Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More accurate learning typically requires Markov chain Monte Carlo (MCMC) Boltzmann sampling, but it is time-consuming due to the difficulty of parallelization for more expressive models. To address this limitation, we first propose a new Boltzmann sampler inspired by a quantum-inspired combinatorial optimization called simulated bifurcation (SB). This SB-inspired approach, which we name Langevin SB (LSB), enables parallelized sampling while maintaining accuracy comparable to MCMC. Furthermore, this is applicable not only to RBMs but also to BMs with general couplings. However, LSB cannot control the inverse temperature of the output Boltzmann distribution, which hinders learning and degrades performance. To overcome this limitation, we also developed an efficient method for estimating the inverse temperature during the learning process, which we call conditional expectation matching (CEM). By combining LSB and CEM, we establish an efficient learning framework for BMs with greater expressive power than RBMs. We refer to this framework as sampler-adaptive learning (SAL). SAL opens new avenues for energy-based generative modeling beyond RBMs.

Increasing climate change and habitat loss are driving unprecedented shifts in species distributions. Conservation professionals urgently need timely, high-resolution predictions of biodiversity risks, especially in ecologically diverse regions like Africa. We propose EcoCast, a spatio-temporal model designed for continual biodiversity and climate risk forecasting. Utilizing multisource satellite imagery, climate data, and citizen science occurrence records, EcoCast predicts near-term (monthly to seasonal) shifts in species distributions through sequence-based transformers that model spatio-temporal environmental dependencies. The architecture is designed with support for continual learning to enable future operational deployment with new data streams. Our pilot study in Africa shows promising improvements in forecasting distributions of selected bird species compared to a Random Forest baseline, highlighting EcoCast's potential to inform targeted conservation policies. By demonstrating an end-to-end pipeline from multi-modal data ingestion to operational forecasting, EcoCast bridges the gap between cutting-edge machine learning and biodiversity management, ultimately guiding data-driven strategies for climate resilience and ecosystem conservation throughout Africa.

The analysis of non-real-valued data, such as binary time series, has attracted great interest in recent years. This manuscript proposes a post-selection estimator for estimating the coefficient matrices of a high-dimensional generalized binary vector autoregressive process and establishes a Gaussian approximation theorem for the proposed estimator. Furthermore, it introduces a second-order wild bootstrap algorithm to enable statistical inference on the coefficient matrices. Numerical studies and empirical applications demonstrate the good finite-sample performance of the proposed method.

We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a sparsifying penalty, we formulate the problem by imposing an explicit cardinality constraint on the kernel weights and add an l2 penalty for robustness. We solve the resulting non-convex minimax problem via an alternating best response algorithm with two subproblems: the alpha subproblem is a standard kernel SVM dual solved via LIBSVM, while the beta subproblem admits an efficient solution via the Greedy Selector and Simplex Projector algorithm. We reformulate SMKL as a mixed integer semidefinite optimization problem and derive a hierarchy of semidefinite convex relaxations which can be used to certify near-optimality of the solutions returned by our best response algorithm and also to warm start it. On ten UCI benchmarks, our method with random initialization outperforms state-of-the-art MKL approaches in out-of-sample prediction accuracy on average by 3.34 percentage points (relative to the best performing benchmark) while selecting a small number of candidate kernels in comparable runtime. With warm starting, our method outperforms the best performing benchmark's out-of-sample prediction accuracy on average by 4.05 percentage points. Our convex relaxations provide a certificate that in several cases, the solution returned by our best response algorithm is the globally optimal solution.

Algorithms developed under stationary Markov Decision Processes (MDPs) often face challenges in non-stationary environments, and infinite-horizon formulations may not directly apply to finite-horizon tasks. To address these limitations, we introduce the Non-stationary and Varying-discounting MDP (NVMDP) framework, which naturally accommodates non-stationarity and allows discount rates to vary with time and transitions. Infinite-horizon, stationary MDPs emerge as special cases of NVMDPs for identifying an optimal policy, and finite-horizon MDPs are also subsumed within the NVMDP formulations. Moreover, NVMDPs provide a flexible mechanism to shape optimal policies, without altering the state space, action space, or the reward structure. We establish the theoretical foundations of NVMDPs, including assumptions, state- and action-value formulation and recursion, matrix representation, optimality conditions, and policy improvement under finite state and action spaces. Building on these results, we adapt dynamic programming and generalized Q-learning algorithms to NVMDPs, along with formal convergence proofs. For problems requiring function approximation, we extend the Policy Gradient Theorem and the policy improvement bound in Trust Region Policy Optimization (TRPO), offering proofs in both scalar and matrix forms. Empirical evaluations in a non-stationary gridworld environment demonstrate that NVMDP-based algorithms successfully recover optimal trajectories under multiple reward and discounting schemes, whereas original Q-learning fails. These results collectively show that NVMDPs provide a theoretically sound and practically effective framework for reinforcement learning, requiring only minor algorithmic modifications while enabling robust handling of non-stationarity and explicit optimal policy shaping.

