A Buddhist temple in Seoul introduced South Korea's first humanoid robot monk ahead of celebrations for Buddha's birthday. The robot, named Gabi, bowed, prayed and pledged to devote itself to Buddhism during an ordination ceremony at Jogye Temple. US court releases alleged Jeffrey Epstein'suicide note' Iran's stance on US war negotiations explained

We decompose the Kullback--Leibler generalization error (GE) -- the expected KL divergence from the data distribution to the trained model -- of unsupervised learning into three non-negative components: model error, data bias, and variance. The decomposition is exact for any e-flat model class and follows from two identities of information geometry: the generalized Pythagorean theorem and a dual e-mixture variance identity. As an analytically tractable demonstration, we apply the framework to $ε$-PCA, a regularized principal component analysis in which the empirical covariance is truncated at rank $N_K$ and discarded directions are pinned at a fixed noise floor $ε$. Although rank-constrained $ε$-PCA is not itself e-flat, it admits a technical reformulation with the same total GE on isotropic Gaussian data, under which each component of the decomposition takes closed form. The optimal rank emerges as the cutoff $λ_{\mathrm{cut}}^{*} = ε$ -- the model retains exactly those empirical eigenvalues exceeding the noise floor -- with the cutoff reflecting a marginal-rate balance between model-error gain and data-bias cost. A boundary comparison further yields a three-regime phase diagram -- retain-all, interior, and collapse -- separated by the lower Marchenko--Pastur edge and an analytically computable collapse threshold $ε_{*}(α)$, where $α$ is the dimension-to-sample-size ratio. All claims are verified numerically.

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max characterization of key statistics, enabling approximation of the mean $μ_{\hatθ}$ and covariance $C_{\hatθ}$ of the ERM estimator $\hatθ$. Specifically, under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that for a test covariate $x$ independent of the training data, the projection $\hatθ^\top x$ approximately follows the convolution of the (generally non-Gaussian) distribution of $μ_{\hatθ}^\top x$ with an independent centered Gaussian variable of variance $\text{Tr}(C_{\hatθ}\mathbb{E}[xx^\top])$. This result clarifies the scope and limits of Gaussian universality for ERMs. Additionally, we prove that any $\mathcal{C}^2$ regularizer is asymptotically equivalent to a quadratic form determined solely by its Hessian at zero and gradient at $μ_{\hatθ}$. Numerical simulations across diverse losses and models are provided to validate our theoretical predictions and qualitative insights.

Spring Break travelers facing TSA hell fume as it's revealed why only certain airports crippled by shutdown Chappell Roan apologises to Jude Law's daughter as she insists she did not ask security guard to approach her and says'I do not hate fans of my music or children' Democratic enclave tears down tent city in its latest'whack-a-mole' move as homeless crisis laid bare Infertile influencer Clavicular's dark fetish is far more alarming than anyone feared, claim high school enemies as they leak unrecognizable photos and humiliating secrets I was a producer on The Bachelor. I've seen what happens when the cameras stop rolling: JANA HOCKING reveals the humiliating crisis talks, sex secrets and forbidden relationships Under fire again: Embattled sheriff in Nancy Guthrie case was accused of'assaulting deputy'...as decades of complaints emerge My daughters begged me not to send them back to their mother... Inside Enya's off-grid life in a £2.5M remote castle with 12 cats and no partner or children after turning her back on fame and admitting she's'dark and difficult' to be around'He just didn't protect him': Insiders reveal REAL reason Justin Bieber and Usher's secret feud hit'boiling point' at Oscars MORE bad news for Austin's housing market as Texan city leads in plummeting prices Hawaii's worst flooding in 20 years caused over $1BILLION in damage as crews desperately search for woman swept away in deluge Princess Beatrice puts on united front with husband Edo during lunch out amid fears her'marriage is in trouble' in wake of Epstein scandal Friends reveal fears Princess Beatrice's'marriage is in trouble' in wake of Epstein scandal. I was the only one JFK Jr and Carolyn Bessette trusted when they burdened me with an extraordinarily intimate secret. Iran war live: Trump threatens to'obliterate' Tehran's power plants if Strait of Hormuz does not'fully open' in next 48 hours Trump's White House ballroom architect'has totally baffled colleagues' by taking on controversial project Oscars PANIC as ratings hemorrhage: Insiders reveal'existential crisis' inside the Academy... and why Hollywood's biggest night was a'big fat dud' My husband's filthy habit is so revolting I don't even want to kiss him: DEAR JANE READ MORE: Britain's best supermarket hot cross buns revealed There's nothing quite like a toasted hot cross bun slathered in butter. Now, experts have suggested an unusual way to make them taste even better - by slicing them into thirds.

