World economic and finance chiefs want an off-ramp from the worst global trade crisis in a century. Washington makes for a turbulent backdrop to the spring meetings of the International Monetary Fund and World Bank, headquartered in the U.S. capital as anchors of America's economic and financial clout. President Donald Trump's tariff war hasn't just roiled markets and raised recession fears: it's also called into question U.S. economic and security leadership -- a pillar of the post-World War II global order -- like never before. The stage is set for "one of the most stark and dramatic meetings I can think of in recent history," says Josh Lipsky, senior director of the GeoEconomics Center at the Atlantic Council and former IMF adviser. "You have at this moment a deep challenge to the multilateral rules-based system which the U.S. helped build."

At least three blasts were heard in the Russian-controlled Donetsk region in eastern Ukraine amid an Easter ceasefire declared by Moscow, Russian state news agency TASS reported, citing local "operative services." Ukraine's forces reported nearly 3,000 violations of Russia's own ceasefire pledge, Ukrainian President Volodymyr Zelenskyy said, adding that Kyiv's forces were instructed to mirror the Russian Army's actions. Russia's Ministry of Defence said Ukraine had broken the Easter ceasefire declared by the Kremlin more than a thousand times, claiming that Ukrainian forces shot at Russian positions 444 times. The ministry also said Kremlin forces encountered more than 900 Ukrainian drone attacks during this time. At least three blasts were heard in the Russian-controlled Donetsk region in eastern Ukraine amid an Easter ceasefire declared by Moscow, Russian state news agency TASS reported, citing local "operative services."

HBO's The Last of Us showed viewers in season one that it would lean heavily on the source video games for major plot points and general direction of the season while expanding on the universe, and season two has followed that to the most extreme end possible. Episode two sees Tommy and Maria lead the town of Jackson Hole against a massive wave of Infected, the likes of which we haven't seen in the show (or video games) yet. This was a complete invention for the show, one that gives the episode Game of Thrones vibes, or calls to mind a battle like the siege of Helm's Deep in Lord of the Rings: The Two Towers. It's epic in scale, with the overmatched defenders showing their skill and bravery against overwhelming odds; there is loss and pain but the good guys eventually triumph. That mass-scale battle is paired with the most intimate and brutal violence we've seen in the entire series so far, as Joel's actions finally catch up with him.

On a misty Saturday afternoon in Shenzhen's Central Park, a gaggle of teenage girls are sheltering from the drizzle under a concrete canopy. With their bags of crisps piled high in front of them, they crowd around a couple of smartphones to sing along to Mandopop ballads. The sound of their laughter rings out across the surrounding lawn – until it is pierced by a mechanical buzzing sound. A few metres away from the impromptu karaoke session is an "airdrop cabinet", one of more than 40 in Shenzhen that is operated by Meituan, China's biggest food delivery platform. Hungry park-goers can order anything from rice noodles to Subway sandwiches to bubble tea.

Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly convex. Existing methods often face limitations, including slow convergence rates or reliance on double-loop algorithmic designs. To overcome these challenges, we introduce a novel single-loop penalty-based stochastic algorithm. Following the classical exact penalty method, our approach employs a {\bf hinge-based penalty}, which permits the use of a constant penalty parameter, enabling us to achieve a {\bf state-of-the-art complexity} for finding an approximate Karush-Kuhn-Tucker (KKT) solution. We further extend our algorithm to address finite-sum coupled compositional objectives, which are prevalent in artificial intelligence applications, establishing improved complexity over existing approaches. Finally, we validate our method through experiments on fair learning with receiver operating characteristic (ROC) fairness constraints and continual learning with non-forgetting constraints.

