Extreme weather events are widely studied in fields such as agriculture, ecology, and meteorology. The spatio-temporal co-occurrence of extreme events can strengthen or weaken under changing climate conditions. In this paper, we propose a novel approach to model spatio-temporal extremes by integrating climate indices via a conditional variational autoencoder (cXVAE). A convolutional neural network (CNN) is embedded in the decoder to convolve climatological indices with the spatial dependence within the latent space, thereby allowing the decoder to be dependent on the climate variables. There are three main contributions here. First, we demonstrate through extensive simulations that the proposed conditional XVAE accurately emulates spatial fields and recovers spatially and temporally varying extremal dependence with very low computational cost post training. Second, we provide a simple, scalable approach to detecting condition-driven shifts and whether the dependence structure is invariant to the conditioning variable. Third, when dependence is found to be condition-sensitive, the conditional XVAE supports counterfactual experiments allowing intervention on the climate covariate and propagating the associated change through the learned decoder to quantify differences in joint tail risk, co-occurrence ranges, and return metrics. To demonstrate the practical utility and performance of the model in real-world scenarios, we apply our method to analyze the monthly maximum Fire Weather Index (FWI) over eastern Australia from 2014 to 2024 conditioned on the El Niño/Southern Oscillation (ENSO) index.

We theoretically demonstrate that the generalization error of interpolators for machine learning models under teacher-student settings becomes 0 once the number of training samples exceeds a certain threshold. Understanding the high generalization ability of large-scale models such as deep neural networks (DNNs) remains one of the central open problems in machine learning theory. While recent theoretical studies have attributed this phenomenon to the implicit bias of stochastic gradient descent (SGD) toward well-generalizing solutions, empirical evidences indicate that it primarily stems from properties of the model itself. Specifically, even randomly sampled interpolators, which are parameters that achieve zero training error, have been observed to generalize effectively. In this study, under a teacher-student framework, we prove that the generalization error of randomly sampled interpolators becomes exactly zero once the number of training samples exceeds a threshold determined by the geometric structure of the interpolator set in parameter space. As a proof technique, we leverage tools from algebraic geometry to mathematically characterize this geometric structure.

Stochastic Reaction Networks (SRNs) are a fundamental modeling framework for systems ranging from chemical kinetics and epidemiology to ecological and synthetic biological processes. A central computational challenge is the estimation of expected outputs across initial conditions and times, a task that is rarely solvable analytically and becomes computationally prohibitive with current methods such as Finite State Projection or the Stochastic Simulation Algorithm. Existing deep learning approaches offer empirical scalability, but provide neither interpretability nor reliability guarantees, limiting their use in scientific analysis and in applications where model outputs inform real-world decisions. Here we introduce DeepSKA, a neural framework that jointly achieves interpretability, guaranteed reliability, and substantial computational gains. DeepSKA yields mathematically transparent representations that generalise across states, times, and output functions, and it integrates this structure with a small number of stochastic simulations to produce unbiased, provably convergent, and dramatically lower-variance estimates than classical Monte Carlo. We demonstrate these capabilities across nine SRNs, including nonlinear and non-mass-action models with up to ten species, where DeepSKA delivers accurate predictions and orders-of-magnitude efficiency improvements. This interpretable and reliable neural framework offers a principled foundation for developing analogous methods for other Markovian systems, including stochastic differential equations.

Semi-supervised learning (SSL) constructs classifiers from datasets in which only a subset of observations is labelled, a situation that naturally arises because obtaining labels often requires expert judgement or costly manual effort. This motivates methods that integrate labelled and unlabelled data within a learning framework. Most SSL approaches assume that label absence is harmless, typically treated as missing completely at random or ignored, but in practice, the missingness process can be informative, as the chances of an observation being unlabelled may depend on the ambiguity of its feature vector. In such cases, the missingness indicators themselves provide additional information that, if properly modelled, may improve estimation efficiency. The \textbf{SSLfmm} package for R is designed to capture this behaviour by estimating the Bayes' classifier under a finite mixture model in which each component corresponding to a class follows a multivariate normal distribution. It incorporates a mixed-missingness mechanism that combines a missing completely at random (MCAR) component with a (non-ignorable) missing at random (MAR) component, the latter modelling the probability of label missingness as a logistic function of the entropy based on the features. Parameters are estimated via an Expectation--Conditional Maximisation algorithm. In the two-class Gaussian setting with arbitrary covariance matrices, the resulting classifier trained on partially labelled data may, in some cases, achieve a lower misclassification rate than the supervised version in the case where all the labels are known. The package includes a practical tool for modelling and illustrates its performance through simulated examples.

