Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite variance, as the relevant limiting distributions depend on unknown nuisance parameters. In this paper, we develop an efficient, model-agnostic methodology for constructing confidence regions from SGD trajectories that applies in both finite- and infinite-variance regimes. The procedure is based on a joint weak convergence result for the Polyak-Ruppert averaged estimator and an empirical second-moment normalizer constructed from stochastic gradients along the SGD trajectory. This joint limit yields a self-normalized statistic in which the leading tail-dependent scaling terms cancel. We then use a subsampling calibration scheme to estimate the relevant critical values, avoiding explicit estimation of tail indices, slowly varying functions, or stable-law parameters. The resulting confidence regions are straightforward to implement and are asymptotically valid under both the finite- and infinite-second-moment regimes. Simulation studies show reliable coverage in various settings, supporting the proposed method as a practical tool for uncertainty quantification in stochastic optimization.

Frontier LLMs now perform strongly across a wide range of physics evaluations, but it is hard to disentangle genuine reasoning from recall of established science. We introduce DiscoverPhysics, an interactive benchmark that asks a LLM agent to discover the laws of motion of a simulated world whose physics deliberately deviates from our own. We construct 22 worlds governed by, among others, screened and fractional-power gravity, multi-species couplings, hidden dark-matter-like particles, non-coordinate-free physics, and time-varying interactions. Each world is generated on demand by an N-body simulator, for which the agent proposes several rounds of experiments, observes raw trajectory data, and ultimately submits both a natural-language explanation of the world's physics and a Python implementation of the inferred law. Because solving a world requires the agent to design informative experiments and revise its hypotheses, the benchmark probes long-horizon reasoning over an experimental history. We evaluate submissions along two complementary axes: trajectory MSE on held-out particles and an LLM-judged explanation score following an expert-written rubric assessing conceptual understanding of each world. Across eleven frontier models, we find that the strongest agents pass only half of the worlds and consistently fail on those where latent structure must be uncovered. Open-source models lag substantially behind commercial models, both in their ability to design informative experiments and in extracting conclusions from the data. We further find that good predictive accuracy does not guarantee high explanation quality and that conceptual understanding depends on hypothesis refinement through well-chosen experiments.

Bayesian optimal experimental design (BOED) selects experiments to maximize information gain about model parameters. However, in decision-critical settings, reducing parameter uncertainty does not necessarily improve downstream decisions, as only specific parameter directions relevant to the objective truly matter. We propose GoBOED, a goal-driven BOED framework that directly optimizes experimental designs for a specified decision-making objective. GoBOED combines an amortized variational posterior surrogate with a differentiable convex decision layer, enabling gradient-based design optimization that is fully decision-focused. We theoretically show that GoBOED gradients are insensitive to parameter directions irrelevant to the decision objective, providing a formal justification for why goal-driven design achieves equivalent decision quality over a wider set of experimental designs than information-gain maximization. Empirically, across source localization, epidemic management, and pharmacokinetic control, GoBOED identifies designs that better align with downstream decision objectives and reveals that near-optimal design windows are substantially wider than those predicted by goal-agnostic BOED approaches.

Notre Dame's Josh Yago delivers Memorial Day salute during anthem before lacrosse championship game Dak Prescott reunites with ex-fiancée Sarah Jane Ramos to celebrate daughter's first birthday Celtics guard Jaylen Brown challenges ESPN's Stephen A Smith to a debate at Harvard or MIT Wyndham Clark adds to his funky resume, TPC Craig Ranch slander and LIV Golf's pitch to new investors Unearthed fan video shows who Kyle Busch really was, NASCAR's darkest hour & Bubba Wallace's'Rowdy' story California mom speaks with compassion but brutal honesty about presence of trans athlete in daughter's sport Curt Cignetti jokes he had to'coach the hell out' of undefeated Hoosiers to be Indy 500 pace car driver A screenshot has WNBA fans asking: did a player endorse a threat toward Caitlin Clark? MLB reporter Tricia Whitaker hit with line drive during Orioles' game Defense expert argues Iran has never been'so isolated' Joey Jones calls out Dem candidate Platner for'hiding behind the Purple Hearts' of fellow vets Trump doesn't want Iran to become his Afghanistan: Mike Sarraille Any Iran deal will be judged by'how much it cost' to secure, ex-CIA station chief says Dr Rebecca Grant: Iran has'no place to go,' will have to sign a deal Pope Leo XIV calls for AI to be'disarmed' in critical warning about emerging tech Kyle Busch's family reveals NASCAR champion died from severe pneumonia that led to sepsis NEW details emerge on suspected White House gunman's prior arrests OutKick-Sports Lincoln Riley claims USC was'snaps away' from the playoff, says he's a better coach now than when at Oklahoma Lincoln Riley joins Colin Cowherd to discuss USC's schedule and their number one recruiting class, and the development of QB Jayden Maiava. Lincoln Riley's tenure as head coach of the USC Trojans hasn't been smooth sailing. When he took over ahead of the 2022 season, expectations were high that a coach with his track record would bring the Trojans back to their heyday. While with the Oklahoma Sooners, he went 55-10 and 33-7 in conference, coached in four New Year's Six games, and won 12 games three consecutive seasons.

