Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $ϕ$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $ϕ$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.

Differential privacy changes the effective sample size governing CVaR learning. For tail mass $τ$, the privacy-relevant sample size is not $n$, but $nτ$; equivalently, the effective private tail sample size is $εnτ$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $Θ(B \min\{1,(nτ)^{-1/2}+(εnτ)^{-1}\})$, and finite classes of size $M$ have rate $Θ(B \min\{1,\sqrt{\log(2M)/(nτ)}+\log(2M)/(εnτ)\})$. These complete rates hold under pure DP, and their lower bounds extend to approximate DP in the stated small-$δ$ regimes. For convex Lipschitz learning, modular upper and lower reductions show that the CVaR-specific privacy term necessarily scales as $1/(εnτ)$, with dimension dependence inherited from private stochastic convex optimization. Together, these results identify ordinary private learning on $Θ(nτ)$ informative tail records as the canonical hard subproblem inside private CVaR learning.

Why does Amazon have no Western rivals? Vitamins, repair tape and a jar of mango chutney - just some of what my household bought last month via Amazon's sprawling online shopping platform. We also shopped at the company's supermarket chain Whole Foods, streamed its TV shows, read books on Kindle e-readers, and browsed countless websites no doubt powered by Amazon Web Services (AWS), its highly profitable cloud-computing business. And that isn't half of the interconnected products and services offered by the global behemoth, which earlier this year overtook US superstore giant Walmart to become the world's largest company by annual sales. But why does Amazon, launched by Jeff Bezos in 1995 as an online bookstore out of a rented garage, have so few serious rivals in the West when it comes to e-commerce?

Inside the'kill-zone' on Ukraine's front line, where new weapons have transformed war After 225 days stuck in a front-line foxhole, the Ukrainian infantryman's muscles were so weak he could barely walk. His commanders had tried five times to swap him with another soldier - but they could never reach him. Rotating soldiers on the front line in eastern Ukraine is extremely difficult because of the constant threat of drones. This area near Kostyantynivka is currently one of the most dangerous hotspots and the Ukrainian military admits that Russian forces have reached its outskirts. Known as Kenya, the infantryman took two days to walk 11km (6.8 miles) to get back to his brigade, avoiding mines and hiding from drones to get out.

ISIS shadow commander Abu-Bilal al-Minuki was killed in a precision strike in Nigeria after human intelligence penetrated defenses that had shielded him for years, analyst says.

Nothing to see here: Cowboys quarterback Dak Prescott and his ex's bridesmaid are just friends Can't sleep, Japanese bear-fighting robo-wolves will eat me and a gorilla trade captivates the nation A replica of KITT from'Knight Rider' got a traffic ticket in another state despite being in a museum Jena Sims covers her butt with a bow at the SI Swimsuit party, the NFL saves us from Romo & is Star Wars dead? Taylor Sheridan shocks'Yellowstone' fans with new spinoff series, provides viewers with dark ride Early reviews for new'Star Wars' movie are generally horrific, but does anyone even care at this point? Retired Navy admiral makes bombshell claim about UFOs and'non-human intelligence' controlling them Mother's Day chaos at a steakhouse includes knives thrown at waiters and a touching mother-daughter arrest Japanese bear-fightin' robo-wolves are pure unleaded nightmare fuel but they're working Jennifer Lopez's dress holds on for dear life at her Netflix event, Trump powers through some wine & Kay Adams Trump warns Iran'clock is ticking' amid Strait of Hormuz tensions Sen. John Kennedy reacts to Bill Cassidy's primary loss in Louisiana Peter Doocy gives BEHIND-THE-SCENES look at Trump's China visit Speaker Johnson says Trump admin'laid the groundwork' for new China deal Sen. Bill Cassidy ousted in Louisiana primary by Trump-backed opponent Donald Trump rejects Xi Jinping's offer on Iran conflict Senate Republicans narrowly block Democrats' effort to end Iran conflict Cignetti reflected on his time at Alabama under Nick Saban, describing the intensity of a program where every day felt like 4th and 1. Footage from a high-speed chase in Wisconsin earlier this month shows the fleeing driver going airborne and jumping his car over another. It's one of the most insane dashcam videos you'll ever see. The Fond du Lac County Sheriff's Office released the now-viral footage of the arrest, which took place on Saturday morning, May 9. A fleeing driver goes airborne and flies his car over another one during a high-speed police chase in Wisconsin.