Clustering in stationary and nonstationary settings, where data distributions remain static or evolve over time, requires models that can adapt to distributional shifts while preserving previously learned cluster structures. This paper proposes an Adaptive Resonance Theory (ART)-based topological clustering algorithm that autonomously adjusts its recalculation interval and vigilance threshold through a diversity-driven adaptation mechanism. This mechanism enables hyperparameter-free learning that maintains cluster stability and continuity in dynamic environments. Experiments on 24 real-world datasets demonstrate that the proposed algorithm outperforms state-of-the-art methods in both clustering performance and continual learning capability. These results highlight the effectiveness of the proposed parameter adaptation in mitigating catastrophic forgetting and maintaining consistent clustering in evolving data streams. Source code is available at https://github.com/Masuyama-lab/IDAT

The application of Vision-Language Models (VLMs) in medicine is critically hampered by the scarcity of high-quality, expert-annotated data. Supervised Fine-Tuning (SFT) on existing datasets often leads to poor generalization on unseen modalities and tasks, while Reinforcement Learning (RL), a promising alternative, is stymied by the lack of reliable reward signals in this data-scarce domain. To break this impasse, we introduce Generative Reward Learning for Medical Reasoning (MedGR$^2$), a novel framework that creates a self-improving virtuous cycle. MedGR$^2$ co-develops a data generator and a reward model, enabling the automated, continuous creation of high-quality, multi-modal medical data that serves as both a superior training source for SFT and RL. Our experiments demonstrate that SFT with MedGR$^2$-produced data already surpasses baselines trained on large-scale, human-curated datasets. Crucially, when leveraging this data for RL via Group Relative Policy Optimization (GRPO), our model achieves state-of-the-art cross-modality and cross-task generalization, significantly outperforming specialized RL-based methods. Furthermore, our compact model, empowered by MedGR$^2$, achieves performance competitive with foundation models possessing over 10 times more parameters. MedGR$^2$ presents a new paradigm for data-efficient learning in high-stakes domains, transforming the problem from data scarcity to data generation and unlocking the full potential of RL for building truly generalizable medical AI.

Magnetic resonance imaging (MRI) inpainting supports numerous clinical and research applications. We introduce the first generative model that conditions on voxel-level, continuous tumor concentrations to synthesize high-fidelity brain tumor MRIs. For the BraTS 2025 Inpainting Challenge, we adapt this architecture to the complementary task of healthy tissue restoration by setting the tumor concentrations to zero. Our latent diffusion model conditioned on both tissue segmentations and the tumor concentrations generates 3D spatially coherent and anatomically consistent images for both tumor synthesis and healthy tissue inpainting. For healthy inpainting, we achieve a PSNR of 18.5, and for tumor inpainting, we achieve 17.4. Our code is available at: https://github.com/valentin-biller/ldm.git

Significant Others (SOs) stabilize identity, regulate emotion, and support narrative meaning-making, yet many people today lack access to such relational anchors. Recent advances in large language models and memory-augmented AI raise the question of whether artificial systems could support some of these functions. Existing empathic AIs, however, remain reactive and short-term, lacking autobiographical memory, identity modeling, predictive emotional regulation, and narrative coherence. This manuscript introduces Significant Other Artificial Intelligence (SO-AI) as a new domain of relational AI. It synthesizes psychological and sociological theory to define SO functions and derives requirements for SO-AI, including identity awareness, long-term memory, proactive support, narrative co-construction, and ethical boundary enforcement. A conceptual architecture is proposed, comprising an anthropomorphic interface, a relational cognition layer, and a governance layer. A research agenda outlines methods for evaluating identity stability, longitudinal interaction patterns, narrative development, and sociocultural impact. SO-AI reframes AI-human relationships as long-term, identity-bearing partnerships and provides a foundational blueprint for investigating whether AI can responsibly augment the relational stability many individuals lack today.

Large Language Models (LLMs) offer powerful capabilities, but their significant size and computational requirements hinder deployment on resource-constrained mobile devices. This paper investigates Post-Training Quantization (PTQ) for compressing LLMs for mobile execution. We apply 4-bit PTQ using the BitsAndBytes library with the Hugging Face Transformers framework to Meta's Llama 3.2 3B model. The quantized model is converted to GGUF format using llama.cpp tools for optimized mobile inference. The PTQ workflow achieves a 68.66% reduction in model size through 4-bit quantization, enabling the Llama 3.2 3B model to run efficiently on an Android device. Qualitative validation shows that the 4-bit quantized model can perform inference tasks successfully. We demonstrate the feasibility of running the quantized GGUF model on an Android device using the Termux environment and the Ollama framework. PTQ, especially at 4-bit precision combined with mobile-optimized formats like GGUF, provides a practical pathway for deploying capable LLMs on mobile devices, balancing model size and performance.

Assessing language proficiency is essential for education, as it enables instruction tailored to learners needs. This paper investigates the use of Large Language Models (LLMs) for automatically classifying German texts according to the Common European Framework of Reference for Languages (CEFR) into different proficiency levels. To support robust training and evaluation, we construct a diverse dataset by combining multiple existing CEFR-annotated corpora with synthetic data. We then evaluate prompt-engineering strategies, fine-tuning of a LLaMA-3-8B-Instruct model and a probing-based approach that utilizes the internal neural state of the LLM for classification. Our results show a consistent performance improvement over prior methods, highlighting the potential of LLMs for reliable and scalable CEFR classification.