We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT). While current randomized solvers for least-squares optimization prescribe an embedding dimension at least greater than the data dimension, we show that the embedding dimension can be reduced to the effective dimension of the optimization problem, and still preserve high-probability convergence guarantees. In this regard, we derive sharp matrix deviation inequalities over ellipsoids for both Gaussian and SRHT embeddings. Specifically, we improve on the constant of a classical Gaussian concentration bound whereas, for SRHT embeddings, our deviation inequality involves a novel technical approach. Leveraging these bounds, we are able to design a practical and adaptive algorithm which does not require to know the effective dimension beforehand. Our method starts with an initial embedding dimension equal to 1 and, over iterations, increases the embedding dimension up to the effective one at most. Hence, our algorithm improves the state-of-the-art computational complexity for solving regularized least-squares problems. Further, we show numerically that it outperforms standard iterative solvers such as the conjugate gradient method and its pre-conditioned version on several standard machine learning datasets.

FREE GAMING MONITOR: The Samsung Odyssey G9 49-inch monitor is on sale for 799.99 at Samsung. Save 500 and get a free 27-inch Samsung Odyssey G55C. We thought it was neat that LG were offering up free gaming monitors for Memorial Day, but it turns out that everyone is getting in on the act. The Samsung Odyssey G9 49-inch curved gaming monitor is on sale for 799.99 at Samsung, saving you 500 on list price. That's a strong standalone deal, but this purchase comes with a 27-inch Samsung Odyssey G55C for free.

I just added an entire new feature to my software, including UI and functionality, just by typing four paragraphs of instructions. I have screenshots, and I'll try to make sense of it in this article. I can't tell if we're living in the future or we've just descended to a new plane of hell (or both). Let's take a step back. Google's Jules is the latest in a flood of new coding agents released just this week. I wrote about OpenAI Codex and Microsoft's GitHub Copilot Coding Agent at the beginning of the week, and ZDNET's Webb Wright wrote about Google's Jules. All of these coding agents will perform coding operations on a GitHub repository.

People are already using AI to date (and to flirt), but what about marrying one? In an April 2025 survey of 2,000 Gen Z respondents by AI company Joi AI, eight in 10 said they'd consider marrying an AI partner. AI companions appear to be Joi AI's bread and butter. On its website, you can chat with pre-made characters or make your own. The company calls these connections "AI-lationships."

Just a few weeks left in the school year, warmer temperatures, and weekend barbecues on the calendar mean we've made it out of winter's hibernation. But that doesn't mean sleep should get put on the backburner. Sleep is one of life's basic pillars, and it impacts our mood, health, brain function, and much more. If you've ever had a terrible month of sleep, you know how detrimental a sleep deficit can be on pretty much every aspect of waking hours. Instead of putting the milk in the cupboard on account of a sleepy brain, prioritize sleep this summer by snagging a luxurious new mattress while it's on sale.

Somehow, we've already reached the unofficial start of summer: the Memorial Day 2025 deals are here. Though Memorial Day isn't technically until May 26, plenty of brands kicked off their sales early. Leading the way are mattress deals, followed by home and kitchen deals. Below, we've gathered all the best deals so far ahead of Memorial Day, and will be adding to this list as more deals go live.

PongBot is an artificial intelligence-powered tennis robot. American tennis player Danielle Collins had some choice words for the cameraman during her Internationaux de Strasbourg match against Emma Raducanu on Wednesday afternoon. Collins was in the middle of a changeover when she felt the cameraman's hovering was a bit too close for comfort in the middle of the third and defining set. She got off the bench and made the point clear. Danielle Collins celebrates during her match against Madison Keys in the third round of the women's singles at the 2025 Australian Open at Melbourne Park in Melbourne, Australia, on Jan. 18, 2025.

Localized receptive fields--neurons that are selective for certain contiguous spatiotemporal features of their input--populate early sensory regions of the mammalian brain. Unsupervised learning algorithms that optimize explicit sparsity or independence criteria replicate features of these localized receptive fields, but fail to explain directly how localization arises through learning without efficient coding, as occurs in early layers of deep neural networks and might occur in early sensory regions of biological systems. We consider an alternative model in which localized receptive fields emerge without explicit top-down efficiency constraints--a feedforward neural network trained on a data model inspired by the structure of natural images. Previous work identified the importance of non-Gaussian statistics to localization in this setting but left open questions about the mechanisms driving dynamical emergence. We address these questions by deriving the effective learning dynamics for a single nonlinear neuron, making precise how higher-order statistical properties of the input data drive emergent localization, and we demonstrate that the predictions of these effective dynamics extend to the many-neuron setting. Our analysis provides an alternative explanation for the ubiquity of localization as resulting from the nonlinear dynamics of learning in neural circuits.

The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network. We introduce a semidefinite programming hierarchy to estimate the global and local Lipschitz constant of a multiple layer deep neural network. The novelty is to combine a polynomial lifting for ReLU functions derivatives with a weak generalization of Putinar's positivity certificate. This idea could also apply to other, nearly sparse, polynomial optimization problems in machine learning. We empirically demonstrate that our method provides a trade-off with respect to state of the art linear programming approach, and in some cases we obtain better bounds in less time.

Special cases of problem include the well-known Fermat-Weber problem - or geometric median problem - where z = 1, the mean or centroid where z = 2, and the Minimum Enclosing Ball problem, where z = . We consider these problem in the big data regime. Here, we are interested in sampling as few points as possible such that we can accurately estimate m. More specifically, we consider sublinear algorithms as well as coresets for these problems. Sublinear algorithms have a random query access to the set A and the goal is to minimize the number of queries.