The information exponent (Ben Arous et al. [2021]) and its extensions --- which are equivalent to the lowest degree in the Hermite expansion of the link function (after a potential label transform) for Gaussian single-index models --- have played an important role in predicting the sample complexity of online stochastic gradient descent (SGD) in various learning tasks. In this work, we demonstrate that, for multi-index models, focusing solely on the lowest degree can miss key structural details of the model and result in suboptimal rates. Specifically, we consider the task of learning target functions of form $f_*(x) = \sum_{k=1}^{P} \phi(v_k^* \cdot x)$, where $P \le d$, the ground-truth directions $\\{ v_k^* \\}_{k=1}^P$ are orthonormal, and the information exponent of $\phi$ is $L$. Based on the theory of information exponent, when $L = 2$, only the relevant subspace (not the exact directions) can be recovered due to the rotational invariance of the second-order terms, and when $L > 2$, recovering the directions using online SGD require $\tilde{O}(P d^{L-1})$ samples. In this work, we show that by considering both second-and higher-order terms, we can first learn the relevant space using the second-order terms, and then the exact directions using the higher-order terms, and the overall sample and complexity of online SGD is $\tilde{O}( d P^{L-1})$.

Intent classification models have made a significant progress in recent years. However, previous studies primarily focus on high-resource language datasets, which results in a gap for low-resource languages and for regions with high rates of illiteracy, where languages are more spoken than read or written. This is the case in Senegal, for example, where Wolof is spoken by around 90\% of the population, while the national illiteracy rate remains at of 42\%. Wolof is actually spoken by more than 10 million people in West African region. To address these limitations, we introduce the Wolof Banking Speech Intent Classification Dataset (WolBanking77), for academic research in intent classification.

Pat McAfee wages war on Omaha's famous Jell-o shot bar after crew gets cold reception at College World Series NASCAR legend Tony Stewart calls mourning fans'a--holes' in tone-deaf rant about Kyle Busch Brewers' Jacob Misiorowski breaks brains and radar guns with hardest pitch ever by a starting pitcher US fans were out in full force ahead of the USMNT's first match of the 2026 FIFA World Cup MLB announces drive-in theater screenings of'The Sandlot' with live games and fireworks for July 4th California Democratic Party under fire for'you're not allowed to watch' World Cup post Victor Wembanyama isn't good or mature enough to be the face of the NBA -- at least not yet Trump praised for having'lots of energy' ahead of 80th birthday Trump calls Maine Democratic Senate candidate Graham Platner a'thug' Charter Space founder responds to critics' worries about SpaceX impact on market Rep. Byron Donalds shares his faith redemption story amid Florida gubernatorial run Iran's foreign minister says peace with US'has never been closer' GOP lawmaker says it's'really important' that US continues cartel crackdown Spencer Pratt's use of AI to boost campaign sparks debate FBI arrests first suspect on'most wanted fraudsters' list Brazil favored at -145 with the over at 2.5 +115, while Japan's tactical play could neutralize Haaland INSTANT REACTION FIFA World Cup Now reacts to USA's 4-1 dominant win over Paraguay Melissa Ortiz, Peter Crouch, Sacha Kljestan, Bob Bradley, Stu Holden, Brad Guzan and Mo Edu react to USA's 4-1 win over Paraguay. We are all jazzed up about the World Cup, right? I mean it is in our own backyard this year and the USA Men's National Team just won their first game with a dominant 4-1 victory over Paraguay. More importantly to me, we just won 1.35 units on the game because we took the over for it. I'm headed back to the pitch today for a couple of different plays.

