Online restless multi-armed bandits (RMABs) typically assume that each arm follows a stationary Markov Decision Process (MDP) with fixed state transitions and rewards. However, in real-world applications like healthcare and recommendation systems, these assumptions often break due to non-stationary dynamics, posing significant challenges for traditional RMAB algorithms. In this work, we specifically consider $N$-armd RMAB with non-stationary transition constrained by bounded variation budgets $B$. Our proposed \rmab\; algorithm integrates sliding window reinforcement learning (RL) with an upper confidence bound (UCB) mechanism to simultaneously learn transition dynamics and their variations. We further establish that \rmab\; achieves $\widetilde{\mathcal{O}}(N^2 B^{\frac{1}{4}} T^{\frac{3}{4}})$ regret bound by leveraging a relaxed definition of regret, providing a foundational theoretical framework for non-stationary RMAB problems for the first time.

Scientific progress is tightly coupled to the emergence of new research tools. Today, machine learning (ML)-especially deep learning (DL)-has become a transformative instrument for quantum science and technology. Owing to the intrinsic complexity of quantum systems, DL enables efficient exploration of large parameter spaces, extraction of patterns from experimental data, and data-driven guidance for research directions. These capabilities already support tasks such as refining quantum control protocols and accelerating the discovery of materials with targeted quantum properties, making ML/DL literacy an essential skill for the next generation of quantum scientists. At the same time, DL's power brings risks: models can overfit noisy data, obscure causal structure, and yield results with limited physical interpretability. Recognizing these limitations and deploying mitigation strategies is crucial for scientific rigor. These lecture notes provide a comprehensive, graduate-level introduction to DL for quantum applications, combining conceptual exposition with hands-on examples. Organized as a progressive sequence, they aim to equip readers to decide when and how to apply DL effectively, to understand its practical constraints, and to adapt AI methods responsibly to problems across quantum physics, chemistry, and engineering.

Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC) such as simulated annealing or parallel tempering, one assumes homogeneous (equilibrium) temperature profiles across input. This instance independent approach was shown to be ineffective for the hardest benchmarks near a computational phase transition when the so-called overlap-gap-property holds. In these regimes conventional MCMC struggles to unfreeze rigid variables, escape suboptimal basins of attraction, and sample high-quality and diverse solutions. In order to mitigate these challenges, Nonequilibrium Nonlocal Monte Carlo (NMC) algorithms were proposed that leverage inhomogeneous temperature profiles thereby accelerating exploration of the configuration space without compromising its exploitation. Here, we employ deep reinforcement learning (RL) to train the nonlocal transition policies of NMC which were previously designed phenomenologically. We demonstrate that the resulting solver can be trained solely by observing energy changes of the configuration space exploration as RL rewards and the local minimum energy landscape geometry as RL states. We further show that the trained policies improve upon the standard MCMC-based and nonlocal simulated annealing on hard uniform random and scale-free random 4-SAT benchmarks in terms of residual energy, time-to-solution, and diversity of solutions metrics.

Abstract: With the advent of Joint Embedding Predictive Architectures (JEPAs), which appear to be more capable than reconstruction-based methods, this paper introduces a novel technique for creating world models using continuous-time dynamic systems from arbitrary observation data. The proposed method integrates sequence embeddings with neural ordinary differential equations (neural ODEs). It employs loss functions that enforce contractive embeddings and Lipschitz constants in state transitions to construct a well-organized latent state space. The approach's effectiveness is demonstrated through the generation of structured latent state-space models for a simple pendulum system using only image data. This opens up a new technique for developing more general control algorithms and estimation techniques with broad applications in robotics.

This work demonstrates how the concept of the entropic potential of events -- a parameter quantifying the influence of discrete events on the expected future entropy of a system -- can enhance uncertainty quantification, decision-making, and interpretability in artificial intelligence (AI). Building on its original formulation in physics, the framework is adapted for AI by introducing an event-centric measure that captures how actions, observations, or other discrete occurrences impact uncertainty at future time horizons. Both the original and AI-adjusted definitions of entropic potential are formalized, with the latter emphasizing conditional expectations to account for counterfactual scenarios. Applications are explored in policy evaluation, intrinsic reward design, explainable AI, and anomaly detection, highlighting the metric's potential to unify and strengthen uncertainty modeling in intelligent systems. Conceptual examples illustrate its use in reinforcement learning, Bayesian inference, and anomaly detection, while practical considerations for computation in complex AI models are discussed. The entropic potential framework offers a theoretically grounded, interpretable, and versatile approach to managing uncertainty in AI, bridging principles from thermodynamics, information theory, and machine learning.

Background: Cirrhosis is a progressive liver disease with high mortality and frequent complications, notably acute kidney injury (AKI), which occurs in up to 50% of hospitalized patients and worsens outcomes. AKI stems from complex hemodynamic, inflammatory, and metabolic changes, making early detection essential. Many predictive tools lack accuracy, interpretability, and alignment with intensive care unit (ICU) workflows. This study developed an interpretable machine learning model for early AKI prediction in critically ill patients with cirrhosis. Methods: We conducted a retrospective analysis of the MIMIC-IV v2.2 database, identifying 1240 adult ICU patients with cirrhosis and excluding those with ICU stays under 48 hours or missing key data. Laboratory and physiological variables from the first 48 hours were extracted. The pipeline included preprocessing, missingness filtering, LASSO feature selection, and SMOTE class balancing. Six algorithms-LightGBM, CatBoost, XGBoost, logistic regression, naive Bayes, and neural networks-were trained and evaluated using AUROC, accuracy, F1-score, sensitivity, specificity, and predictive values. Results: LightGBM achieved the best performance (AUROC 0.808, 95% CI 0.741-0.856; accuracy 0.704; NPV 0.911). Key predictors included prolonged partial thromboplastin time, absence of outside-facility 20G placement, low pH, and altered pO2, consistent with known cirrhosis-AKI mechanisms and suggesting actionable targets. Conclusion: The LightGBM-based model enables accurate early AKI risk stratification in ICU patients with cirrhosis using routine clinical variables. Its high negative predictive value supports safe de-escalation for low-risk patients, and interpretability fosters clinician trust and targeted prevention. External validation and integration into electronic health record systems are warranted.

The automatic curation of discussion forums in online courses requires constant updates, making frequent retraining of Large Language Models (LLMs) a resource-intensive process. To circumvent the need for costly fine-tuning, this paper proposes and evaluates the use of Bayesian fusion. The approach combines the multidimensional classification scores of a pre-trained generic LLM with those of a classifier trained on local data. The performance comparison demonstrated that the proposed fusion improves the results compared to each classifier individually, and is competitive with the LLM fine-tuning approach

Structural Causal Models (SCM) framework introduced by Pearl [2009].

Instead, we impose a condition on the residual variances that is closely related to previous work on linear models with equal variances.

The bound is based on a novel parametric form of the Chebyshev-Cantelli inequality (a.k.a.