Recent advancements in artificial intelligence (AI), particularly foundation models (FMs), have revolutionized medical image analysis, demonstrating strong zero- and few-shot performance across diverse medical imaging tasks, from segmentation to report generation. Unlike traditional task-specific AI models, FMs leverage large corpora of labeled and unlabeled multimodal datasets to learn generalized representations that can be adapted to various downstream clinical applications with minimal fine-tuning. However, despite the rapid proliferation of FM research in medical imaging, the field remains fragmented, lacking a unified synthesis that systematically maps the evolution of architectures, training paradigms, and clinical applications across modalities. To address this gap, this review article provides a comprehensive and structured analysis of FMs in medical image analysis. We systematically categorize studies into vision-only and vision-language FMs based on their architectural foundations, training strategies, and downstream clinical tasks. Additionally, a quantitative meta-analysis of the studies was conducted to characterize temporal trends in dataset utilization and application domains. We also critically discuss persistent challenges, including domain adaptation, efficient fine-tuning, computational constraints, and interpretability along with emerging solutions such as federated learning, knowledge distillation, and advanced prompting. Finally, we identify key future research directions aimed at enhancing the robustness, explainability, and clinical integration of FMs, thereby accelerating their translation into real-world medical practice.

This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale atmospheric predictors such as 500 hPa geopotential height (Z500), which exhibit higher predictability than surface variables and can be downscaled to obtain more localised information. Previous work by Tian et al. (2024) demonstrated that stochastic perturbations based on model residuals can improve ensemble dispersion representation in statistical downscaling frameworks, but this method fails to represent spatial correlations and physical consistency adequately. More sophisticated approaches are needed to capture the complex relationships between large-scale predictors and local-scale predictands while maintaining physical consistency. Probabilistic deep learning models offer promising solutions for capturing complex spatial dependencies. This study evaluates three probabilistic methods with distinct uncertainty quantification mechanisms: Quantile Regression Neural Network that directly models distribution quantiles, Variational Autoencoders that leverage latent space sampling, and Diffusion Models that utilise iterative denoising. These models are trained on ERA5 reanalysis data and applied to ECMWF sub-seasonal hindcasts to regress probabilistic wind speed ensembles. Our results show that probabilistic downscaling approaches provide more realistic spatial uncertainty representations compared to simpler stochastic methods, with each probabilistic model offering different strengths in terms of ensemble dispersion, deterministic skill, and physical consistency. These findings establish probabilistic downscaling as an effective enhancement to operational sub-seasonal wind forecasts for renewable energy planning and risk assessment.

We present a novel architecture for safely integrating Large Language Models (LLMs) into interactive game engines, allowing players to "program" new behaviors using natural language. Our framework mitigates risks by using an LLM to translate commands into a constrained Domain-Specific Language (DSL), which configures a custom Entity-Component-System (ECS) at runtime. We evaluated this system in a 2D spell-crafting game prototype by experimentally assessing models from the Gemini, GPT, and Claude families with various prompting strategies. A validated LLM judge qualitatively rated the outputs, showing that while larger models better captured creative intent, the optimal prompting strategy is task-dependent: Chain-of-Thought improved creative alignment, while few-shot examples were necessary to generate more complex DSL scripts. This work offers a validated LLM-ECS pattern for emergent gameplay and a quantitative performance comparison for developers.

Large language models (LLMs) are increasingly used to convert natural language descriptions into mathematical optimization formulations. Current evaluations often treat formulations as a whole, relying on coarse metrics like solution accuracy or runtime, which obscure structural or numerical errors. In this study, we present a comprehensive, component-level evaluation framework for LLM-generated formulations. Beyond the conventional optimality gap, our framework introduces metrics such as precision and recall for decision variables and constraints, constraint and objective root mean squared error (RMSE), and efficiency indicators based on token usage and latency. We evaluate GPT-5, LLaMA 3.1 Instruct, and DeepSeek Math across optimization problems of varying complexity under six prompting strategies. Results show that GPT-5 consistently outperforms other models, with chain-of-thought, self-consistency, and modular prompting proving most effective. Analysis indicates that solver performance depends primarily on high constraint recall and low constraint RMSE, which together ensure structural correctness and solution reliability. Constraint precision and decision variable metrics play secondary roles, while concise outputs enhance computational efficiency. These findings highlight three principles for NLP-to-optimization modeling: (i) Complete constraint coverage prevents violations, (ii) minimizing constraint RMSE ensures solver-level accuracy, and (iii) concise outputs improve computational efficiency. The proposed framework establishes a foundation for fine-grained, diagnostic evaluation of LLMs in optimization modeling.

The classical hedging problem entails replicating the payoff of a contingent claim under a certain stochastic model. While we can find a complete hedging strategy in a complete market like Black-Scholes, a market is in general incomplete, including jump diffusion, and stochastic volatility models. While there are several hedging approaches in an incomplete market, it is often very difficult to get a closed form solution or even calculate numerically. Even in a complete market like Black-Scholes, there are drawbacks to this strategy in both execution and the theory it is based on. A traditional asset pricing and hedging method assumes frictionless markets, perfect liquidity, and normally distributed returns among many other conditions.

