Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow references to Wirtinger calculus. Unfortunately, the equivalence $\mathbb{C}^d \cong \mathbb{R}^{2d}$ becomes insufficient as soon as we need to derive custom gradient rules, e.g., to avoid differentiating "through" expensive linear algebra functions or differential equation simulators. To combat such a lack of documentation, this article surveys forward- and reverse-mode automatic differentiation with complex numbers, covering topics such as Wirtinger derivatives, a modified chain rule, and different gradient conventions while explicitly avoiding holomorphicity and the Cauchy--Riemann equations (which would be far too restrictive). To be precise, we will derive, explain, and implement a complex version of Jacobian-vector and vector-Jacobian products almost entirely with linear algebra without relying on complex analysis or differential geometry. This tutorial is a call to action, for users and developers alike, to take complex values seriously when implementing custom gradient propagation rules -- the manuscript explains how.

Group processes refer to the dynamics that occur within a group and are critical for understanding how groups function. With robots being increasingly placed within small groups, improving these processes has emerged as an important application of social robotics. Social Mediation Robots elicit behavioral change within groups by deliberately influencing the processes of groups. While research in this field has demonstrated that robots can effectively affect interpersonal dynamics, there is a notable gap in integrating these insights to develop coherent understanding and theory. We present a scoping review of literature targeting changes in social interactions between multiple humans through intentional action from robotic agents. To guide our review, we adapt the classical Input-Process-Output (I-P-O) models that we call "Mediation I-P-O model". We evaluated 1633 publications, which yielded 89 distinct social mediation concepts. We construct 11 mediation approaches robots can use to shape processes in small groups and teams. This work strives to produce generalizable insights and evaluate the extent to which the potential of social mediation through robots has been realized thus far. We hope that the proposed framework encourages a holistic approach to the study of social mediation and provides a foundation to standardize future reporting in the domain.

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is therefore to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.

Reliable uncertainty estimation has become a crucial requirement for the industrial deployment of deep learning algorithms, particularly in high-risk applications such as autonomous driving and medical diagnosis. However, mainstream uncertainty estimation methods, based on deep ensembling or Bayesian neural networks, generally impose substantial computational overhead. To address this challenge, a novel paradigm called Evidential Deep Learning (EDL) has emerged, providing reliable uncertainty estimation with minimal additional computation in a single forward pass. This survey provides a comprehensive overview of the current research on EDL, designed to offer readers a broad introduction to the field without assuming prior knowledge. Specifically, we first delve into the theoretical foundation of EDL, the subjective logic theory, and discuss its distinctions from other uncertainty estimation frameworks. We further present existing theoretical advancements in EDL from four perspectives: reformulating the evidence collection process, improving uncertainty estimation via OOD samples, delving into various training strategies, and evidential regression networks. Thereafter, we elaborate on its extensive applications across various machine learning paradigms and downstream tasks. In the end, an outlook on future directions for better performances and broader adoption of EDL is provided, highlighting potential research avenues.

This book uses the modern theory of artificial intelligence (AI) to understand human suffering or mental pain. Both humans and sophisticated AI agents process information about the world in order to achieve goals and obtain rewards, which is why AI can be used as a model of the human brain and mind. This book intends to make the theory accessible to a relatively general audience, requiring only some relevant scientific background. The book starts with the assumption that suffering is mainly caused by frustration. Frustration means the failure of an agent (whether AI or human) to achieve a goal or a reward it wanted or expected. Frustration is inevitable because of the overwhelming complexity of the world, limited computational resources, and scarcity of good data. In particular, such limitations imply that an agent acting in the real world must cope with uncontrollability, unpredictability, and uncertainty, which all lead to frustration. Fundamental in such modelling is the idea of learning, or adaptation to the environment. While AI uses machine learning, humans and animals adapt by a combination of evolutionary mechanisms and ordinary learning. Even frustration is fundamentally an error signal that the system uses for learning. This book explores various aspects and limitations of learning algorithms and their implications regarding suffering. At the end of the book, the computational theory is used to derive various interventions or training methods that will reduce suffering in humans. The amount of frustration is expressed by a simple equation which indicates how it can be reduced. The ensuing interventions are very similar to those proposed by Buddhist and Stoic philosophy, and include mindfulness meditation. Therefore, this book can be interpreted as an exposition of a computational theory justifying why such philosophies and meditation reduce human suffering.

Since the first instances of online education, where courses were uploaded to accessible and shared online platforms, this form of scaling the dissemination of human knowledge to reach a broader audience has sparked extensive discussion and widespread adoption. Recognizing that personalized learning still holds significant potential for improvement, new AI technologies have been continuously integrated into this learning format, resulting in a variety of educational AI applications such as educational recommendation and intelligent tutoring. The emergence of intelligence in large language models (LLMs) has allowed for these educational enhancements to be built upon a unified foundational model, enabling deeper integration. In this context, we propose MAIC (Massive AI-empowered Course), a new form of online education that leverages LLM-driven multi-agent systems to construct an AI-augmented classroom, balancing scalability with adaptivity. Beyond exploring the conceptual framework and technical innovations, we conduct preliminary experiments at Tsinghua University, one of China's leading universities. Drawing from over 100,000 learning records of more than 500 students, we obtain a series of valuable observations and initial analyses. This project will continue to evolve, ultimately aiming to establish a comprehensive open platform that supports and unifies research, technology, and applications in exploring the possibilities of online education in the era of large model AI. We envision this platform as a collaborative hub, bringing together educators, researchers, and innovators to collectively explore the future of AI-driven online education.