Artificial intelligence (AI) is increasingly integrated into modern healthcare, offering powerful support for clinical decision-making. However, in real-world settings, AI systems may experience performance degradation over time, due to factors such as shifting data distributions, changes in patient characteristics, evolving clinical protocols, and variations in data quality. These factors can compromise model reliability, posing safety concerns and increasing the likelihood of inaccurate predictions or adverse outcomes. This review presents a forward-looking perspective on monitoring and maintaining the "health" of AI systems in healthcare. We highlight the urgent need for continuous performance monitoring, early degradation detection, and effective self-correction mechanisms. The paper begins by reviewing common causes of performance degradation at both data and model levels. We then summarize key techniques for detecting data and model drift, followed by an in-depth look at root cause analysis. Correction strategies are further reviewed, ranging from model retraining to test-time adaptation. Our survey spans both traditional machine learning models and state-of-the-art large language models (LLMs), offering insights into their strengths and limitations. Finally, we discuss ongoing technical challenges and propose future research directions. This work aims to guide the development of reliable, robust medical AI systems capable of sustaining safe, long-term deployment in dynamic clinical settings.

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods either focus on input-oriented feature extraction, such as supervised probes and Sparse Autoencoders (SAEs), or on output distribution inspection, such as logit-oriented approaches. A full understanding of LLM vector spaces, however, requires integrating both perspectives, something existing approaches struggle with due to constraints on latent feature definitions. We introduce the Hyperdimensional Probe, a hybrid supervised probe that combines symbolic representations with neural probing. Leveraging Vector Symbolic Architectures (VSAs) and hypervector algebra, it unifies prior methods: the top-down interpretability of supervised probes, SAE's sparsity-driven proxy space, and output-oriented logit investigation. This allows deeper input-focused feature extraction while supporting output-oriented investigation. Our experiments show that our method consistently extracts meaningful concepts across LLMs, embedding sizes, and setups, uncovering concept-driven patterns in analogy-oriented inference and QA-focused text generation. By supporting joint input-output analysis, this work advances semantic understanding of neural representations while unifying the complementary perspectives of prior methods.

Large language model-powered chatbots have transformed how people seek information, especially in high-stakes contexts like mental health. Despite their support capabilities, safe detection and response to crises such as suicidal ideation and self-harm are still unclear, hindered by the lack of unified crisis taxonomies and clinical evaluation standards. We address this by creating: (1) a taxonomy of six crisis categories; (2) a dataset of over 2,000 inputs from 12 mental health datasets, classified into these categories; and (3) a clinical response assessment protocol. We also use LLMs to identify crisis inputs and audit five models for response safety and appropriateness. First, we built a clinical-informed crisis taxonomy and evaluation protocol. Next, we curated 2,252 relevant examples from over 239,000 user inputs, then tested three LLMs for automatic classification. In addition, we evaluated five models for the appropriateness of their responses to a user's crisis, graded on a 5-point Likert scale from harmful (1) to appropriate (5). While some models respond reliably to explicit crises, risks still exist. Many outputs, especially in self-harm and suicidal categories, are inappropriate or unsafe. Different models perform variably; some, like gpt-5-nano and deepseek-v3.2-exp, have low harm rates, but others, such as gpt-4o-mini and grok-4-fast, generate more unsafe responses. All models struggle with indirect signals, default replies, and context misalignment. These results highlight the urgent need for better safeguards, crisis detection, and context-aware responses in LLMs. They also show that alignment and safety practices, beyond scale, are crucial for reliable crisis support. Our taxonomy, datasets, and evaluation methods support ongoing AI mental health research, aiming to reduce harm and protect vulnerable users.

In the face of accelerating global urbanization and the increasing frequency of extreme weather events, highresolution urban rainfall monitoring is crucial for building resilient smart cities. Commercial Microwave Links (CMLs) are an emerging data source with great potential for this task.While traditional rainfall retrieval from CMLs relies on physicsbased models, these often struggle with real-world complexities like signal noise and nonlinear attenuation. To address these limitations, this paper proposes a novel hybrid deep learning architecture based on the Transformer and a Bidirectional Gated Recurrent Unit (BiGRU), which we name TabGRU. This design synergistically captures both long-term dependencies and local sequential features in the CML signal data. The model is further enhanced by a learnable positional embedding and an attention pooling mechanism to improve its dynamic feature extraction and generalization capabilities. The model was validated on a public benchmark dataset from Gothenburg, Sweden (June-September 2015). The evaluation used 12 sub-links from two rain gauges (Torp and Barl) over a test period (August 22-31) covering approximately 10 distinct rainfall events. The proposed TabGRU model demonstrated consistent advantages, outperforming deep learning baselines and achieving high coefficients of determination (R2) at both the Torp site (0.91) and the Barl site (0.96). Furthermore, compared to the physics-based approach, TabGRU maintained higher accuracy and was particularly effective in mitigating the significant overestimation problem observed in the PL model during peak rainfall events. This evaluation confirms that the TabGRU model can effectively overcome the limitations of traditional methods, providing a robust and accurate solution for CML-based urban rainfall monitoring under the tested conditions.