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.

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.

Texas high school student Elliston Berry joins'Fox & Friends' to discuss the House's passage of a new bill that criminalizes the sharing of non-consensual intimate images, including content created with artificial intelligence. The Chicago Sun-Times admitted on Tuesday that it published an AI-generated list of books that don't exist for its summer reading list. On Sunday, the publication released a special 64-page section titled "Heat Index: Your Guide to the Best of Summer" which featured a list of 15 recommended books for summer. However, upon further look, it was found that 10 of the 15 books on the list were not real. One example included a book called "Nightshade Market" by Min Jin Lee, which was described as a "riveting tale set in Seoul's underground economy" and follows "three women whose paths intersect in an illegal night market" exploring "class, gender and the shadow economies beneath prosperous societies."

The best results are highlighted by bold. It can be clearly seen that our alternating reverse filtering network performs the best compared with other state-of-the-art methods in all the indexes, indicating the superiority of our proposed method. Images in the last row are the MSE residues between the fused results and the ground truth. Compared with other competing methods, our model has minor spatial and spectral distortions. It can be easily concluded from the observation of MSE maps.

Training regimes based on Maximum Likelihood Estimation (MLE) suffer from known limitations, often leading to poorly generated text sequences. At the root of these limitations is the mismatch between training and inference, i.e. the so-called exposure bias, exacerbated by considering only the reference texts as correct, while in practice several alternative formulations could be as good. Generative Adversarial Networks (GANs) can mitigate those limitations but the discrete nature of text has hindered their application to language generation: the approaches proposed so far, based on Reinforcement Learning, have been shown to underperform MLE. Departing from previous works, we analyze the exploration step in GANs applied to text generation, and show how classical sampling results in unstable training. We propose to consider alternative exploration strategies in a GAN framework that we name ColdGANs, where we force the sampling to be close to the distribution modes to get smoother learning dynamics. For the first time, to the best of our knowledge, the proposed language GANs compare favorably to MLE, and obtain improvements over the state-of-the-art on three generative tasks, namely unconditional text generation, question generation, and abstractive summarization.

Over the past year, veteran software engineer Jay Prakash Thakur has spent his nights and weekends prototyping AI agents that could, in the near future, order meals and engineer mobile apps almost entirely on their own. His agents, while surprisingly capable, have also exposed new legal questions that await companies trying to capitalize on Silicon Valley's hottest new technology. Agents are AI programs that can act mostly independently, allowing companies to automate tasks such as answering customer questions or paying invoices. While ChatGPT and similar chatbots can draft emails or analyze bills upon request, Microsoft and other tech giants expect that agents will tackle more complex functions--and most importantly, do it with little human oversight. The tech industry's most ambitious plans involve multi-agent systems, with dozens of agents someday teaming up to replace entire workforces.

During the 33rd International Joint Conference on Artificial Intelligence (IJCAI), held in Jeju, I had the opportunity to meet with one of the keynote speakers, Gillian Hadfield. We spoke about her interdisciplinary research, career trajectory, path into AI alignment, law, and general thoughts on AI systems. Transcript: Note: the transcript has been lightly edited for clarity. This is an interview with Professor Gillian Hadfield who was a keynote speaker at IJCAI 2024. She gave a very insightful talk about normative infrastructures and how they can guide our search for AI alignment. Kumar Kshitij Patel (KKP): Could you talk a bit about your background and career trajectory? I want our readers to understand how much interdisciplinary work you've done over the years. Gillian Hadfield (GH): I did a PhD in economics and a law degree, a JD, at Stanford, originally motivated by wanting to think about the big questions about the world. So I read John Rawls' theory of justice when I was an undergraduate, and those are the big questions: how do we organize the world and just institutions, but I was very interested in using more formal methods and social scientific approaches. That's why I decided to do that joint degree. So, this is in the 1980s, and in the early days of starting to use a lot of game theory. I studied information theory, a student of Canaro and Paul Milgram at the economics department at Stanford. I did work on contract theory, bargaining theory, but I was still very interested in going to law school, not to practice law, but to learn about legal institutions and how those work. I was a member of this emerging area of law and economics early in my career, which of course, was interdisciplinary, using economics to think about law and legal institutions.