Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present a general framework of runtime verification of algorithmic fairness for systems whose models are unknown, but are assumed to have a Markov chain structure, with or without full observation of the state space. We introduce a specification language that can model many common algorithmic fairness properties, such as demographic parity, equal opportunity, and social burden. We build monitors that observe a long sequence of events as generated by a given system, and output, after each observation, a quantitative estimate of how fair or biased the system was on that run until that point in time. The estimate is proven to be correct modulo a variable error bound and a given confidence level, where the error bound gets tighter as the observed sequence gets longer. We present two categories of monitoring algorithms, namely ones with a uniform error bound across all time points, and ones with weaker non-uniform, pointwise error bounds at different time points. Our monitoring algorithms use statistical tools that are adapted to suit the dynamic requirements of monitoring and the special needs of the fairness specifications. Using a prototype implementation, we show how we can monitor if a bank is fair in giving loans to applicants from different social backgrounds, and if a college is fair in admitting students while maintaining a reasonable financial burden on the society. In these experiments, our monitors took less than a millisecond to update their verdicts after each observation.

The proliferation of ride-hailing aggregator platforms presents significant growth opportunities for ride-service providers by increasing order volume and gross merchandise value (GMV). On most ride-hailing aggregator platforms, service providers that offer lower fares are ranked higher in listings and, consequently, are more likely to be selected by passengers. This competitive ranking mechanism creates a strong incentive for service providers to adopt coupon strategies that lower prices to secure a greater number of orders, as order volume directly influences their long-term viability and sustainability. Thus, designing an effective coupon strategy that can dynamically adapt to market fluctuations while optimizing order acquisition under budget constraints is a critical research challenge. However, existing studies in this area remain scarce. To bridge this gap, we propose FCA-RL, a novel reinforcement learning-based subsidy strategy framework designed to rapidly adapt to competitors' pricing adjustments. Our approach integrates two key techniques: Fast Competition Adaptation (FCA), which enables swift responses to dynamic price changes, and Reinforced Lagrangian Adjustment (RLA), which ensures adherence to budget constraints while optimizing coupon decisions on new price landscape. Furthermore, we introduce RideGym, the first dedicated simulation environment tailored for ride-hailing aggregators, facilitating comprehensive evaluation and benchmarking of different pricing strategies without compromising real-world operational efficiency. Experimental results demonstrate that our proposed method consistently outperforms baseline approaches across diverse market conditions, highlighting its effectiveness in subsidy optimization for ride-hailing service providers.

By recursively nesting sums and products, probabilistic circuits have emerged in recent years as an attractive class of generative models as they enjoy, for instance, polytime marginalization of random variables. In this work we study these machine learning models using the framework of quantum information theory, leading to the introduction of positive unital circuits (PUnCs), which generalize circuit evaluations over positive real-valued probabilities to circuit evaluations over positive semi-definite matrices. As a consequence, PUnCs strictly generalize probabilistic circuits as well as recently introduced circuit classes such as PSD circuits.

In many real-world planning tasks, agents must tackle uncertainty about the environment's state and variability in the outcomes of any chosen policy. We address both forms of uncertainty as a first step toward safer algorithms in partially observable settings. Specifically, we extend Distributional Reinforcement Learning (DistRL)--which models the entire return distribution for fully observable domains--to Partially Observable Markov Decision Processes (POMDPs), allowing an agent to learn the distribution of returns for each conditional plan. Concretely, we introduce new distributional Bellman operators for partial observability and prove their convergence under the supremum p-Wasserstein metric. We also propose a finite representation of these return distributions via ψ -vectors, generalizing the classical α -vectors in POMDP solvers. Building on this, we develop Distributional Point-Based V alue Iteration (DPBVI), which integrates ψ -vectors into a standard point-based backup procedure-- bridging DistRL and POMDP planning . By tracking return distributions, DPBVI lays the foundation for future risk-sensitive control in domains where rare, high-impact events must be carefully managed. We provide source code to foster further research in robust decision-making under partial observability.

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic) gradient descent, and related topics into dynamical statements. We also tackle three concrete challenges. First, we consider the process of information propagation through a neural network, i.e., we study the input-output map for different architectures. We explain the universal embedding property for augmented neural ODEs representing arbitrary functions of given regularity, the classification of multilayer perceptrons and neural ODEs in terms of suitable function classes, and the memory-dependence in neural delay equations. Second, we consider the training aspect of neural networks dynamically. We describe a dynamical systems perspective on gradient descent and study stability for overdetermined problems. We then extend this analysis to the overparameterized setting and describe the edge of stability phenomenon, also in the context of possible explanations for implicit bias. For stochastic gradient descent, we present stability results for the overparameterized setting via Lyapunov exponents of interpolation solutions. Third, we explain several results regarding mean-field limits of neural networks. We describe a result that extends existing techniques to heterogeneous neural networks involving graph limits via digraph measures. This shows how large classes of neural networks naturally fall within the framework of Kuramoto-type models on graphs and their large-graph limits. Finally, we point out that similar strategies to use dynamics to study explainable and reliable AI can also be applied to settings such as generative models or fundamental issues in gradient training methods, such as backpropagation or vanishing/exploding gradients.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

