Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical foundations of this success remain poorly understood. We follow the idea that the compositional structure of the learning task is the key factor determining when deep networks outperform other approaches. Taking a step towards formalizing this idea, we consider a simple compositional model, namely the multi-index model (MIM). In this context, we introduce and study hyper-kernel ridge regression (HKRR), an approach blending neural networks and kernel methods. Our main contribution is a sample complexity result demonstrating that HKRR can adaptively learn MIM, overcoming the curse of dimensionality. Further, we exploit the kernel nature of the estimator to develop ad hoc optimization approaches. Indeed, we contrast alternating minimization and alternating gradient methods both theoretically and numerically. These numerical results complement and reinforce our theoretical findings.

This study evaluates the performance of Soft Actor Critic (SAC), Greedy Actor Critic (GAC), and Truncated Quantile Critics (TQC) in high-dimensional decision-making tasks using fully observable environments. The focus is on parametrized action (PA) spaces, eliminating the need for recurrent networks, with benchmarks Platform-v0 and Goal-v0 testing discrete actions linked to continuous action-parameter spaces. Hyperparameter optimization was performed with Microsoft NNI, ensuring reproducibility by modifying the codebase for GAC and TQC. Results show that Parameterized Action Greedy Actor-Critic (PAGAC) outperformed other algorithms, achieving the fastest training times and highest returns across benchmarks, completing 5,000 episodes in 41:24 for the Platform game and 24:04 for the Robot Soccer Goal game. Its speed and stability provide clear advantages in complex action spaces. Compared to PASAC and PATQC, PAGAC demonstrated superior efficiency and reliability, making it ideal for tasks requiring rapid convergence and robust performance. Future work could explore hybrid strategies combining entropy-regularization with truncation-based methods to enhance stability and expand investigations into generalizability.

Large Language Models (LLMs) are rapidly being adopted in conservation to address the biodiversity crisis, yet their reliability for species evaluation is uncertain. This study systematically validates five leading models on 21,955 species across four core IUCN Red List assessment components: taxonomy, conservation status, distribution, and threats. A critical paradox was revealed: models excelled at taxonomic classification (94.9%) but consistently failed at conservation reasoning (27.2% for status assessment). This knowledge-reasoning gap, evident across all models, suggests inherent architectural constraints, not just data limitations. Furthermore, models exhibited systematic biases favoring charismatic vertebrates, potentially amplifying existing conservation inequities. These findings delineate clear boundaries for responsible LLM deployment: they are powerful tools for information retrieval but require human oversight for judgment-based decisions. A hybrid approach is recommended, where LLMs augment expert capacity while human experts retain sole authority over risk assessment and policy.

Abstract--This study examines the application of artificial intelligence (AI) and large language models (LLM) to improve access to legal texts in Senegal's judicial system. The emphasis is on the difficulties of extracting and organizing legal documents, highlighting the need for better access to judicial information. The research successfully extracted 7,967 articles from various legal documents, particularly focusing on the Land and Public Domain Code. A detailed graph database was developed, which contains 2,872 nodes and 10,774 relationships, aiding in the visualization of interconnections within legal texts. In addition, advanced triple extraction techniques were utilized for knowledge, demonstrating the effectiveness of models such as GPT - 4o, GPT -4, and Mistral-Large in identifying relationships and relevant metadata. Through these technologies, the aim is to create a solid framework that allows Senegalese citizens and legal professionals to more effectively understand their rights and responsibilities. Artificial intelligence (AI) is a transformative technology that raises significant ethical considerations regarding its use. Initiatives like Microsoft's "AI for Humanitarian Action" and Google's "AI for Social Good" focus on enhancing jurisprudence and human rights [1]. Moreover, the Center for Social Good Data Science at the University of Chicago applies AI to improve criminal justice systems.

How China is challenging Nvidia's AI chip dominance The US has dominated the global technology market for decades. But China wants to change that. The world's second largest economy is pouring huge amounts of money into artificial intelligence (AI) and robotics. Crucially, Beijing is also investing heavily to produce the high-end chips that power these cutting-edge technologies. Last month, Jensen Huang - the boss of the global AI chip industry leader, Nvidia - warned that China was just nanoseconds behind the US in chip development.

Science Space Deep Space Exoplanets Rogue planet is gobbling up 6.6 billion tons of dust per second The cosmic oddities experience their own growth spurts. Breakthroughs, discoveries, and DIY tips sent every weekday. About 620 light-years from Earth, a gigantic rogue proto-planet is currently devouring 6.6 billion tons of dust and gas per second. Based on recent observations, the relatively new resident of the Chamaeleon constellation isn't stopping anytime soon--and the situation may get even more intense. But according to astronomers, that may be pretty standard behavior for these cosmic objects.

Can Ukraine restore its pre-war borders? Why are Tomahawk missiles for Ukraine a'red line' for Russia? Is Russia testing NATO with aerial incursions in Europe? Five people have been killed in Ukraine after Russia launched hundreds of drones and missiles across the country overnight, which officials said targeted civilian infrastructure. Ukraine's President Volodymyr Zelenskyy said on Sunday that Russia fired approximately 50 missiles and 500 attack drones.

Russia pounded Ukraine with missile and drone attacks overnight on Saturday and into Sunday morning, focusing on the major western city of Lviv. Ukraine's neighbour Poland scrambled fighter jets in order to ensure the safety of Polish airspace, the Polish military confirmed. Allied Nato aircraft were also deployed. Lviv's regional head Maksym Kozytskyi said two people were killed in strikes in the region, and two more injured. Elsewhere, Russia again targeted Ukraine's power plants - and one was struck in an overnight attack on Zaporizhzhia, where the mayor said one person died and more than 73,000 people were without electricity.

Can Ukraine restore its pre-war borders? Why are Tomahawk missiles for Ukraine a'red line' for Russia? Is Russia testing NATO with aerial incursions in Europe? One person was killed and about 30 others injured after two Russian drones struck trains at a station in Ukraine's northern Sumy region. Ukrainian President Volodymyr Zelenskyy accused Russia of "terrorism", while Foreign Minister Andrii Sybiha said Moscow deliberately targeted civilians during the attack.

A hatter and a railway clerk's 1925 medical breakthrough became one of the most profound events in medical history. Breakthroughs, discoveries, and DIY tips sent every weekday. In 1925,, one of the world's most prestigious medical journals, published a blockbuster finding so significant that its editors offered a rare prelude: "The two communications which follow mark an event in the history of medicine . They form a detailed description of a prolonged and intensive research into the origin of malignant new growths, and they may present a solution of the central problem of cancer." On the day the studies were scheduled to be released, word began to spread beyond the scientific community.