The lack of theoretical results for Layer Normalization and feedforward Hessians has left a gap in the study of Transformer optimization landscapes. We address this by deriving explicit second-order expressions for these components, thereby completing the Hessian characterization of full Transformer blocks. Our results generalize prior self-attention analyses and yield estimations for the role of each sublayer in curvature propagation. We demonstrate how these Hessian structures inform both convergence dynamics and the empirical scaling laws governing large-model performance. Further, we propose a Taylor-expansion-based framework for analyzing loss differences to quantify convergence trajectories. By extending Hessian theory to the full Transformer architecture, this work establishes a new foundation for theoretical and empirical investigations of optimization in large-scale deep learning.

Knowledge editing offers an efficient way to update model knowledge without full retraining, but prior work has concentrated almost exclusively on textual or visual modalities. We introduce SAKE, the first benchmark specifically designed for editing auditory attribute knowledge in Large Audio-Language Models (LALMs). Unlike factual updates, SAKE targets several abstract auditory attributes, capturing knowledge types that go beyond conventional textual and visual domains. We benchmark seven editing methods on two LALMs along four dimensions: reliability, generality, audio/text locality, and portability. Results highlight challenges such as preserving intra-attribute knowledge unrelated to the edit, generalizing edits to multimodal reasoning, and maintaining edits under sequential updates. SAKE provides a principled framework to study how knowledge editing extends to the auditory modalities, opening new directions for maintaining and adapting LALMs in more diverse real-world scenarios.

How can short-term energy consumption be accurately forecasted when sensor data is noisy, incomplete, and lacks contextual richness? This question guided our participation in the \textit{2025 Competition on Electric Energy Consumption Forecast Adopting Multi-criteria Performance Metrics}, which challenged teams to predict next-day power demand using real-world high-frequency data. We proposed a robust yet lightweight Deep Learning (DL) pipeline combining hourly downsizing, dual-mode imputation (mean and polynomial regression), and comprehensive normalization, ultimately selecting Standard Scaling for optimal balance. The lightweight GRU-LSTM sequence-to-one model achieves an average RMSE of 601.9~W, MAE of 468.9~W, and 84.36\% accuracy. Despite asymmetric inputs and imputed gaps, it generalized well, captured nonlinear demand patterns, and maintained low inference latency. Notably, spatiotemporal heatmap analysis reveals a strong alignment between temperature trends and predicted consumption, further reinforcing the model's reliability. These results demonstrate that targeted preprocessing paired with compact recurrent architectures can still enable fast, accurate, and deployment-ready energy forecasting in real-world conditions.

A key challenge in training Vision-Language Model (VLM) agents, compared to Language Model (LLM) agents, lies in the shift from textual states to complex visual observations. This transition introduces partial observability and demands robust world modeling. We ask: Can VLM agents construct internal world models through explicit visual state reasoning? To address this question, we architecturally enforce and reward the agent's reasoning process via reinforcement learning (RL), formulating it as a Partially Observable Markov Decision Process (POMDP). We find that decomposing the agent's reasoning into State Estimation ("what is the current state?") and Transition Modeling ("what comes next?") is critical for success, as demonstrated through five reasoning strategies. Our investigation into how agents represent internal beliefs reveals that the optimal representation is task-dependent: Natural Language excels at capturing semantic relationships in general tasks, while Structured formats are indispensable for precise manipulation and control. Building on these insights, we design a World Modeling Reward that provides dense, turn-level supervision for accurate state prediction, and introduce Bi-Level General Advantage Estimation (Bi-Level GAE) for turn-aware credit assignment. Through this form of visual state reasoning, a 3B-parameter model achieves a score of 0.82 across five diverse agent benchmarks, representing a 3$\times$ improvement over its untrained counterpart (0.21) and outperforming proprietary reasoning models such as GPT-5 (0.75), Gemini 2.5 Pro (0.67) and Claude 4.5 (0.62). All experiments are conducted within our VAGEN framework, a scalable system for training and analyzing multi-turn VLM agents in diverse visual environments. Code and data are publicly available at https://vagen-ai.github.io.

Accurate prediction of electricity prices is crucial for stakeholders in the energy market, particularly for grid operators, energy producers, and consumers. This study focuses on developing a predictive model leveraging Long Short-Term Memory (LSTM) networks to forecast day-ahead electricity prices in the California energy market. The model incorporates a variety of features, including historical price data, weather conditions, and the energy generation mix. A novel custom loss function that integrates Mean Absolute Error (MAE), Jensen-Shannon Divergence (JSD), and a smoothness penalty is introduced to enhance the prediction accuracy and interpretability. Additionally, an online learning approach is implemented to allow the model to adapt to new data incrementally, ensuring continuous relevance and accuracy. The results demonstrate that the custom loss function can improve the model's performance, aligning predicted prices more closely with actual values, particularly during peak intervals. Also, the online learning model outperforms other models by effectively incorporating real-time data, resulting in lower prediction error and variability. The inclusion of the energy generation mix further enhances the model's predictive capabilities, highlighting the importance of comprehensive feature integration. This research provides a robust framework for electricity price forecasting, offering valuable insights and tools for better decision-making in dynamic electricity markets.