Bayesian optimization (BO) is an effective technique for black-box optimization. However, its applicability is typically limited to moderate-budget problems due to the cubic complexity in computing the Gaussian process (GP) surrogate model. In large-budget scenarios, directly employing the standard GP model faces significant challenges in computational time and resource requirements. In this paper, we propose a novel approach, gradient-based sample selection Bayesian Optimization (GSSBO), to enhance the computational efficiency of BO. The GP model is constructed on a selected set of samples instead of the whole dataset. These samples are selected by leveraging gradient information to maintain diversity and representation. We provide a theoretical analysis of the gradient-based sample selection strategy and obtain explicit sublinear regret bounds for our proposed framework. Extensive experiments on synthetic and real-world tasks demonstrate that our approach significantly reduces the computational cost of GP fitting in BO while maintaining optimization performance comparable to baseline methods.

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these models have been derived using principles of variational inference, denoising, statistical signal processing, and stochastic differential equations. In contrast to the conventional presentation, in this study we derive diffusion models using ideas from linear partial differential equations and demonstrate that this approach has several benefits that include a constructive derivation of the forward and reverse processes, a unified derivation of multiple formulations and sampling strategies, and the discovery of a new class of models. We also apply the conditional version of these models to solving canonical conditional density estimation problems and challenging inverse problems. These problems help establish benchmarks for systematically quantifying the performance of different formulations and sampling strategies in this study, and for future studies. Finally, we identify and implement a mechanism through which a single diffusion model can be applied to measurements obtained from multiple measurement operators. Taken together, the contents of this manuscript provide a new understanding and several new directions in the application of diffusion models to solving physics-based inverse problems.

This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those that can be expressed as a power of a seminorm. We then show that such functionals can be approximated to arbitrary precision with the help of polyhedral norms. In particular, we identify two dual parameterizations of such systems: (i) a synthesis form with an $\ell_1$-penalty that involves some learnable dictionary; and (ii) an analysis form with an $\ell_\infty$-penalty that involves a trainable regularization operator. After having provided geometric insights and proved that the two forms are universal, we propose an implementation that relies on a specific architecture (tight frame with a weighted $\ell_1$ penalty) that is easy to train. We illustrate its use for denoising and the reconstruction of biomedical images. We find that the proposed framework outperforms the sparsity-based methods of compressed sensing, while it offers essentially the same convergence and robustness guarantees.

Power grid operation is becoming increasingly complex due to the rising integration of renewable energy sources and the need for more adaptive control strategies. Reinforcement Learning (RL) has emerged as a promising approach to power network control (PNC), offering the potential to enhance decision-making in dynamic and uncertain environments. The Learning To Run a Power Network (L2RPN) competitions have played a key role in accelerating research by providing standardized benchmarks and problem formulations, leading to rapid advancements in RL-based methods. This survey provides a comprehensive and structured overview of RL applications for power grid topology optimization, categorizing existing techniques, highlighting key design choices, and identifying gaps in current research. Additionally, we present a comparative numerical study evaluating the impact of commonly applied RL-based methods, offering insights into their practical effectiveness. By consolidating existing research and outlining open challenges, this survey aims to provide a foundation for future advancements in RL-driven power grid optimization.

We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral analysis gives access to the reconstruction performance. These results shed light on and specify the loss of performance induced by an artificial reduction of the memory cost of a tensor via the deletion of a random part of its entries.

We propose an innovative design for an all-optical Echo State Network (ESN), an advanced type of reservoir computer known for its universal computational capabilities. Our design enables fully optical implementation of arbitrary ESNs, featuring complete flexibility in optical matrix multiplication and nonlinear activation. Leveraging the nonlinear characteristics of stimulated Brillouin scattering (SBS), the architecture efficiently realizes measurement-free operations crucial for reservoir computing. The approach significantly reduces computational overhead and energy consumption compared to traditional software-based methods. Comprehensive simulations validate the system's memory capacity, nonlinear processing strength, and polynomial algebra capabilities, showcasing performance comparable to software ESNs across key benchmark tasks. Our design establishes a feasible, scalable, and universally applicable framework for optical reservoir computing, suitable for diverse machine learning applications.

Kurt'CyberGuy' Knutsson joins'Fox & Friends' to warn about a disturbing new scam where criminals use AI to clone the voices of loved ones and trick victims into sending money. Charges have been filed against an Oklahoma woman who is being accused of laundering nearly 1.5 million in funds obtained through online romance scams, targeting elderly women. Attorney General Gentner Drummond announced that Christine Joan Echohawk, 53, was arrested Monday, and is accused of laundering money from out-of-state victims between Sept. 30, 2024, and Dec. 26, 2024. Officials said that all the victims were women between the ages of 64 and 79. The victims believed they were sending money to a male subject whom they thought they were in an online relationship with, according to a news release from Drummond's office.

'The Big Weekend Show' co-hosts discuss Tinder user traffic peaking during'Dating Sunday.' A New Jersey woman is accused of hiring a man she met on Tinder to kill her police officer ex-boyfriend and his daughter, according to authorities. Camden County Prosecutor Grace C. MacAulay charged Jaclyn Diiorio, 26, with two counts of attempted first-degree murder, one count of conspiracy to commit murder and one count of third-degree possession of a controlled dangerous substance in connection with the alleged crime. Diiorio, of Runnemede, allegedly told a confidential informant she met on Tinder that she wanted her ex, a 53-year-old Philadelphia Police Department officer, and his 19-year-old daughter killed, Gloucester New Jersey Township Police said in a news release. The informant and Diiorio allegedly exchanged several phone calls and text messages after meeting on the dating app and later in person at a Wawa, according to court documents obtained by Fox News Digital.

A group of organizations, including nonprofits like LatinoProsperity and labor groups like the California Teamsters, are petitioning California Attorney General Rob Bonta to stop OpenAI from becoming a for-profit entity, The Los Angeles Times reports. OpenAI announced plans to transition to a public-benefit corporation in 2024, and reportedly has two years to pull it off or risk a large portion of the money its raised become debt. The group's primary concerns are that OpenAI "failed to protect its charitable assets" and is actively "subverting its charitable mission to advance safe artificial intelligence." OpenAI started as a nonprofit research organization studying AI, but transitioned to a for-profit company that's overseen and run by a nonprofit in 2019. That structure is legally allowed in the state of California, but the group's petition claims that OpenAI's decision to pursue a new structure is driven by a desire not to further its mission, but to provide "AI's benefits -- the potential for untold profits and control over what may become powerful world-altering technologies -- to a handful of corporate investors and high-level employees."

Google has now confirmed that Reddit uses Gemini to power Reddit Answers, an internal AI search tool for Reddit users. Contrary to some early reports, a Google PR representative told Mashable that Reddit Answers was already integrated with Gemini prior to the announcement. A beta version of Reddit Answers launched last December. And at the Google Cloud Next event on Wednesday, Google shared new details about how Reddit Answers works with Gemini. The tool uses Gemini "to help people more effectively find information, recommendations, discussions, and insights directly from the conversations and communities across Reddit," according to a press release.