Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron (Bach, 2017). In this paper, we study a suitable function space for over-parameterized two-layer neural networks with bounded norms (e.g., the path norm, the Barron norm) in the perspective of sample complexity and generalization properties. First, we show that the path norm (as well as the Barron norm) is able to obtain width-independence sample complexity bounds, which allows for uniform convergence guarantees. Based on this result, we derive the improved result of metric entropy for $\epsilon$-covering up to $O(\epsilon^{-\frac{2d}{d+2}})$ ($d$ is the input dimension and the depending constant is at most linear order of $d$) via the convex hull technique, which demonstrates the separation with kernel methods with $\Omega(\epsilon^{-d})$ to learn the target function in a Barron space. Second, this metric entropy result allows for building a sharper generalization bound under a general moment hypothesis setting, achieving the rate at $O(n^{-\frac{d+2}{2d+2}})$. Our analysis is novel in that it offers a sharper and refined estimation for metric entropy with a linear dimension dependence and unbounded sampling in the estimation of the sample error and the output error.

Dr. Ronny Jackson joins'Sunday Morning Futures' to discuss his five letters asking President Biden to submit to a cognitive test and his next letter addressed to Biden's physician and the Cabinet. EXCLUSIVE: Rep. Earl "Buddy" Carter, R-Ga., wrote a letter to the White House on Monday calling on President Biden to take a cognitive assessment over concerns about his "fragile mental state" and ability to uphold his duties. In a letter obtained exclusively by Fox News Digital, Carter, who is also a pharmacist, wrote to White House Chief of Staff Jeff Zients expressing "serious concern" with Biden's cognitive state and "ability to execute the duties of the Presidency." "After numerous examples of the President's declining mental acuity, it is imperative that the White House remains transparent about the President of the United States' honest ability to uphold the duties of the office to which he swore an oath," Carter wrote. This comes after a recent report from The Wall Street Journal stating that the 81-year-old president was showing signs of poor cognitive performance in private meetings with congressional lawmakers, including by closing his eyes for extended periods, speaking so softly at times that people struggled to hear him and forgetting details about his own energy policy.

It was the most highly anticipated feature to be unveiled at Apple's Worldwide Developers Conference (WWDC) this year. But Apple now says Apple Intelligence and two other big updates won't be coming to devices in the European Union until next year at the latest. In a statement, the tech giant revealed that it would be delaying the EU rollout of its huge AI update due to privacy concerns stemming from the Digital Markets Act (DMA). Apple says it will also hold back iPhone Mirroring for Macs as well as SharePlay Screen Sharing enhancements due to'regulatory uncertainties'. MailOnline has contacted Apple for further information but it is not yet clear whether this will affect UK users.

Apple has become the first big tech company to be charged with breaking the European Union's new digital markets rules, three days after the tech giant said it would not release artificial intelligence in the bloc due to regulation. On Monday, the European Commission said that Apple's App Store was preventing developers from communicating with their users and promoting offers to them directly, a practice known as anti-steering. "Our preliminary position is that Apple does not fully allow steering. Steering is key to ensure that app developers are less dependent on gatekeepers' app stores and for consumers to be aware of better offers," Margrethe Vestager, the EU's competition chief said in a statement. On X, the European commissioner for the internal market, Thierry Breton, gave a more damning assessment.

Geologists have raised concerns about potential Chinese censorship and bias in a chatbot being developed with the backing of the International Union of Geological Sciences (IUGS), one of the world's largest scientific organisations and a Unesco partner. The GeoGPT chatbot is aimed at geoscientists and researchers, particularly in the global south, to help them develop their understanding of earth sciences by drawing on swaths of data and research on billions of years of the planet's history. It is an initiative from Deep-time Digital Earth (DDE), a largely Chinese-funded programme founded in 2019 to enhance international scientific cooperation and help countries to realise the UN's sustainable development goals. Part of the underlying AI for GeoGPT is Qwen, a large language model built by the Chinese tech company Alibaba. Responding to the article, DDE representatives Michael Stephenson, Hans Thybo, Chengshan Wang and Ishwaran Natarajan said the chatbot also used Meta's Llama, another large language model, and that during testing they had not noticed any state censorship, which they said was "unlikely" given that the system was "based entirely in geoscience information".

