Masayoshi Son, chairman and chief executive officer of SoftBank Group, speaks during the Future Investment Initiative (FII) Institute Priority Asia conference in Tokyo in December. SoftBank Group has halted talks about an acquisition of U.S. data center operator Switch, a setback to founder Masayoshi Son's ambition to roll out Stargate artificial intelligence infrastructure, according to people familiar with the matter. For months, Son pursued a deal of around $50 billion for Switch, convinced that direct control of the latter's network of energy-efficient data centers would help the $500 billion Stargate push to generate computing power for partner OpenAI. But earlier this month, Son conceded that a full acquisition was off the table and scrapped a planned January announcement, the people said, asking not to be named because the matter is private. The two sides remain in active discussions about a partial investment or a partnership, they said. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' More than 1,300 apartment buildings in the Ukrainian capital, Kyiv, were still without heating following Russia's missile and drone attacks on Saturday, according to Mayor Vitalii Klitschko. Over the past week alone, Russia launched more than 1,700 attack drones, at least 1,380 guided aerial bombs, and 69 missiles on Ukraine, mainly targeting the energy sector, critical infrastructure, and residential buildings, according to Ukrainian President Volodymyr Zelenskyy.

Iranian drone swarms pose serious threat to U.S. military assets as reports emerge that Iran's Supreme Leader has gone underground, according to military drone expert Cameron Chell.

Understanding the curvature evolution of the loss landscape is fundamental to analyzing the training dynamics of neural networks. The most commonly studied measure, Hessian sharpness ($λ_{\max}^H$) -- the largest eigenvalue of the loss Hessian -- determines local training stability and interacts with the learning rate throughout training. Despite its significance in analyzing training dynamics, direct measurement of Hessian sharpness remains prohibitive for Large Language Models (LLMs) due to high computational cost. We analyze $\textit{critical sharpness}$ ($λ_c$), a computationally efficient measure requiring fewer than $10$ forward passes given the update direction $Δ\mathbfθ$. Critically, this measure captures well-documented Hessian sharpness phenomena, including progressive sharpening and Edge of Stability. Using this measure, we provide the first demonstration of these sharpness phenomena at scale, up to $7$B parameters, spanning both pre-training and mid-training of OLMo-2 models. We further introduce $\textit{relative critical sharpness}$ ($λ_c^{1\to 2}$), which quantifies the curvature of one loss landscape while optimizing another, to analyze the transition from pre-training to fine-tuning and guide data mixing strategies. Critical sharpness provides practitioners with a practical tool for diagnosing curvature dynamics and informing data composition choices at scale. More broadly, our work shows that scalable curvature measures can provide actionable insights for large-scale training.

We introduce FedSGM, a unified framework for federated constrained optimization that addresses four major challenges in federated learning (FL): functional constraints, communication bottlenecks, local updates, and partial client participation. Building on the switching gradient method, FedSGM provides projection-free, primal-only updates, avoiding expensive dual-variable tuning or inner solvers. To handle communication limits, FedSGM incorporates bi-directional error feedback, correcting the bias introduced by compression while explicitly understanding the interaction between compression noise and multi-step local updates. We derive convergence guarantees showing that the averaged iterate achieves the canonical $\boldsymbol{\mathcal{O}}(1/\sqrt{T})$ rate, with additional high-probability bounds that decouple optimization progress from sampling noise due to partial participation. Additionally, we introduce a soft switching version of FedSGM to stabilize updates near the feasibility boundary. To our knowledge, FedSGM is the first framework to unify functional constraints, compression, multiple local updates, and partial client participation, establishing a theoretically grounded foundation for constrained federated learning. Finally, we validate the theoretical guarantees of FedSGM via experimentation on Neyman-Pearson classification and constrained Markov decision process (CMDP) tasks.

Weather conditions can drastically alter the state of crops and rangelands, and in turn, impact the incomes and food security of individuals worldwide. Satellite-based remote sensing offers an effective way to monitor vegetation and climate variables on regional and global scales. The annual peak Normalized Difference Vegetation Index (NDVI), derived from satellite observations, is closely associated with crop development, rangeland biomass, and vegetation growth. Although various machine learning methods have been developed to forecast NDVI over short time ranges, such as one-month-ahead predictions, long-term forecasting approaches, such as one-year-ahead predictions of vegetation conditions, are not yet available. To fill this gap, we develop a two-phase machine learning model to forecast the one-year-ahead peak NDVI over high-resolution grids, using the Four Corners region of the Southwestern United States as a testbed. In phase one, we identify informative climate attributes, including precipitation and maximum vapor pressure deficit, and develop the generalized parallel Gaussian process that captures the relationship between climate attributes and NDVI. In phase two, we forecast these climate attributes using historical data at least one year before the NDVI prediction month, which then serve as inputs to forecast the peak NDVI at each spatial grid. We developed open-source tools that outperform alternative methods for both gross NDVI and grid-based NDVI one-year forecasts, providing information that can help farmers and ranchers make actionable plans a year in advance.