The limitations of the Poisson process were more evident when modeling high-speed network traffic, particularly real-time data traffic modeling for next-generation networks. For example, Liji et al. [85] demonstrated that the Stationary Poison Increment Process can only model Short Range Dependence (SRD) but not LRD. To address this limitation, the authors proposed using second-order self-similarity models, such as fractional Gaussian noise and fractional ARIMA processes, as a more appropriate approach. In the meantime, researchers also explored modeling data center network traffic using poisson processes. To better simulate realistic traffic in data center environments, the generation of flow-level network traffic matrices based on the poisson shot-noise model is proposed in [172]. By incorporating factors such as flow arrival rates, intra-rack traffic ratios, flow sizes and durations, the poisson shot-noise process offers a more accurate representation of traffic patterns in data centers. B. Weibull distribution As discussed earlier, the limitations of Poisson processes for modeling network traffic led to exploring other distributions. One such promising model was the Weibull distribution, mainly due to its flexibility to model both heavy and non-heavy tailed distributions [11].

Support and resistance (SR) levels are central to technical analysis, guiding traders in entry, exit, and risk management. Despite widespread use, traditional SR identification methods often fail to adapt to the complexities of modern, volatile markets. Recent research has introduced machine learning techniques to address the following challenges, yet most focus on price prediction rather than structural level identification. This paper presents DeepSupp, a new deep learning approach for detecting financial support levels using multi-head attention mechanisms to analyze spatial correlations and market microstructure relationships. Deep-Supp integrates advanced feature engineering, constructing dynamic correlation matrices that capture evolving market relationships, and employs an attention-based autoencoder for robust representation learning. The final support levels are extracted through unsupervised clustering, leveraging DBSCAN to identify significant price thresholds. Comprehensive evaluations on S&P 500 tickers demonstrate that DeepSupp outperforms six baseline methods, achieving state-of-the-art performance across six financial metrics, including essential support accuracy and market regime sensitivity. With consistent results across diverse market conditions, DeepSupp addresses critical gaps in SR level detection, offering a scalable and reliable solution for modern financial analysis. Our approach highlights the potential of attention-based architectures to uncover nuanced market patterns and improve technical trading strategies.

Existing visual model-based reinforcement learning (MBRL) algorithms with observation reconstruction often suffer from information conflicts, making it difficult to learn compact representations and hence result in less robust policies, especially in the presence of task-irrelevant visual distractions. In this paper, we first reveal that the information conflicts in current visual MBRL algorithms stem from visual representation learning and latent dynamics modeling with an information-theoretic perspective. Based on this finding, we present a new algorithm to resolve information conflicts for visual MBRL, named MInCo, which mitigates information conflicts by leveraging negative-free contrastive learning, aiding in learning invariant representation and robust policies despite noisy observations. To prevent the dominance of visual representation learning, we introduce time-varying reweighting to bias the learning towards dynamics modeling as training proceeds. We evaluate our method on several robotic control tasks with dynamic background distractions. Our experiments demonstrate that MInCo learns invariant representations against background noise and consistently outperforms current state-of-the-art visual MBRL methods. Code is available at https://github.com/ShiguangSun/minco.

--Next activity prediction represents a fundamental challenge for optimizing business processes in service-oriented architectures such as microservices environments, distributed enterprise systems, and cloud-native platforms, which enables proactive resource allocation and dynamic service composition. Despite the prevalence of sequence-based methods, these approaches fail to capture non-sequential relationships that arise from parallel executions and conditional dependencies. Even though graph-based approaches address structural preservation, they suffer from homogeneous representations and static structures that apply uniform modeling strategies regardless of individual process complexity characteristics. T o address these limitations, we introduce RLHGNN, a novel framework that transforms event logs into heterogeneous process graphs with three distinct edge types grounded in established process mining theory. Our approach creates four flexible graph structures by selectively combining these edges to accommodate different process complexities, and employs reinforcement learning formulated as a Markov Decision Process to automatically determine the optimal graph structure for each specific process instance. RLHGNN then applies heterogeneous graph convolution with relation-specific aggregation strategies to effectively predict the next activity. This adaptive methodology enables precise modeling of both sequential and non-sequential relationships in service interactions. Comprehensive evaluation on six real-world datasets demonstrates that RLHGNN consistently outperforms state-of-the-art approaches. Furthermore, it maintains an inference latency of approximately 1 ms per prediction, representing a highly practical solution suitable for real-time business process monitoring applications. Service-oriented architectures have fundamentally transformed modern business process implementation, which enables distributed services to coordinate through well-defined interfaces for delivering substantial business value [1], [2]. Jiaxing Wang, Yifeng Y u, Jiahan Song, Bin Cao, and Jing Fan are with the College of Computer Science and Technology, Zhejiang University of Technology, 310023, Hangzhou, China, and also with Zhejiang Key Laboratory of Visual Information Intelligent Processing, 310023, Hangzhou, China (email: wjx@zjut.edu.cn,