White dwarfs (WDs) polluted by exoplanetary material provide the unprecedented opportunity to directly observe the interiors of exoplanets. However, spectroscopic surveys are often limited by brightness constraints, and WDs tend to be very faint, making detections of large populations of polluted WDs difficult. In this paper, we aim to increase considerably the number of WDs with multiple metals in their atmospheres. Using 96,134 WDs with Gaia DR3 BP/RP (XP) spectra, we constructed a 2D map using an unsupervised machine learning technique called Uniform Manifold Approximation and Projection (UMAP) to organize the WDs into identifiable spectral regions. The polluted WDs are among the distinct spectral groups identified in our map. We have shown that this selection method could potentially increase the number of known WDs with 5 or more metal species in their atmospheres by an order of magnitude. Such systems are essential for characterizing exoplanet diversity and geology.

In a post-ChatGPT world, this paper explores the potential of leveraging scalable artificial intelligence for scientific discovery. We propose that scaling up artificial intelligence on high-performance computing platforms is essential to address such complex problems. This perspective focuses on scientific use cases like cognitive simulations, large language models for scientific inquiry, medical image analysis, and physics-informed approaches. The study outlines the methodologies needed to address such challenges at scale on supercomputers or the cloud and provides exemplars of such approaches applied to solve a variety of scientific problems. In light of ChatGPT's growing popularity, the transformative potential of AI in science becomes increasingly evident. Although a number of recent articles highlight the transformative power of AI in science [1, 2, 3], few provide specifics how to implement such methods at scale on supercomputers. Using ChatGPT as an archetype, we argue that the success of such complex AI models results from two primary advancements: (1) the development of the transformer architecture, (2) the ability to train on vast amounts of internet-scale data. This process represents a broader trend within the field of AI where combining massive amounts of training data with large-scale computational resources becomes the foundation of scientific breakthroughs. Several examples underscore the integral role of using large-scale computational resources and colossal amounts of data to achieve scientific breakthroughs. For instance, Khan et al. [4] used AI and large-scale computing for advanced models of black hole mergers, leveraging a dataset of 14 million waveforms on the Summit supercomputer. Riley et al. [5] made significant progress towards the understanding the physics of stratified fluid turbulence by being able to model the Prandtl number of seven, which represents ocean water at 20 Such simulations required being simulated using four trillion grid points, which required petabytes of storage [6].

In this work, we introduce an open-source integrated CAD-CFD tool, Anvil, which combines FreeCAD for CAD modeling and OpenFOAM for CFD analysis, along with an AI-based optimization method (Bayesian optimization) and other sampling algorithms. Anvil serves as a scientific machine learning tool for shape optimization in three modes: data generation, CFD evaluation, and shape optimization. In data generation mode, it automatically runs CFD evaluations and generates data for training a surrogate model. In optimization mode, it searches for the optimal design under given requirements and optimization metrics. In CFD mode, a single CAD file can be evaluated with a single OpenFOAM run. To use Anvil, experimenters provide a JSON configuration file and a parametric CAD seed design. Anvil can be used to study solid-fluid dynamics for any subsonic flow conditions and has been demonstrated in various simulation and optimization use cases. The open-source code for the tool, installation process, artifacts (such as CAD seed designs and example STL models), experimentation results, and detailed documentation can be found at \url{https://github.com/symbench/Anvil}.

As large language models (LLMs) become increasingly prevalent in a wide variety of applications, concerns about the safety of their outputs have become more significant. Most efforts at safety-tuning or moderation today take on a predominantly Western-centric view of safety, especially for toxic, hateful, or violent speech. In this paper, we describe LionGuard, a Singapore-contextualized moderation classifier that can serve as guardrails against unsafe LLM outputs. When assessed on Singlish data, LionGuard outperforms existing widely-used moderation APIs, which are not finetuned for the Singapore context, by 14% (binary) and up to 51% (multi-label). Our work highlights the benefits of localization for moderation classifiers and presents a practical and scalable approach for low-resource languages.

Language models are transforming the ways that their users engage with the world. Despite impressive capabilities, over-consumption of language model outputs risks propagating unchecked errors in the short-term and damaging human capabilities for critical thinking in the long-term, particularly in knowledge-based tasks. How can we develop scaffolding around language models to curate more appropriate use? We propose selective frictions for language model experiences, inspired by behavioral science interventions, to dampen misuse. Frictions involve small modifications to a user's experience, e.g., the addition of a button impeding model access and reminding a user of their expertise relative to the model. Through a user study with real humans, we observe shifts in user behavior from the imposition of a friction over LLMs in the context of a multi-topic question-answering task as a representative task that people may use LLMs for, e.g., in education and information retrieval. We find that frictions modulate over-reliance by driving down users' click rates while minimally affecting accuracy for those topics. Yet, frictions may have unintended effects. We find marked differences in users' click behaviors even on topics where frictions were not provisioned. Our contributions motivate further study of human-AI behavioral interaction to inform more effective and appropriate LLM use.