Can't sleep, Japanese bear-fighting robo-wolves will eat me and a gorilla trade captivates the nation A replica of KITT from'Knight Rider' got a traffic ticket in another state despite being in a museum Jena Sims covers her butt with a bow at the SI Swimsuit party, the NFL saves us from Romo & is Star Wars dead? Taylor Sheridan shocks'Yellowstone' fans with new spinoff series, provides viewers with dark ride Early reviews for new'Star Wars' movie are generally horrific, but does anyone even care at this point? Retired Navy admiral makes bombshell claim about UFOs and'non-human intelligence' controlling them Mother's Day chaos at a steakhouse includes knives thrown at waiters and a touching mother-daughter arrest Japanese bear-fightin' robo-wolves are pure unleaded nightmare fuel but they're working Jennifer Lopez's dress holds on for dear life at her Netflix event, Trump powers through some wine & Kay Adams Eric Church's uses his guitar to deliver one of the most powerful addresses ever at UNC commencement Speaker Johnson says Trump admin'laid the groundwork' for new China deal Sen. Bill Cassidy ousted in Louisiana primary by Trump-backed opponent Donald Trump rejects Xi Jinping's offer on Iran conflict Senate Republicans narrowly block Democrats' effort to end Iran conflict General Jack Keane warns of China's ambitions on Taiwan Gen Z driving'spiritual revival' with increased church attendance Pastor says Trump's visit to Detroit church meant'everything' David Perdue discusses Trump's new China trade commitments amid renewed relations OutKick Nothing to see here: Cowboys quarterback Dak Prescott and his ex's bridesmaid are just friends Dan Dakich reacts to the bombshell new photos of Mike Vrabel and Dianna Russini in Arizona that officially debunk the girls trip narrative. Sometimes a relationship leads to marriage. Sometimes those marriages end in divorce.

The United Arab Emirates is investigating the source of a drone strike which triggered a fire near a nuclear power station, officials have said. The country's defence ministry said three drones had entered the UAE from the western border direction on Sunday. While two were intercepted, the third drone struck an electrical generator outside the inner perimeter of the Barakah Nuclear Power Plant in Abu Dhabi. No injuries were reported and there was no impact on radiological safety levels, local authorities said. The country's defence ministry said in a statement that investigations were under way to determine the source of the attacks.

Could the war trigger a hunger crisis? How well do you know Iran? Drone strike sparks fire on perimeter of UAE's Barakah nuclear power plant A drone strike has sparked a fire on the perimeter of the Barakah Nuclear Energy Plant in the United Arab Emirates (UAE), raising new concerns over a potential new regional escalation amid a fragile ceasefire between Iran and the United States. Authorities in Abu Dhabi said the blaze broke out at an electrical generator outside the plant's inner perimeter in the Al Dhafra region on Sunday. No injuries were reported, and officials said radiation levels remained normal.

SNL season finale cold open sees ghost of Jeffrey Epstein played by Will Ferrell'haunt' Trump as dark jokes leave viewers shocked Jordon Hudson blasts double standards over Mike Vrabel and Dianna Russini'affair' scandal: 'What is going on?' No one wants to hang out with her': Why Meghan and Harry have been ditched by A-list friends as insiders reveal Oprah's merciless snub, why the Clooneys now want nothing to do with them - and how SHE'S the problem Truth about Kate Middleton's past before Prince William... we Americans see this for what it is: KENNEDY Kim Kardashian roasted over'ridiculous' outfit at Gucci show as she sits front row with Anna Wintour and Mariah Carey I was on track to make $1 million... then I quit my job and moved into an off-grid tiny home with no running water or electricity Professional tasters decide best and worst fast food cheeseburger - do you agree? Hamptons cancer cluster: Rates are spiking in summer enclave of New York's wealthy elite... and doctors think they know the tragic reason why Disturbing trove of images woke Los Angeles mayor Karen Bass doesn't want you to see: Filthy truth is so much worse than people think... Taylor Swift dazzles in glittering gown as she and Travis Kelce steal the spotlight at friend's wedding in NYC Golf star becomes instant fan favorite after stopping to smoke a cigarette with crowd in the middle of the PGA Championship: 'Man of the people' New kind of penis enlargement surgery will add inches, claims the doctor set to offer it... but there is a gruesome detail that may make some think twice She was every bit the adoring mother... then a leaked video exposed a'sadistic' secret even cops said'will bring tears to your eyes' I saw a 40-year-old middle-class mom in a psychiatric ward after a single hit of this drug. Her symptoms were terrifying but it's so common now... here's what you must know: DR MAX PEMBERTON Expert reveals the best way to cut the bread - and why you should never leave a'hinge' 'I saw things I can never unsee': Man who snuck into Air India crash morgue reveals what he saw... why it could blow apart the pilot suicide theory... and what happened when we visited the lone survivor Scientists are baffled by mysterious blue flashes coming from deep space that are'unlike anything we have observed before' For almost a decade, scientists have been baffled by a series of mysterious blue flashes emerging from deep space. Since the first lit up astronomers' telescopes in 2018, only 14 of these strange pulses have been detected, making them some of the rarest astronomical events on record. Known as Luminous Fast Blue Optical Transients (LFBOTs), these lights burn faster and up to 100 times brighter than anything else scientists have seen .