Furious Trump issues threat to Iran demanding Strait of Hormuz is'FULLY OPENED' in hours or America will'obliterate their power plants'... and there's already a key target in sight Nancy Guthrie's desperate family releases emotional new statement as they plead for'renewed attention to our mom's case' 50 days after she vanished Chappell Roan accused of'leaving Jude Law's 11-year-old daughter in tears and using security guard to threaten her' I was the only one JFK Jr and Carolyn Bessette trusted when they burdened me with an extraordinarily intimate secret. How Iran's ruthless enforcers use rape to crush dissent: Brutal sex attacks on victims as young as 12 used to strike fear into protesters, rights groups reveal amid fury over sickening nurse gang rape Shia LaBeouf suffers public meltdown in Rome as he's caught screaming'f*** off' at woman... after battery arrests'He just didn't protect him': Insiders reveal REAL reason Justin Bieber and Usher's secret feud hit'boiling point' at Oscars I thought I was losing my mind... then doctors told me I had'exploding head syndrome'. America is about to be torn apart by a financial tsunami - and it's not just an oil crisis to fear. Denise Richards's plastic surgeon reveals stunning before-and-after photos of her facelift'Get the f*** out of my life,' JFK Jr screamed at Carolyn Bessette... what she cruelly told friends about his manhood... the cuckolding, cocaine - and moment that sent her truly psychotic: MAUREEN CALLAHAN has the untold REAL story'Meteorite' CRASHES into woman's home as residents are left terrified by massive sonic boom YouTuber who exposed Somali'fraudsters' in bombshell investigation reveals terrifying threats from left-wing activists... as he begs for cash to help pay for security Sabine Getty's gown gets STUCK in escalator at Oscars during dramatic moment Charlie's Angels bombshell Jaclyn Smith looks nowhere near her 80 years in Beverly Hills... see her now Florida's Olivier Rioux, tallest player in college basketball history, dwarfs 6ft8 March Madness rival as defending champs roll to win RFK Jr reveals his strange daily routine... including not eating until noon and meditating with'dead people' Iran ballistic missile hits Israeli city in terrifying strike near top-secret facility that is key to country's atomic weapons program Ted Cruz proposes dramatic change to ICE funding in repsonse to'extreme and unreasonable' Democrats in effort to end bitter standoff causing airport chaos And now it turns out you've probably been doing your laundry wrong this entire time. Experts at AO.com have revealed why you should never close the washing machine door after a wash.

