Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore, the convergence guarantee of stochastic gradient descent is of fundamental importance. In this work, we establish the linear convergence of stochastic gradient descent / flow in training over-parameterized two layer PINNs for a general class of activation functions in the sense of high probability. These results extend the existing result [18] in which gradient descent was analyzed. The challenge of the analysis lies in handling the dynamic randomness introduced by stochastic optimization methods. The key of the analysis lies in ensuring the positive definiteness of suitable Gram matrices during the training. The analysis sheds insight into the dynamics of the optimization process, and provides guarantees on the neural networks trained by stochastic algorithms.

Large Language Models (LLMs) are being applied in a wide array of settings, well beyond the typical language-oriented use cases. In particular, LLMs are increasingly used as a plug-and-play method for fitting data and generating predictions. Prior work has shown that LLMs, via in-context learning or supervised fine-tuning, can perform competitively with many tabular supervised learning techniques in terms of predictive performance. However, we identify a critical vulnerability of using LLMs for data fitting -- making changes to data representation that are completely irrelevant to the underlying learning task can drastically alter LLMs' predictions on the same data. For example, simply changing variable names can sway the size of prediction error by as much as 82% in certain settings. Such prediction sensitivity with respect to task-irrelevant variations manifests under both in-context learning and supervised fine-tuning, for both close-weight and open-weight general-purpose LLMs. Moreover, by examining the attention scores of an open-weight LLM, we discover a non-uniform attention pattern: training examples and variable names/values which happen to occupy certain positions in the prompt receive more attention when output tokens are generated, even though different positions are expected to receive roughly the same attention. This partially explains the sensitivity in the presence of task-irrelevant variations. We also consider a state-of-the-art tabular foundation model (TabPFN) trained specifically for data fitting. Despite being explicitly designed to achieve prediction robustness, TabPFN is still not immune to task-irrelevant variations. Overall, despite LLMs' impressive predictive capabilities, currently they lack even the basic level of robustness to be used as a principled data-fitting tool.

We propose a general-purpose approach for improving the ability of Large Language Models (LLMs) to intelligently and adaptively gather information from a user or other external source using the framework of sequential Bayesian experimental design (BED). This enables LLMs to act as effective multi-turn conversational agents and interactively interface with external environments. Our approach, which we call BED-LLM (Bayesian Experimental Design with Large Language Models), is based on iteratively choosing questions or queries that maximize the expected information gain (EIG) about the task of interest given the responses gathered previously. We show how this EIG can be formulated in a principled way using a probabilistic model derived from the LLM's belief distribution and provide detailed insights into key decisions in its construction. Further key to the success of BED-LLM are a number of specific innovations, such as a carefully designed estimator for the EIG, not solely relying on in-context updates for conditioning on previous responses, and a targeted strategy for proposing candidate queries. We find that BED-LLM achieves substantial gains in performance across a wide range of tests based on the 20-questions game and using the LLM to actively infer user preferences, compared to direct prompting of the LLM and other adaptive design strategies.

--Context recognition (SR) is a fundamental task in computer vision that aims to extract structured semantic summaries from images by identifying key events and their associated entities. Specifically, given an input image, the model must first classify the main visual events (verb classification), then identify the participating entities and their semantic roles (semantic role labeling), and finally localize these entities in the image (semantic role localization). Existing methods treat verb classification as a single-label problem, but we show through a comprehensive analysis that this formulation fails to address the inherent ambiguity in visual event recognition, as multiple verb categories may reasonably describe the same image. This paper makes three key contributions: First, we reveal through empirical analysis that verb classification is inherently a multi-label problem due to the ubiquitous semantic overlap between verb categories. Second, given the impracticality of fully annotating large-scale datasets with multiple labels, we propose to reformulate verb classification as a single positive multi-label learning (SPMLL) problem - a novel perspective in SR research. Third, we design a comprehensive multi-label evaluation benchmark for SR that is carefully designed to fairly evaluate model performance in a multi-label setting. T o address the challenges of SPMLL, we futher develop the Graph Enhanced V erb Multilayer Perceptron (GE-V erbMLP), which combines graph neural networks to capture label correlations and adversarial training to optimize decision boundaries. Extensive experiments on real-world datasets show that our approach achieves more than 3% improvement on the more meaningful multi-label A verage Precision (MAP) metric while remaining competitive on traditional top-1 and top-5 accuracy metrics. T o our knowledge, our research is the first work that the formulate, solving, and evaluating of verb classification in the SPMLL fashion, which provides theoretical insights and practical tools for advancing situation recognition research. Modern multimedia applications increasingly demand systems that can understand images at both the object level (recognizing individual entities) and the event level (comprehending interactions and activities). Situation Recognition (SR) has emerged as a crucial task addressing this need by extracting structured semantic representations from images [25], [26].