NASCAR legend Tony Stewart calls mourning fans'a--holes' in tone-deaf rant about Kyle Busch Brewers' Jacob Misiorowski breaks brains and radar guns with hardest pitch ever by a starting pitcher US fans were out in full force ahead of the USMNT's first match of the 2026 FIFA World Cup MLB announces drive-in theater screenings of'The Sandlot' with live games and fireworks for July 4th California Democratic Party under fire for'you're not allowed to watch' World Cup post Victor Wembanyama isn't good or mature enough to be the face of the NBA -- at least not yet Rep. Byron Donalds shares his faith redemption story amid Florida gubernatorial run Iran's foreign minister says peace with US'has never been closer' GOP lawmaker says it's'really important' that US continues cartel crackdown Spencer Pratt's use of AI to boost campaign sparks debate FBI arrests first suspect on'most wanted fraudsters' list Accused Charlie Kirk killer's attorneys seek to BLOCK death penalty Kayleigh McEnany: Capitalism isn't the big evil Bernie Sanders would have you believe OutKick Sports Pat McAfee wages war on Omaha's famous Jell-o shot bar after crew gets cold reception at College World Series McAfee says the general manager was unhappy he didn't call ahead and mocked his ability to pay for shots Dan Dakich asks how ESPN's relevance has changed since adding Pat McAfee. We've got drama at the College World Series, and it has nothing to do with baseball. Pat McAfee has waged war with Rocco's -- the famous Omaha-based bar known for its Jell-O shot challenge during the 12-day tournament. And by war, I mean McAfee stuffed the GM in a locker during a heated segment on his ESPN and YouTube show Friday afternoon. It was nowhere near what I thought it was going to be like, McAfee said of the crew's experience at the bar earlier this week.

The Restricted Boltzmann Machine (RBM) is one of the simplest generative neural networks capable of learning input distributions. Despite its simplicity, the analysis of its performance in learning from the training data is only well understood in cases that essentially reduce to singular value decomposition of the data. Here, we consider the limit of a large dimension of the input space and a constant number of hidden units. In this limit, we simplify the standard RBM training objective into a form that is equivalent to the multi-index model with non-separable regularization. This opens a path to analyze training of the RBM using methods that are established for multi-index models, such as Approximate Message Passing (AMP) and its state evolution, and the analysis of Gradient Descent (GD) via the dynamical mean-field theory. We then give rigorous asymptotics of the training dynamics of RBMs on data generated by the spiked covariance model as a prototype of a structure suitable for unsupervised learning. We show in particular that RBMs reach the optimal computational weak recovery threshold, aligning with the Baik-Ben Arous-Péché (BBP) transition, in the spiked covariance model.

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Drone strikes on the central Sudanese city of el-Obeid have killed up to 23 people, officials and a rights group have reported. Both sources reported on Thursday that overnight attacks had killed several people across the key hub in the southern Kordofan region. The reports concerned the latest in a series of attacks using unmanned aircraft, illustrating that drone warfare has become an increasingly prominent feature in the conflict, which erupted in April 2023 between the military government and paramilitary Rapid Support Forces (RSF). Health officials at el-Obeid Hospital said that 15 were killed and more than 10 wounded in the attacks, which hit residential areas, a funeral gathering and a truck carrying food supplies, as well as areas near army positions. Emergency Lawyers blamed the attack on the RSF, which did not immediately claim responsibility.

Portions of the rock date back billions of years to when the moon was molten rock. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. NWA 12593 was discovered in Mali in 2017. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

Fully autonomous drones with no human oversight have killed soldiers on the battlefield for the first time. This is according to a senior figure in the Ukrainian defence industry, marking a watershed moment in warfare. The one-off test involved 10 AI-controlled "Terminator" drones on the front line of the Ukraine war. "We tried it," says drone-maker Alexander Kokhanovskyy, who supplied the technology and spoke to at a press event hosted by the Ukrainian embassy. We never implemented it [more widely]." The test took place two years ago and involved quadcopter drones that were programmed to fly towards the front line, cover between 3 and 5 kilometres over around 10 minutes and then engage "Terminator mode", in which an AI model searches for and intercepts targets. "We just launch it and we know everything will be dead - everything that will be found there in this particular area will be dead," says Kokhanovskyy. "There is no connection to the drone at all, you cannot see the video, ...

Follow this author to personalize your feed and get instant alerts. Follow Go to your personalized feed WHY FOLLOW? Smart Alerts: Get notified about major news as it happens. Temba Bavuma has always carried more than the weight of his shirt. As one of just a handful of Black South African cricketers, his successes were lauded as a turning point for the sport.