We develop a framework for analyzing the training and learning rate dynamics on a variety of high- dimensional optimization problems trained using one-pass stochastic gradient descent (SGD) with data generated from multiple anisotropic classes. We give exact expressions for a large class of functions of the limiting dynamics, including the risk and the overlap with the true signal, in terms of a deterministic solution to a system of ODEs. We extend the existing theory of high-dimensional SGD dynamics to Gaussian-mixture data and a large (growing with the parameter size) number of classes. We then investigate in detail the effect of the anisotropic structure of the covariance of the data in the problems of binary logistic regression and least square loss. We study three cases: isotropic covariances, data covariance matrices with a large fraction of zero eigenvalues (denoted as the zero-one model), and covariance matrices with spectra following a power-law distribution. We show that there exists a structural phase transition. In particular, we demonstrate that, for the zero-one model and the power-law model with sufficiently large power, SGD tends to align more closely with values of the class mean that are projected onto the "clean directions" (i.e., directions of smaller variance). This is supported by both numerical simulations and analytical studies, which show the exact asymptotic behavior of the loss in the high-dimensional limit.

In this paper we develop a deforestation detection pipeline that incorporates optical and Synthetic Aperture Radar (SAR) data. A crucial component of the pipeline is the construction of anomaly maps of the optical data, which is done using the residual space of a discrete Karhunen-Loève (KL) expansion. Anomalies are quantified using a concentration bound on the distribution of the residual components for the nominal state of the forest. This bound does not require prior knowledge on the distribution of the data. This is in contrast to statistical parametric methods that assume knowledge of the data distribution, an impractical assumption that is especially infeasible for high dimensional data such as ours. Once the optical anomaly maps are computed they are combined with SAR data, and the state of the forest is classified by using a Hidden Markov Model (HMM). We test our approach with Sentinel-1 (SAR) and Sentinel-2 (Optical) data on a $92.19\,km \times 91.80\,km$ region in the Amazon forest. The results show that both the hybrid optical-radar and optical only methods achieve high accuracy that is superior to the recent state-of-the-art hybrid method. Moreover, the hybrid method is significantly more robust in the case of sparse optical data that are common in highly cloudy regions.

Large Language Models (LLMs) are increasingly integral to information dissemination and decision-making processes. Given their growing societal influence, understanding potential biases, particularly within the political domain, is crucial to prevent undue influence on public opinion and democratic processes. This work investigates political bias and stereotype propagation across eight prominent LLMs using the two-dimensional Political Compass Test (PCT). Initially, the PCT is employed to assess the inherent political leanings of these models. Subsequently, persona prompting with the PCT is used to explore explicit stereotypes across various social dimensions. In a final step, implicit stereotypes are uncovered by evaluating models with multilingual versions of the PCT. Key findings reveal a consistent left-leaning political alignment across all investigated models. Furthermore, while the nature and extent of stereotypes vary considerably between models, implicit stereotypes elicited through language variation are more pronounced than those identified via explicit persona prompting. Interestingly, for most models, implicit and explicit stereotypes show a notable alignment, suggesting a degree of transparency or "awareness" regarding their inherent biases. This study underscores the complex interplay of political bias and stereotypes in LLMs.

Red blood cells (RBCs) are essential to human health, and their precise morphological analysis is important for diagnosing hematological disorders. Despite the promise of foundation models in medical diagnostics, comprehensive AI solutions for RBC analysis remain scarce. We present RedDino, a self-supervised foundation model designed for RBC image analysis. RedDino uses an RBC-specific adaptation of the DINOv2 self-supervised learning framework and is trained on a curated dataset of 1.25 million RBC images from diverse acquisition modalities and sources. Extensive evaluations show that RedDino outperforms existing state-of-the-art models on RBC shape classification. Through assessments including linear probing and nearest neighbor classification, we confirm its strong feature representations and generalization ability. Our main contributions are: (1) a foundation model tailored for RBC analysis, (2) ablation studies exploring DINOv2 configurations for RBC modeling, and (3) a detailed evaluation of generalization performance. RedDino addresses key challenges in computational hematology by capturing nuanced morphological features, advancing the development of reliable diagnostic tools. The source code and pretrained models for RedDino are available at https://github.com/Snarci/RedDino, and the pretrained models can be downloaded from our Hugging Face collection at https://huggingface.co/collections/Snarcy/reddino-689a13e29241d2e5690202fc

Sam Fender has won the 2025 Mercury Prize for his third album, People Watching, a steely-eyed dissection of working-class life in the north of England. The singer looked stunned when his name was announced. I didn't think that was going to happen at all, he told the BBC as he came off stage. I've spent the last 10 minutes crying. Fender beat the likes of Pulp and Wolf Alice - both former winners of the £25,000 prize for the best British or Irish album of the year - at a star-studded ceremony in Newcastle's Utilita Arena.

Trump says he will meet Putin in Hungary for Ukraine talks after'very productive' call US President Donald Trump says great progress was made during a phone call with Russian President Vladimir Putin on Thursday, with the pair agreeing to face-to-face talks in Hungary. He said the call, the first with Putin since mid-August, was very productive, adding that teams from Washington and Moscow will meet next week. Trump did not confirm a date for his meeting with Putin in Budapest. The Kremlin said work on the summit would begin immediately after the extremely frank and trustful call. The talks came a day before Ukraine's President Zelensky was to visit the White House, and with Trump weighing whether to arm Ukraine with Tomahawk missiles capable of striking deep into Russia.

Researchers in Kenya excavated the first hand and foot bones belonging to'Paranthropis boisei.' Breakthroughs, discoveries, and DIY tips sent every weekday. When it comes to our evolutionary cousins, Neanderthals get most of the attention. Part of this is understandable, since there was a time in Earth's history when the role of dominant primate was up for grabs . Tweak any number of environmental factors, and the tool-wielding, yarn-weaving may have outlasted its cousins (aka humans) instead of going extinct around 40,000 years ago.

The special glands located on their legs were first mistaken for'ears.' Breakthroughs, discoveries, and DIY tips sent every weekday. For many insects, their "ears" aren't located anywhere near their heads. Crickets have evolved organs on their front legs that allow them to detect sound. Meanwhile, moths, mantises, and cicadas gather auditory information from similar appendages on their thoraxes or abdomens.

EU foreign policy chief Kaja Kallas has said a new anti-drone system should be fully operational by the end of 2027, as part of a drive to toughen defences against Russia and be fully prepared for possible conflict by 2030. Drones are already redefining warfare. Having drone defences is no longer optional for anyone, Kallas said, referring to Russia's ongoing war in Ukraine and fears that Moscow may attack the EU. The European Commission's defence roadmap also proposes strengthening the EU's eastern borders and building air and space shields. Several EU nations have faced Russian incursions into their airspace and US President Donald Trump has urged the bloc to do more to defend itself.

ByteDance's Doubao app has overtaken DeepSeek, proving that user-friendly design often matters more than having the most advanced AI model. When Chinese AI startup DeepSeek became a global sensation in January, it not only shocked Silicon Valley but also startled ByteDance, TikTok's parent company. The Chinese tech giant had already launched Doubao, its own flagship AI assistant app with tens of millions of users. But when DeepSeek became the best-known Chinese AI company overnight, no one was talking about Doubao anymore. Now, ByteDance has gotten its revenge.