenner biographer and Robin Riker's ex William Hasley found dead on hiking trail at 78 Karmelo Anthony's mother sobs with shock as son is found guilty of murdering Austin Metcalf, 17, in stabbing that horrified America: Live updates Disgraceful texts'hot' teacher sent boy, 17, who she had illegal sex with where she moaned about her HUSBAND Everyone always said I cleared my throat a lot. But then I developed shoulder pain and doctors discovered the sinister cause... the world's deadliest cancer. Don't leave it too late like I did Leaked transcript of UNAIRED 60 Minutes interview exposes REAL reason'callous' CBS star Scott Pelley'deserved to be fired' Urgent recall for 1.1m vehicles over fears they could spontaneously CATCH FIRE even when parked Disturbing new death scene photos show tech whistleblower's haunting final moments... as forensic report casts doubt on suicide claims: 'Execution angle' 'Great' mom, 32, tried to gas herself and her three young kids to death after inviting them to'popcorn sleepover' in car, prosecutors allege The porn-fuelled fantasy middle-class husbands are desperate to try with their wives... and it almost always ends in divorce: JANA HOCKING Grim-faced former Louisiana mayor Misty Roberts arrives in court for sentencing after being found guilty of having sex with son's teenage friend John Oliver's private panic: Late-night curse spreads and host prepares for worst as insiders reveal his desperate'plan B'... and the industry whispers swirling about his fate Woke Vegas school compared boy to racist cross burner over pro-ICE stickers and expelled him... but did not punish pro-migrant students for class walkout, lawsuit alleges Medical student, 24, died by suicide in his white coat a day after he was suspended for alleged'inappropriate' behavior towards female patient, lawsuit alleges, as his heartbreaking goodbye note to parents is revealed Mother's final words before she was shot dead'by new husband' in front of her two young children All the backstage gossip from Miami Swim Week: Insider exposes'catty' VIP's diva demands... STEALING... and'morbidly embarrassing' celeb moment everyone is whispering about The brewing super El Niño will likely be the strongest ever recorded, new predictions suggest. The latest modelling from the European Centre for Medium-Range Weather Forecasts (ECMWF) shows that sea temperatures will be well above average later this year. Scientists measure the intensity of El Niño using the Niño 3.4 index, which records sea surface temperature anomalies between 5 degrees north and 5 degrees south latitude, and 120 degrees west and 170 degrees west longitude.

"The Lost Soldiers," "Homebound," "Once Upon a Time There Was Truth," and "My World Is Melting." The year is 1919, the midst of Bolshevik takeover in Ukraine, and twenty-eight Red Army soldiers have vanished into thin air, last seen at a bathhouse. Kolechko must track them down. He gets little help from the absurd locals, who range from obstinately useless to selfishly malicious. Kolechko is a kind of anti-Poirot--a fairly conventional man whose powers of detection lie not in a dazzling intuition but in a supernatural severed ear, which has a bug-like ability to pick up dialogue.

Is Elon Musk's SpaceX Really Worth $1.75 Trillion? The billionaire spent more than two decades creating a successful space company. Now he's pitching it as an A.I. play. Later this week, Elon Musk's SpaceX is expected to issue stock to investors in what is shaping up to be the biggest initial public offering ever. The company has said it will issue 555,555,555 shares at a price of $135, which would value it at about $1.75 trillion.

Why this year's World Cup ball may not fly as far A team of outside researchers has been studying how Adidas's redesigned soccer ball cuts through the air. Much is new about this month's upcoming FIFA World Cup tournament, which will be held in the US, Canada, and Mexico. It hosts more teams than ever before. It's the first to occur in three different host countries. And, like predecessor cups for over half a century, it will employ a soccer ball with a brand-new design. One group of researchers that has been testing the physics of World Cup balls for the past 20 years recently studied this new entry, called the Trionda.