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used throughout the book and serve at a reminder of basic concepts in calculus, linear algebra and probability and also introduces some measure theoretic terminology, which can be used as a reading guide for the sections that use these tools. The introductory chapters also provide background material on matrix analysis and optimization. The latter chapter provides theoretical support to many algorithms that are used in the book, including stochastic gradient descent, proximal methods, etc. After discussing basic concepts for statistical prediction, the book includes an introduction to reproducing kernel theory and Hilbert space techniques, which are used in many places, before addressing the description of various algorithms for supervised statistical learning, including linear methods, support vector machines, decision trees, boosting, or neural networks. The subject then switches to generative methods, starting with a chapter that presents sampling methods and an introduction to the theory of Markov chains. The following chapter describe the theory of graphical models, an introduction to variational methods for models with latent variables, and to deep-learning based generative models. The next chapters focus on unsupervised learning methods, for clustering, factor analysis and manifold learning. The final chapter of the book is theory-oriented and discusses concentration inequalities and generalization bounds.

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a comprehensive introduction to two key TML techniques, persistent homology and the Mapper algorithm, with an emphasis on practical applications. Persistent homology captures multi-scale topological features such as clusters, loops, and voids, while the Mapper algorithm creates an interpretable graph summarizing high-dimensional data. To enhance accessibility, we adopt a data-centric approach, enabling readers to gain hands-on experience applying these techniques to relevant tasks. We provide step-by-step explanations, implementations, hands-on examples, and case studies to demonstrate how these tools can be applied to real-world problems. The goal is to equip researchers and practitioners with the knowledge and resources to incorporate TML into their work, revealing insights often hidden from conventional machine learning methods. The tutorial code is available at https://github.com/cakcora/TopologyForML

In this article, we propose the R2GQA system, a Retriever-Reader-Generator Question Answering system, consisting of three main components: Document Retriever, Machine Reader, and Answer Generator. The Retriever module employs advanced information retrieval techniques to extract the context of articles from a dataset of legal regulation documents. The Machine Reader module utilizes state-of-the-art natural language understanding algorithms to comprehend the retrieved documents and extract answers. Finally, the Generator module synthesizes the extracted answers into concise and informative responses to questions of students regarding legal regulations. Furthermore, we built the ViRHE4QA dataset in the domain of university training regulations, comprising 9,758 question-answer pairs with a rigorous construction process. This is the first Vietnamese dataset in the higher regulations domain with various types of answers, both extractive and abstractive. In addition, the R2GQA system is the first system to offer abstractive answers in Vietnamese. This paper discusses the design and implementation of each module within the R2GQA system on the ViRHE4QA dataset, highlighting their functionalities and interactions. Furthermore, we present experimental results demonstrating the effectiveness and utility of the proposed system in supporting the comprehension of students of legal regulations in higher education settings. In general, the R2GQA system and the ViRHE4QA dataset promise to contribute significantly to related research and help students navigate complex legal documents and regulations, empowering them to make informed decisions and adhere to institutional policies effectively. Our dataset is available for research purposes.

Recently, the design of wireless receivers using deep neural networks (DNNs), known as deep receivers, has attracted extensive attention for ensuring reliable communication in complex channel environments. To adapt quickly to dynamic channels, online learning has been adopted to update the weights of deep receivers with over-the-air data (e.g., pilots). However, the fragility of neural models and the openness of wireless channels expose these systems to malicious attacks. To this end, understanding these attack methods is essential for robust receiver design. In this paper, we propose a transfer-based adversarial poisoning attack method for online receivers.Without knowledge of the attack target, adversarial perturbations are injected to the pilots, poisoning the online deep receiver and impairing its ability to adapt to dynamic channels and nonlinear effects. In particular, our attack method targets Deep Soft Interference Cancellation (DeepSIC)[1] using online meta-learning. As a classical model-driven deep receiver, DeepSIC incorporates wireless domain knowledge into its architecture. This integration allows it to adapt efficiently to time-varying channels with only a small number of pilots, achieving optimal performance in a multi-input and multi-output (MIMO) scenario.The deep receiver in this scenario has a number of applications in the field of wireless communication, which motivates our study of the attack methods targeting it.Specifically, we demonstrate the effectiveness of our attack in simulations on synthetic linear, synthetic nonlinear, static, and COST 2100 channels. Simulation results indicate that the proposed poisoning attack significantly reduces the performance of online receivers in rapidly changing scenarios.