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 .

Neural networks are widely used, yet their analysis and verification remain challenging. In this work, we present a Lean 4 formalization of neural networks, covering both deterministic and stochastic models. We first formalize Hopfield networks, recurrent networks that store patterns as stable states. We prove convergence and the correctness of Hebbian learning, a training rule that updates network parameters to encode patterns, here limited to the case of pairwise-orthogonal patterns. We then consider stochastic networks, where updates are probabilistic and convergence is to a stationary distribution. As a canonical example, we formalize the dynamics of Boltzmann machines and prove their ergodicity, showing convergence to a unique stationary distribution using a new formalization of the Perron-Frobenius theorem.

The creative potential of computers has intrigued researchers for decades. Since the emergence of Generative AI (Gen AI), computer creativity has found many new dimensions and applications. As Gen AI permeates mainstream discourse and usage, researchers are delving into how it can improve and complement what humans do. Creative potential is a highly relevant notion to design practice and research, especially in the initial stages of ideation and conceptualisation. There is scope to improve creative potential in these stages, especially using machine intelligence. We propose a structured ideation session involving inspirational stimuli and utilise Gen AI in delivering this structure to designers through ALIA: Analogical LLM Ideation Agent, a tool for small-group ideation scenarios. The tool is developed by enabling speech based interactions with a Large Language Model (LLM) for inference generation. Inspiration is drawn from the synectic ideation method and the dialectics philosophy to design the optimal stimuli in group ideation. The tool is tested in design ideation sessions to compare the output of the AI-assisted ideation sessions to that of tradi tional ideation sessions. Preliminary findings showcase that participants have rated their ideas better when assisted by ALIA and respond favourably to speech-based interactions.

What does Elon Musk do with all his money? Tesla boss Elon Musk has been one of the world's richest people for several years now, and that wealth recently went stratospheric when he became the first half-trillionaire. Despite this, Musk has insisted he leads a largely unglamorous lifestyle. He said in 2021 that he lived in a Texas home valued at $50,000 (£38,000). His former partner Grimes, with whom he has two children, told Vanity Fair in 2022 he does not live the extravagant life of excess luxury many assume.

Recent advances in reinforcement learning (RL) have significantly enhanced the agentic capabilities of large language models (LLMs). In long-term and multi-turn agent tasks, existing approaches driven solely by outcome rewards often suffer from the problem of sparse supervision. To address the challenge, we propose Tree-based Group Relative Policy Optimization (Tree-GRPO), a grouped agent RL method based on tree search, where each tree node represents the complete agent interaction step. By sharing common prefixes, the tree search sampling increases the number of rollouts achievable within a fixed budget of tokens or tool calls. Moreover, we find that the tree-structured trajectory naturally allows the construction of step-wise process supervised signals even using only the outcome reward. Based on this, Tree-GRPO estimates the grouped relative advantages both on intra-tree and inter-tree levels. Through theoretical analysis, we demonstrate that the objective of intra-tree level group relative policy optimization is equivalent to that of step-level direct preference learning. Experiments across 11 datasets and 3 types of QA tasks demonstrate the superiority of the proposed tree-based RL over the chain-based RL method.Figure 1: Comparison of chain-based and tree-based sampling strategies in LLM multi-turn agent RL. The tree structure brings two major advantages: (i) less rollout budget (both on tokens and tool-calls); (ii) higher performance. Reinforcement Learning (RL) has emerged as a pivotal post-training paradigm for Large Language Models (LLMs), catalyzing the development of several frontier models (DeepSeek-AI Team, 2025; Y ang et al., 2025a; OpenAI, 2024). RL-tuned LLMs trained only with outcome rewards acquire complex reasoning abilities and achieve remarkable gains in single-turn tasks, such as mathematical proof and code generation (Team et al., 2025b; Y u et al., 2025; Chu et al., 2025a; Shao et al., 2024; Xin et al., 2024). This suggests that LLMs can learn not only through static imitation, but also by actively interacting with dynamic environments. Guided by this prospect, recent works have extended this RL paradigm to more complex agent settings involving dynamic, multi-turn interactions (Feng et al., 2025b; Singh et al., 2025; Wang et al., 2025b; Qian et al., 2025; Feng et al., Work done during internship at AMAP, Alibaba Group. Right (Ours): Tree search with nodes corresponding to complete agent step.

As the particle physics community needs higher and higher precisions in order to test our current model of the subatomic world, larger and larger datasets are necessary. With upgrades scheduled for the detectors of colliding-beam experiments around the world, and specifically at the Large Hadron Collider at CERN, more collisions and more complex interactions are expected. This directly implies an increase in data produced and consequently in the computational resources needed to process them. At CERN, the amount of data produced is gargantuan. This is why the data have to be heavily filtered and selected in real time before being permanently stored. This data can then be used to perform physics analyses, in order to expand our current understanding of the universe and improve the Standard Model of physics. This real-time filtering, known as triggering, involves complex processing happening often at frequencies as high as 40 MHz. This thesis contributes to understanding how machine learning models can be efficiently deployed in such environments, in order to maximize throughput and minimize energy consumption. Inevitably, modern hardware designed for such tasks and contemporary algorithms are needed in order to meet the challenges posed by the stringent, high-frequency data rates. In this work, I present our graph neural network-based pipeline, developed for charged particle track reconstruction at the LHCb experiment at CERN. The pipeline was implemented end-to-end inside LHCb's first-level trigger, entirely on GPUs. Its performance was compared against the classical tracking algorithms currently in production at LHCb. The pipeline was also accelerated on the FPGA architecture, and its performance in terms of power consumption and processing speed was compared against the GPU implementation.