As privacy regulations such as the GDPR and HIPAA and responsibility frameworks for artificial intelligence such as the AI Act gain traction, the ethical and responsible use of real-world data faces increasing constraints. Synthetic data generation has emerged as a promising solution to risk-aware data sharing and model development, particularly for tabular datasets that are foundational to sensitive domains such as healthcare. To address both privacy and fairness concerns in this setting, we propose FLIP (Fair Latent Intervention under Privacy guarantees), a transformer-based variational autoencoder augmented with latent diffusion to generate heterogeneous tabular data. Unlike the typical setup in fairness-aware data generation, we assume a task-agnostic setup, not reliant on a fixed, defined downstream task, thus offering broader applicability. To ensure privacy, FLIP employs Rényi differential privacy (RDP) constraints during training and addresses fairness in the input space with RDP-compatible balanced sampling that accounts for group-specific noise levels across multiple sampling rates. In the latent space, we promote fairness by aligning neuron activation patterns across protected groups using Centered Kernel Alignment (CKA), a similarity measure extending the Hilbert-Schmidt Independence Criterion (HSIC). This alignment encourages statistical independence between latent representations and the protected feature. Empirical results demonstrate that FLIP effectively provides significant fairness improvements for task-agnostic fairness and across diverse downstream tasks under differential privacy constraints.

Large language models (LLMs) rely heavily on web-scale datasets like Common Crawl, which provides over 80\% of training data for some modern models. However, the indiscriminate nature of web crawling raises challenges in data quality, safety, and ethics. Despite the critical importance of training data quality, prior research on harmful content has been limited to small samples due to computational constraints. This project presents a framework for indexing and analyzing LLM training datasets using an ElasticSearch-based pipeline. We apply it to SwissAI's FineWeb-2 corpus (1.5TB, four languages), achieving fast query performance--most searches in milliseconds, all under 2 seconds. Our work demonstrates real-time dataset analysis, offering practical tools for safer, more accountable AI systems.

Introduction: Large language models (LLM) have shown great potential in clinical decision support. GPT-5 is a novel LLM system that has been specifically marketed towards oncology use. Methods: Performance was assessed using two complementary benchmarks: (i) the ACR Radiation Oncology In-Training Examination (TXIT, 2021), comprising 300 multiple-choice items, and (ii) a curated set of 60 authentic radiation oncologic vignettes representing diverse disease sites and treatment indications. For the vignette evaluation, GPT-5 was instructed to generate concise therapeutic plans. Four board-certified radiation oncologists rated correctness, comprehensiveness, and hallucinations. Inter-rater reliability was quantified using Fleiss' \k{appa}. Results: On the TXIT benchmark, GPT-5 achieved a mean accuracy of 92.8%, outperforming GPT-4 (78.8%) and GPT-3.5 (62.1%). Domain-specific gains were most pronounced in Dose and Diagnosis. In the vignette evaluation, GPT-5's treatment recommendations were rated highly for correctness (mean 3.24/4, 95% CI: 3.11-3.38) and comprehensiveness (3.59/4, 95% CI: 3.49-3.69). Hallucinations were rare with no case reaching majority consensus for their presence. Inter-rater agreement was low (Fleiss' \k{appa} 0.083 for correctness), reflecting inherent variability in clinical judgment. Errors clustered in complex scenarios requiring precise trial knowledge or detailed clinical adaptation. Discussion: GPT-5 clearly outperformed prior model variants on the radiation oncology multiple-choice benchmark. Although GPT-5 exhibited favorable performance in generating real-world radiation oncology treatment recommendations, correctness ratings indicate room for further improvement. While hallucinations were infrequent, the presence of substantive errors underscores that GPT-5-generated recommendations require rigorous expert oversight before clinical implementation.