The Israeli military says it has begun a wave of strikes across Lebanon following an announcement by Prime Minister Benjamin Netanyahu that his country will intensify its attacks on Hezbollah. The Israel Defense Forces (IDF) said it had launched strikes against Hezbollah sites in the Bekaa Valley in the east of Lebanon and additional areas across the country. It followed a video statement on Monday evening in which Netanyahu said Israel was at war with Hezbollah and that he had given the military instructions to deal them a crushing blow. Earlier this month Lebanon and Israel agreed to extend a 45-day ceasefire, though some fighting has continued. There will be fears in Beirut that these latest Israeli attacks will widen to include Lebanon's capital city.

More than 1.5m foreign pilgrims begin Hajj despite Iran war fears Muslims have begun the annual Hajj pilgrimage in Saudi Arabia against the backdrop of a region deeply shaken by the Iran war. Saudi authorities said last week that some 1.51 million pilgrims had arrived from outside the kingdom. That is 11,000 more than last year, despite concerns in the region about a resumption of the three-month-old conflict between the US, Israel and Iran. Before a fragile ceasefire took effect last month, Iran launched waves of missile and drone attacks on Saudi Arabia and its Gulf neighbours in retaliation for US and Israeli air strikes. Two civilians living in the central city of al-Kharj were killed in an Iranian attack on 8 March, along with a US service member stationed at the nearby Prince Sultan Air Base.

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG . You have a credit freeze; it still isn't enough Turning 65? Month-by-month plan to protect yourself China's AI growth is about'economic and political leverage,' Rep Hinson says Expert warns'red-green-green alliance' helping China gain AI edge AI's impact on jobs, economy debated as youth express growing fears Jury dismisses Elon Musk's lawsuit against OpenAI and Sam Altman China does not'innovate,' they'replicate': Former DHS spokeswoman Trump to press Xi to'open up' China as tech CEOs join key summit CIA calls COVID whistleblower hearing'political theater' in new statement How scammers use military records, VA data and benefit details to target veterans. Kurt'The CyberGuy' Knutsson breaks down the'perfect storm' for scammers to prey on Americans and how to protect yourself.

LaGuardia Airport's Terminal B now features an AI hologram concierge that answers traveler questions and provides step-by-step directions using real-time maps.

The Pope unveiled the Vatican's new encyclical, "Magnifica Humanitas," warning that AI risks becoming a tool of "domination, exclusion and death" without moral limits from governments.

Russia has threatened to launch a fresh wave of systematic strikes against Kyiv, days after carrying out one of its largest attacks on the Ukrainian capital since the start of the war. The new strikes will target decision-making centres and command posts, alongside drone manufacturing facilities in the city, Russia's foreign ministry said in a statement. Moscow has called for foreign nationals and diplomats to leave Kyiv as soon as possible and warned citizens to stay away from administrative and military buildings. Large-scale Russian strikes on Saturday night killed four and injured about 100 people in Kyiv and other areas, Ukrainian President Volodymyr Zelensky said. Moscow said that barrage and threatened further strikes were in response to what it claims was a deliberate Ukrainian attack on a student dormitory in the town of Starobilsk on Friday, in which Russian officials said 21 people were killed.