South Korean President Lee Jae Myung is placing his hopes on former Naver Chief Executive Han Seong Sook to help better use the nation's tech expertise for future growth and ensure its benefits spread more widely through the economy. Han will become the country's second female premier, assuming her appointment is approved by the national assembly, elevating a former technology executive to one of the nation's highest political posts. The tapping of Han underscores Lee's commitment to shoring up future growth of the domestic economy and the need to leverage a wider range of industries. During her five years at the helm of Naver, a company sometimes called the Google of Korea, Han helped broaden its revenue streams beyond its search engine model to also draw on e-commerce, fintech and content generation. In a time of both misinformation and too much information, quality journalism is more crucial than ever. By subscribing, you can help us get the story right.

In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA). We consider on-policy independent and identically distributed (i.i.d.) samples, a constant learning step, and the Polyak-Juditsky averaging method. We establish a new convergence rate, for the Mean-Square Error (MSE) on the approximated function, that is (i) fast in the sense that it admits an optimal dependency in the number of iterations k (i.e., of order 1/k), (ii) robust to ill-conditioning: it only depends on an initial error and modelindependent constants and (iii) sharp up to a multiplicative constant lower than 11. In particular, it does not depend on the smallest eigenvalue of the uncentered covariance matrix of the linear parametrization, unlike all pre-existing O(1/k) rates in the TD(0) literature. We also introduce PCTD(0), a variant of TD(0), which benefits from better convergence properties under an additional assumption of strong mixing on the Markov Chain.

A central mystery in deep learning is how neural networks, despite being highly non-convex and heavily overparameterized, are able to achieve near-zero training error while still generalizing well to unseen data. This paradox has sparked a surge of research aimed at understanding the convergence and generalization behavior of neural networks [1, 2, 6, 7, 15, 38, 41, 49]. The Neural Tangent Kernel (NTK), introduced by [20], has become one of a foundational tool for understanding the behavior of training dynamics for neural networks, especially those trained using gradient-based methods such as gradient descent (GD) and stochastic gradient descent (SGD). The core idea here is to linearize the neural network around its random initialization, which enables the evolution of the network during training to be closely approximated by a kernel method associated with the corresponding NTK. This framework establishes a powerful connection between the evolution of a neural network during training process and the behavior of kernel methods in a reproducing kernel Hilbert space (RKHS) induced by the NTK, allowing insights from the kernel methods to inform our understanding of neural networks. Following this perspective, the influential work [34] showed that for regression problems, shallow neural networks trained by SGD can achieve generalization performance on par with their kernel counterparts.

The transformer's emergent ability to perform in-context learning (ICL) has sparked a wide range of studies designed to understand its underlying mechanisms. Existing works often study how training task diversity, defined either as the number of ICL training task vectors or as the number of function classes from which the task vectors are drawn, shapes both the learning dynamics and generalization capabilities of ICL. While both definitions have uncovered many interesting phenomena, many observations under the latter definition remain theoretically unexplained. This paper presents a minimal analytical model under which these phenomena provably emerge from the properties of the training data. By modeling the training task vectors as a mixture of low-rank Gaussians, we show how training task diversity, defined by the number of non-overlapping columns between subspaces that parameterize the covariance matrices, improves both the generalization and optimization trajectory of ICL with linear attention. In particular, we show that our model can explain (i) why training with task diversity shortens the ICL plateau and (ii) why ICL appears to achieve out-of-distribution generalization. We conclude by empirically demonstrating how our results extend to nonlinear transformers and nonlinear function classes. Overall, our work presents a tractable framework to unify existing observations.

While algorithmic stability is a central tool for understanding generalization of learning algorithms, existing high-probability guarantees typically rely on uniform boundedness or sub-Gaussian/sub-Weibull tail assumptions, which can be overly restrictive for modern settings with heavy-tailed or unbounded losses. We develop a stability-based framework that requires only a finite $L_p$ moment condition. Our first contribution is sharp concentration inequalities for functions of independent random variables under $L_p$ constraints, extending McDiarmid's bounded-differences techniques beyond the classical regime. Leveraging these results, we derive sharp high-probability generalization bounds across a range of learning paradigms, including empirical risk minimization, transductive regression, and meta-learning. These guarantees show that $L_p$ stability suffices for robust generalization even when boundedness fails, substantially weakening the standard assumptions in the stability literature.