Two major tasks in applications of hidden Markov models are to (i) com pute distributions of summary statistics of the hidden state sequence, and (ii) decode the hidden state sequence. We describe finite Markov chain imbedding (FMCI) and hybrid decoding to solve each of t hese two tasks. In the first part of our paper we use FMCI to compute posterior distributions o f summary statistics such as the number of visits to a hidden state, the total time spent in a hidden st ate, the dwell time in a hidden state, and the longest run length. We use simulations from the hidde n state sequence, conditional on the observed sequence, to establish the FMCI framework. In the second part of our paper we apply hybrid segmentation for improved decoding of a HMM. We demonstra te that hybrid decoding shows increased performance compared to Viterbi or Posterior decodin g (often also referred to as global or local decoding), and we introduce a novel procedure for choosing the tuning parameter in the hybrid procedure. Furthermore, we provide an alternative derivation of the hybrid loss function based on weighted geometric means. We demonstrate and apply FMCI and hyb rid decoding on various classical data sets, and supply accompanying code for reproducibility. Key words: Artemis analysis, decoding, finite Markov chain imbedding, hidden Mar kov model, hybrid decoding, pattern distributions.

We study whether and how the choice of optimization algorithm can impact group fairness in deep neural networks. Through stochastic differential equation analysis of optimization dynamics in an analytically tractable setup, we demonstrate that the choice of optimization algorithm indeed influences fairness outcomes, particularly under severe imbalance. Furthermore, we show that when comparing two categories of optimizers, adaptive methods and stochastic methods, RMSProp (from the adaptive category) has a higher likelihood of converging to fairer minima than SGD (from the stochastic category). Building on this insight, we derive two new theoretical guarantees showing that, under appropriate conditions, RMSProp exhibits fairer parameter updates and improved fairness in a single optimization step compared to SGD. We then validate these findings through extensive experiments on three publicly available datasets, namely CelebA, FairFace, and MS-COCO, across different tasks as facial expression recognition, gender classification, and multi-label classification, using various backbones. Considering multiple fairness definitions including equalized odds, equal opportunity, and demographic parity, adaptive optimizers like RMSProp and Adam consistently outperform SGD in terms of group fairness, while maintaining comparable predictive accuracy. Our results highlight the role of adaptive updates as a crucial yet overlooked mechanism for promoting fair outcomes.

We study the complexity of learning $k$-mixtures of Gaussians ($k$-GMMs) on $\mathbb{R}^d$. This task is known to have complexity $d^{\Omega(k)}$ in full generality. To circumvent this exponential lower bound on the number of components, research has focused on learning families of GMMs satisfying additional structural properties. A natural assumption posits that the component weights are not exponentially small and that the components have the same unknown covariance. Recent work gave a $d^{O(\log(1/w_{\min}))}$-time algorithm for this class of GMMs, where $w_{\min}$ is the minimum weight. Our first main result is a Statistical Query (SQ) lower bound showing that this quasi-polynomial upper bound is essentially best possible, even for the special case of uniform weights. Specifically, we show that it is SQ-hard to distinguish between such a mixture and the standard Gaussian. We further explore how the distribution of weights affects the complexity of this task. Our second main result is a quasi-polynomial upper bound for the aforementioned testing task when most of the weights are uniform while a small fraction of the weights are potentially arbitrary.

We study the algorithmic task of learning Boolean disjunctions in the distribution-free agnostic PAC model. The best known agnostic learner for the class of disjunctions over $\{0, 1\}^n$ is the $L_1$-polynomial regression algorithm, achieving complexity $2^{\tilde{O}(n^{1/2})}$. This complexity bound is known to be nearly best possible within the class of Correlational Statistical Query (CSQ) algorithms. In this work, we develop an agnostic learner for this concept class with complexity $2^{\tilde{O}(n^{1/3})}$. Our algorithm can be implemented in the Statistical Query (SQ) model, providing the first separation between the SQ and CSQ models in distribution-free agnostic learning.

We propose a scalable, approximate inference hypernetwork framework for a general model of history-dependent processes. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of internal states together with a trainable observation model subcomponent. The posterior distribution corresponding to the data model parameters (weights and biases) follows a stochastic differential equation with a drift term related to the score of the posterior that is learned jointly with the data model parameters. This Langevin sampling approach offers flexibility in balancing the computational budget between the evaluation cost of the data model and the approximation of the posterior density of its parameters. We demonstrate performance of the hypernetwork on chemical reaction and material physics data and compare it to mean-field variational inference.