Furious Trump issues chilling threat to Iran demanding Strait of Hormuz is'FULLY OPENED' in hours or America will'obliterate their power plants'... and there's already a key target in sight Chappell Roan accused of'leaving Jude Law's 11-year-old daughter in tears and using security guard to threaten her' I was the only one JFK Jr and Carolyn Bessette trusted when they burdened me with an extraordinarily intimate secret. How Iran's ruthless enforcers use rape to crush dissent: Brutal sex attacks on victims as young as 12 used to strike fear into protesters, rights groups reveal amid fury over sickening nurse gang rape Shia LaBeouf suffers public meltdown in Rome as he's caught screaming'f*** off' at woman... after battery arrests'He just didn't protect him': Insiders reveal REAL reason Justin Bieber and Usher's secret feud hit'boiling point' at Oscars Mom-to-be finds out cop who got her pregnant has HIV after baby mama's text... as he is charged with felony I thought I was losing my mind... then doctors told me I had'exploding head syndrome'. America is about to be torn apart by a financial tsunami - and it's not just an oil crisis to fear. Denise Richards's plastic surgeon reveals stunning before-and-after photos of her facelift'Get the f*** out of my life,' JFK Jr screamed at Carolyn Bessette... what she cruelly told friends about his manhood... the cuckolding, cocaine - and moment that sent her truly psychotic: MAUREEN CALLAHAN has the untold REAL story Florida's Olivier Rioux, tallest player in college basketball history, dwarfs 6ft8 March Madness rival as defending champs roll to win YouTuber who exposed Somali'fraudsters' in bombshell investigation reveals terrifying threats from left-wing activists... as he begs for cash to help pay for security Charlie's Angels bombshell Jaclyn Smith looks nowhere near her 80 years in Beverly Hills... see her now Fury over plan for 110 homes near Yosemite Park that will tower up to 24ft and'cause road chaos' Gisele Pelicot tells how she thought she was dying from a brain tumor... then she discovered the horrific truth of her husband's abuse Iran ballistic missile hits Israeli city in terrifying strike near top-secret facility that is key to country's atomic weapons program Couple murdered outside Walgreens near golf's Players Championship were killed by jealous ex, says sheriff As the threat of a nuclear war intensifies, the terrifying reality of what could happen after the bombs explode may cause more fear than the initial cataclysm. For decades, worst-case scenarios have projected that tens of millions could perish within minutes as nuclear warheads struck major metropolitan areas such as New York, Washington, Chicago and Los Angeles .

The return of BTS is a big deal. In case you were in any doubt, just look at the frenzy surrounding the South Koreans' comeback. On Saturday, the band will kick off a sold-out, 82-date world tour with a free concert in Seoul, which is expected to be attended by more than 250,000 in-person fans and will be live-streamed on Netflix to more than 190 countries. When the tour wraps up in 2027, BTS are expected to have generated more than $1billion in revenue. Some more outlandish estimates suggest they will eclipse the $2billion haul of Taylor Swift's Eras tour.

We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $\mathbb{Q}$ and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki--Vlah, Bujanović--Kazalicki--Novak, and Pozdnyakov, we observe high accuracy predictions for the analytic rank across a range of conductors. We interpret the prediction using saliency curves and explore the interesting interplay between murmurations and Mestre--Nagao sums, the details of which vary with the conductor and the (predicted) rank.

I t was March 2016, and at the Four Seasons Hotel in Seoul, the world was gathered to watch the culmination of a battle 2,500 years in the making. On one side was the South Korean Lee Se-dol, the second-highest ranking Go player in the world. On the other was AlphaGo - a computer program developed by London-based artificial intelligence research company DeepMind. "Chess is the greatest game mankind has invented," game designer Alex Randolph once said. "Go is the greatest game mankind has discovered."

U.S. President Donald Trump speaks to reporters aboard Air Force One on a flight to Washington on Sunday. SAN FRANCISCO - U.S. President Donald Trump on Sunday accused Iran of using artificial intelligence as a "disinformation weapon" to misrepresent its wartime successes and support. "AI can be very dangerous, we have to be very careful with it," Trump said to reporters on Air Force One shortly after he made a post on his Truth Social platform where he accused Western media outlets without evidence of "close coordination" with Iran to spread AI-generated fake news." The comments come amid renewed tensions between the Federal Communications Commission and broadcasters after Trump took aim at media coverage of the U.S. and Israel's war with Iran. FCC Chairman Brendan Carr on Saturday threatened to pull licenses of broadcasters who did not "correct course" on their coverage.