In this setting, minibatch gradient estimates are exact (namely, exactly 0) on the set of global minimizers since data can be interpolated exactly.

Jessie Buckley'overwhelmed' to be starring in Oscar-tipped Hamnet The Oscar-tipped Hamnet, starring Jessie Buckley and Paul Mescal, is a film that shows the full range of human emotions, from elation to despair. It begins with a young William Shakespeare falling in love with Agnes (the other name by which the playwright's wife, historically referred to as Anne Hathaway, was known), and goes on to explore their immense grief after tragedy strikes their young family. But while it explores the sad origins of one of Shakespeare's greatest plays, Hamlet, it never portrays Agnes as just the playwright's wife - she is at the heart of the film. She was the full story of what I understand a woman to be, Buckley tells BBC News. And their capacity as women, and as mothers, and as lovers, and as people who have a language unto their own beside gigantic men of literature like Shakespeare.

We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimization tasks with noisy gradient estimates if the noise intensity is proportional to the magnitude of the gradient at every point. Nesterov's method converges at an accelerated rate if the constant of proportionality is below 1, while AGNES accommodates any signal-to-noise ratio. The noise model is motivated by applications in overparametrized machine learning. AGNES requires only two parameters in convex and three in strongly convex minimization tasks, improving on existing methods. We further provide clear geometric interpretations and heuristics for the choice of parameters.

Nanopore sequencing enables real-time long-read DNA sequencing with reads exceeding 10 kilobases, but inherent error rates of 12-15 percent present significant computational challenges for read alignment. The critical seed chaining step must connect exact k-mer matches between reads and reference genomes while filtering spurious matches, yet state-of-the-art methods rely on fixed gap penalty functions unable to adapt to varying genomic contexts including tandem repeats and structural variants. This paper presents RawHash3, a hybrid framework combining graph neural networks with classical dynamic programming for adaptive seed chaining that maintains real-time performance while providing statistical guarantees. We formalize seed chaining as graph learning where seeds constitute nodes with 12-dimensional feature vectors and edges encode 8-dimensional spatial relationships including gap consistency. Our architecture employs three-layer EdgeConv GNN with confidence-based method selection that dynamically switches between learned guidance and algorithmic fallback. Comprehensive evaluation on 1,000 synthetic nanopore reads with 5,200 test seeds demonstrates RawHash3 achieves 99.94 percent precision and 40.07 percent recall, representing statistically significant 25.0 percent relative improvement over baseline with p less than 0.001. The system maintains median inference latency of 1.59ms meeting real-time constraints, while demonstrating superior robustness with 100 percent success rate under 20 percent label corruption versus baseline degradation to 30.3 percent. Cross-validation confirms stability establishing graph neural networks as viable approach for production genomics pipelines.

We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimization tasks with noisy gradient estimates if the noise intensity is proportional to the magnitude of the gradient at every point. Nesterov's method converges at an accelerated rate if the constant of proportionality is below 1, while AGNES accommodates any signal-to-noise ratio. The noise model is motivated by applications in overparametrized machine learning. AGNES requires only two parameters in convex and three in strongly convex minimization tasks, improving on existing methods.

Deep Neural Networks (DNNs) are becoming widespread, particularly in safety-critical areas. One prominent application is image recognition in autonomous driving, where the correct classification of objects, such as traffic signs, is essential for safe driving. Unfortunately, DNNs are prone to backdoors, meaning that they concentrate on attributes of the image that should be irrelevant for their correct classification. Backdoors are integrated into a DNN during training, either with malicious intent (such as a manipulated training process, because of which a yellow sticker always leads to a traffic sign being recognised as a stop sign) or unintentional (such as a rural background leading to any traffic sign being recognised as "animal crossing", because of biased training data). In this paper, we introduce AGNES, a tool to detect backdoors in DNNs for image recognition. We discuss the principle approach on which AGNES is based. Afterwards, we show that our tool performs better than many state-of-the-art methods for multiple relevant case studies.

We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex minimization tasks with noisy gradient estimates if the noise intensity is proportional to the magnitude of the gradient. Nesterov's accelerated gradient descent does not converge under this noise model if the constant of proportionality exceeds one. AGNES fixes this deficiency and provably achieves an accelerated convergence rate no matter how small the signal to noise ratio in the gradient estimate. Empirically, we demonstrate that this is an appropriate model for mini-batch gradients in overparameterized deep learning. Finally, we show that AGNES outperforms stochastic gradient descent with momentum and Nesterov's method in the training of CNNs.

In this work, we consider the problem of clustering partial lexicographic preference trees, intuitive and often compact representations of user preferences over multi-valued attributes. Due to the preordering nature of PLP-trees, we define a variant of Kendall's τ distance metric to be used to compute distances between PLP-trees for clustering. To this end, extending the previous work by Li and Kazimipour (Li and Kazimipour 2018), we propose a polynomial time algorithm PlpDis to compute such distances, and present empirical results comparing it against the brute-force baseline. Based on PlpDis, we use various distance-based clustering methods to cluster PLP-trees learned from a car evaluation dataset. Our experiments show that hierarchical agglomerative nesting (AGNES) is the best choice for clustering PLP-trees, and that the single linkage variant of AGNES is the best fit for clustering large numbers of trees.

This article contains spoilers for the first five episodes of WandaVision. Let's start with the biggest question. What was the deal with "Pietro" at the end of the episode? That was Evan Peters reprising his role as the late Pietro Maximoff, Wanda's brother, but--and here's the twist--it's not the Pietro Maximoff we've seen in the Marvel Cinematic Universe. The MCU's Pietro, played by Aaron Taylor-Johnson, died in Avengers: Age of Ultron.