We study stopping rules for stochastic gradient descent (SGD) for convex optimization from the perspective of anytime-valid confidence sequences. Classical analyses of SGD provide convergence guarantees in expectation or at a fixed horizon, but offer no statistically valid way to assess, at an arbitrary time, how close the current iterate is to the optimum. We develop an anytime-valid, data-dependent upper confidence sequence for the weighted average suboptimality of projected SGD, constructed via nonnegative supermartingales and requiring no smoothness or strong convexity. This confidence sequence yields a simple stopping rule that is provably $\varepsilon$-optimal with probability at least $1-α$, with explicit bounds on the stopping time under standard stochastic approximation stepsizes. To the best of our knowledge, these are the first rigorous, time-uniform performance guarantees and finite-time $\varepsilon$-optimality certificates for projected SGD with general convex objectives, based solely on observable trajectory quantities.

Learned time-series models, whether continuous-or discrete-time, are widely used to forecast the states of a dynamical system. Such models generate multi-step forecasts either directly, by predicting the full horizon at once, or iteratively, by feeding back their own predictions at each step. In both cases, the multi-step forecasts are prone to errors. To address this, we propose a Predictor-Corrector mechanism where the Predictor is any learned time-series model and the Corrector is a neural controlled differential equation. The Predictor forecasts, and the Corrector predicts the errors of the forecasts. Adding these errors to the forecasts improves forecast performance. The proposed Corrector works with irregularly sampled time series and continuous-and discrete-time Predictors. Additionally, we introduce two regularization strategies to improve the extrapolation performance of the Corrector with accelerated training. We evaluate our Corrector with diverse Predictors, e.g., neural ordinary differential equations, Contiformer, and DLinear, on synthetic, physics simulation, and real-world forecasting datasets. The experiments demonstrate that the Predictor-Corrector mechanism consistently improves the performance compared to Predictor alone. Learning time-series models from such datasets has applications ranging from energy demand forecasting, traffic and mobility prediction, weather prediction, anomaly detection, and decision-making in robotics (Zeng et al., 2022; Li et al., 2017; Stankeviciute et al., 2021; Xu et al., 2021; Chua et al., 2018). Several works focused on learning time-series models from data. There are at least two ways to train such models. Early studies focused on training the model to predict one step ahead (Basharat & Shah, 2009; Khansari-Zadeh & Billard, 2011).

Recent advances using Kernel Logistic Regression (KLR) have demonstrated that learning can sculpt these landscapes to achieve capacities far exceeding classical limits [1-3]. Our previous phenomenological analysis identified a Ridge of Optimization where stability is maximized via a mechanism we termed Spectral Concentration, defined as a state where the weight spectrum exhibits a sharp hierarchy [4]. However, a deeper question remains: Why does the learning dynamics self-organize into this specific spectral state? Why does the system operate at the brink of instability? T o answer these questions, we must look beyond the Euclidean geometry of the weight parameters and consider the intrinsic geometry of the probability distributions they represent. This is the domain of Information Geometry [5]. In this work, we reinterpret the KLR Hopfield network as a statistical manifold equipped with a Fisher-Rao metric.

Conformal prediction (CP) provides distribution-free, finite-sample coverage guarantees but critically relies on exchangeability, a condition often violated under distribution shift. We study the robustness of split conformal prediction under adversarial perturbations at test time, focusing on both coverage validity and the resulting prediction set size. Our theoretical analysis characterizes how the strength of adversarial perturbations during calibration affects coverage guarantees under adversarial test conditions. We further examine the impact of adversarial training at the model-training stage. Extensive experiments support our theory: (i) Prediction coverage varies monotonically with the calibration-time attack strength, enabling the use of nonzero calibration-time attack to predictably control coverage under adversarial tests; (ii) target coverage can hold over a range of test-time attacks: with a suitable calibration attack, coverage stays within any chosen tolerance band across a contiguous set of perturbation levels; and (iii) adversarial training at the training stage produces tighter prediction sets that retain high informativeness.

Novo Nordisk's semaglutide will soon be available in a daily pill Americans can take for weight loss. The US Food and Drug Administration today approved a pill version of the blockbuster anti-obesity drug Wegovy. Made by Novo Nordisk, the pill is taken once a day. The company's original version of Wegovy is a weekly injection. Both drugs contain the same active ingredient, semaglutide.

Vince Zampella, who co-created the widely-popular video game Call of Duty, has died in a single-vehicle Ferrari crash in California, aged 55. Zampella's death was confirmed by Electronic Arts, which owns Respawn Entertainment, a game studio he co-founded. This is an unimaginable loss, and our hearts are with Vince's family, his loved ones, and all those touched by his work, a spokesperson for Electronic Arts told the BBC. Officials said the person on the vehicle's passenger seat was ejected while the driver remained trapped. It is unclear if Zampella was driving the car.

One of WIRED's Favorite Chef Knives Is Free With a HelloFresh Membership The 8-inch Zwilling Four Star chef's knife is an excellent carbon steel blade that retails around $100. It's free with some food. I don't know if a good knife is hard to find. But they usually cost at least a hundred dollars, so it's worth noting when HelloFresh is offering one of WIRED's favorite chef's knives for the low, low price of free. This is the time of year when a lot of the best meal kit deals start to happen. And so if you hang around for three weeks of meal delivery service from HelloFresh, your third box will include delivery of a Zwilling Four Star 8-inch chef knife, a $100-plus carbon steel blade that WIRED reviewer Molly Higgins lists as her runner-up favorite blade overall--and her favorite carbon-steel for most people.

Vince Zampella, the co-creator of the Call of Duty video game series, has died aged 55. The head of the video game developer Respawn Entertainment and the co-founder of Infinity Ward was killed in a car crash in California, NBC Los Angeles reported . Zampella led the creation of the bestselling video game series Call of Duty at Infinity Ward, and at his various studios he was involved in several highly successful game series from Medal of Honor to Titanfall. He is reported to have died in a single-car accident on the Angeles Crest Highway, which was reported to the California highway patrol at 12.45pm on Sunday. The vehicle's driver died at the scene, and a passenger died later in hospital.

A blackout in San Francisco revealed a new way for robotaxis to go wrong. Waymo's self-driving robotaxis can successfully nail a tricky left turn, weave through lanes to drop you off at the airport, and safely pass a U-Haul that's idling in the middle of the street. But during a blackout, they apparently turn into four-wheel bricks. On Saturday, when a major power outage in San Francisco knocked out traffic signals, many Waymo vehicles didn't pull over to the side of the road or seek out a parking space. Nor did they treat intersections as four-way stops, as a human would have. Instead, they just sat there with their hazard lights on, like a student driver freezing up before their big parallel-parking test.

A campaigner said: 'This stolen music is almost certain to end up training AI models.' A campaigner said: 'This stolen music is almost certain to end up training AI models.' Platform with 700m users says it is investigating after Anna's Archive claims to have scraped tracks and metadata An activist group has claimed to have scraped millions of tracks from Spotify and is preparing to release them online. Observers said the apparent leak could boost AI companies looking for material to develop their technology. A group called Anna's Archive said it had scraped 86m music files from Spotify and 256m rows of metadata such as artist and album names.