This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution has its fundamental limitation -- high-density bias, irrespective of the algorithms used to perform clustering. Existing density-based clustering algorithms have employed different algorithmic means to counter the effect of the high-density bias with some success, but the fundamental limitation of using density distribution remains an obstacle to discovering clusters of arbitrary shapes, sizes and densities. Using the mass distribution as a better foundation, we propose a new algorithm which maximizes the total mass of all clusters, called mass-maximization clustering (MMC). The algorithm can be easily changed to maximize the total density of all clusters in order to examine the fundamental limitation of using density distribution versus mass distribution. The key advantage of the MMC over the density-maximization clustering is that the maximization is conducted without a bias towards dense clusters.

Prince Harry and Meghan Markle's Sundance screening sparks online row: 'Sussex Squad' brand claims event failed to sell out as'lies' despite photos showing'rows of empty seats' Mick Jagger's family launch desperate hunt for missing relative: His granddaughter's partner vanishes in Cornwall after wandering streets Forensic video analysis of Alex Pretti's final 30 seconds exposes'John Wayne gun' question that can't be ignored Sinister truth about Celine Dion's song All By Myself: Singer's producer reveals bombshell secrets of her 26-year age gap marriage... that he swore not to tell until her husband René died The nastiest clique in Hollywood have had their dirty secret outed... there's no coming back from this: MAUREEN CALLAHAN Ariana Grande and Cynthia Erivo'creeped a lot of people out' says anonymous Oscar voter amid Wicked snubs John Fetterman's own WIFE turns on him over ICE as Senator comes under fire for his silence on shooting of Alex Pretti Lauren Sanchez turns heads in a red skirt suit as she holds hands with billionaire husband Jeff Bezos at Schiaparelli's Paris Haute Couture Fashion Week show Olivia Wilde blasts'inauthentic and unrealistic' sex in modern film and claims it has'been that way for a long time' - despite featuring racy scenes in Don't Worry Darling Sandra Bullock's Blind Side costar Quinton Aaron is'fighting for his life' in hospital after falling at home Seedy underbelly of America's exclusive golf clubs... as cart girls expose ultra-rich world of sex scandals and drunken debauchery Real estate mogul is sensationally found GUILTY of murdering football coach's son outside mall Kelly Clarkson on verge of QUITTING: Staff are all starting to say same thing backstage... as friends let slip the only way she could be convinced to stay Panicking realtors are drowning in unsold homes in America's'most extreme' market. They blame'the Joe Rogan effect' Father of alien archaeology says the pyramids were not built by human hands... and claims he has proof READ MORE: Egypt's Great Pyramid construction rewritten as new evidence exposes how it was actually built The belief that the pyramids were not built by human hands has fascinated conspiracy theorists for decades. No one promoted that idea more persistently than Swiss author Erich von Däniken, often described as the father of ancient alien archaeology. Von Däniken, who died this month aged 90, argued that extraterrestrial visitors played a direct role in helping ancient Egyptians construct monuments that would otherwise have been impossible. In his 1968 bestseller'Chariots of the Gods,' he claimed alien'astronauts' visited early civilizations, including the ancient Egyptians and Mayans, and shared advanced technology.

Environment Animals Wildlife Fish'Walking sharks' lay eggs without breaking a sweat Breakthroughs, discoveries, and DIY tips sent six days a week. Being pregnant and giving birth is hard work for any species--but epaulette sharks () might disagree. These fish and a number of other species are known as " walking sharks " for their ability to traverse both the seafloor and land with their fins. Epaulette sharks' energy use didn't change during their reproduction cycle, as described in a study recently published in the journal . "Reproduction is the ultimate investment you are literally building new life from scratch," Jodie Rummer, a marine biologist at James Cook University and co-author of the recent study, said in a university statement .

Shocking history of handgun Alex Pretti was carrying when he was shot by Border Patrol is revealed... as judge bans Trump administration from'destroying evidence' from scene Homeowners in PANIC as stark map shows just five sellers' markets left - spelling price drops almost everywhere else My secret fantasy appalled my husband... and it has revealed an irreparable rift in our marriage: DEAR JANE Seedy underbelly of America's exclusive golf clubs... as cart girls expose ultra-rich world of sex scandals and drunken debauchery Doomsday Clock will be updated next WEEK to determine our fate - here's how scientists think the hands will move Lisa Rinna's nepo baby daughter Amelia Gray Hamlin, 24, breaks down all the plastic surgery she's had Gay reporter's wild on-air comment about Patriots quarterback Drake Maye goes viral Meteorologist reveals America's most dangerous city in winter storm's corridor of chaos: 'Staying in your home won't be viable' '90s bombshell channels iconic role she took over from Pamela Anderson and looks exactly the same at 59 Crystal clear new video raises horrifying questions about killing of Minneapolis nurse by DHS...as doctor on scene claims agents were counting bullet holes instead of helping him Doomsday Clock will be updated next WEEK to determine our fate - here's how scientists think the hands will move Humanity is about to learn if we have moved closer to self-destruction as the Doomsday Clock is updated. The new time for the symbolic timepiece, which ticks closer to midnight as we approach annihilation, will be revealed on Tuesday, January 27. Since last year, the clock has sat at 89 seconds to midnight - the latest time in its 78-year history. However, experts have told the Daily Mail they now expect the Doomsday Clock to move even closer to midnight . While the Doomsday Clock was initially created to track the risk of nuclear war between Russia and America, the world now faces a far more diverse array of threats.