Matched filters are widely used to localise signal patterns due to their high efficiency and interpretability. However, their effectiveness deteriorates for low signal-to-noise ratio (SNR) signals, such as those recorded on edge devices, where prominent noise patterns can closely resemble the target within the limited length of the filter. One example is the ear-electrocardiogram (ear-ECG), where the cardiac signal is attenuated and heavily corrupted by artefacts. To address this, we propose the Sequential Matched Filter (SMF), a paradigm that replaces the conventional single matched filter with a sequence of filters designed by a Reinforcement Learning agent. By formulating filter design as a sequential decision-making process, SMF adaptively design signal-specific filter sequences that remain fully interpretable by revealing key patterns driving the decision-making. The proposed SMF framework has strong potential for reliable and interpretable clinical decision support, as demonstrated by its state-of-the-art R-peak detection and physiological state classification performance on two challenging real-world ECG datasets. The proposed formulation can also be extended to a broad range of applications that require accurate pattern localisation from noise-corrupted signals.

Large Language Models (LLMs) are transforming AI across industries, but their development and deployment remain complex. This survey reviews 16 key challenges in building and using LLMs and examines how these challenges are addressed by two state-of-the-art models with unique approaches: OpenAI's closed source GPT-4o (May 2024 update) and DeepSeek-V3-0324 (March 2025), a large open source Mixture-of-Experts model. Through this comparison, we showcase the trade-offs between closed source models (robust safety, fine-tuned reliability) and open source models (efficiency, adaptability). We also explore LLM applications across different domains (from chatbots and coding tools to healthcare and education), highlighting which model attributes are best suited for each use case. This article aims to guide AI researchers, developers, and decision-makers in understanding current LLM capabilities, limitations, and best practices.

To reduce the amount of required labeled data for lung disease severity classification from chest X-rays (CXRs) under class imbalance, this study applied deep active learning with a Bayesian Neural Network (BNN) approximation and weighted loss function. This retrospective study collected 2,319 CXRs from 963 patients (mean age, 59.2 $\pm$ 16.6 years; 481 female) at Emory Healthcare affiliated hospitals between January and November 2020. All patients had clinically confirmed COVID-19. Each CXR was independently labeled by 3 to 6 board-certified radiologists as normal, moderate, or severe. A deep neural network with Monte Carlo Dropout was trained using active learning to classify disease severity. Various acquisition functions were used to iteratively select the most informative samples from an unlabeled pool. Performance was evaluated using accuracy, area under the receiver operating characteristic curve (AU ROC), and area under the precision-recall curve (AU PRC). Training time and acquisition time were recorded. Statistical analysis included descriptive metrics and performance comparisons across acquisition strategies. Entropy Sampling achieved 93.7% accuracy (AU ROC, 0.91) in binary classification (normal vs. diseased) using 15.4% of the training data. In the multi-class setting, Mean STD sampling achieved 70.3% accuracy (AU ROC, 0.86) using 23.1% of the labeled data. These methods outperformed more complex and computationally expensive acquisition functions and significantly reduced labeling needs. Deep active learning with BNN approximation and weighted loss effectively reduces labeled data requirements while addressing class imbalance, maintaining or exceeding diagnostic performance.