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In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating factor methods. A second-order scheme is first proposed, which is rigorously proved to be energy-preserving. By using the energy methods, we analyze its optimal convergence in the $H^1$ norm without any restrictions on the grid ratio, where a novel technique and an improved induction argument are proposed to overcome the difficulty posed by the unavailability of a priori $L^\infty$ estimates of numerical solutions. Based on the integrating factor Runge-Kutta methods, we extend the proposed scheme to arbitrarily high order, which is also linear and conservative. Numerical experiments are presented to confirm the theoretical analysis and demonstrate the advantages of the proposed methods.

The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider neural network (NN) learning algorithms, and in particular deep-learning architectures, the models are often trained in a supervised manner. Consequently, the learned relationship between the input and the output must remain valid during the model's deployment. If this stationarity assumption holds, we can conclude that the NN generates accurate predictions. Otherwise, the retraining or rebuilding of the model is required. We propose to consider the latent feature representation of the data (called "embedding") generated by the NN for determining the time point when the data stream starts being nonstationary. To be precise, we monitor embeddings by applying multivariate control charts based on the calculation of the data depth and normalized ranks. The performance of the introduced method is evaluated using various NNs with different underlying data formats.

With nearly 2.5m users, onion services have become the prominent part of the darkweb. Over the last five years alone, the number of onion domains has increased 20x, reaching more than 700k unique domains in January 2022. As onion services host various types of illicit content, they have become a valuable resource for darkweb research and an integral part of e-crime investigation and threat intelligence. However, this content is largely un-indexed by today's search engines and researchers have to rely on outdated or manually-collected datasets that are limited in scale, scope, or both. To tackle this problem, we built Dizzy: An open-source crawling and analysis system for onion services. Dizzy implements novel techniques to explore, update, check, and classify hidden services at scale, without overwhelming the Tor network. We deployed Dizzy in April 2021 and used it to analyze more than 63.3m crawled onion webpages, focusing on domain operations, web content, cryptocurrency usage, and web graph. Our main findings show that onion services are unreliable due to their high churn rate, have a relatively small number of reachable domains that are often similar and illicit, enjoy a growing underground cryptocurrency economy, and have a topologically different graph structure than the regular web.

We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius. To avoid this limitation, our approach is based on higher-order semi-implicit numerical schemes already validated on dissipative systems [3] and for magnetic fields pointing in a fixed direction [9, 10, 12]. It hinges on asymptotic insights gained in [11] at the continuous level. Thus, when the magnitude of the external magnetic field is large, this scheme provides a consistent approximation of the guiding-center system taking into account curvature and variation of the magnetic field. Finally, we carry out a theoretical proof of consistency and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.

Nowadays Artificial Intelligence (AI) has become a fundamental component of healthcare applications, both clinical and remote, but the best performing AI systems are often too complex to be self-explaining. Explainable AI (XAI) techniques are defined to unveil the reasoning behind the system's predictions and decisions, and they become even more critical when dealing with sensitive and personal health data. It is worth noting that XAI has not gathered the same attention across different research areas and data types, especially in healthcare. In particular, many clinical and remote health applications are based on tabular and time series data, respectively, and XAI is not commonly analysed on these data types, while computer vision and Natural Language Processing (NLP) are the reference applications. To provide an overview of XAI methods that are most suitable for tabular and time series data in the healthcare domain, this paper provides a review of the literature in the last 5 years, illustrating the type of generated explanations and the efforts provided to evaluate their relevance and quality. Specifically, we identify clinical validation, consistency assessment, objective and standardised quality evaluation, and human-centered quality assessment as key features to ensure effective explanations for the end users. Finally, we highlight the main research challenges in the field as well as the limitations of existing XAI methods.

In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks with state-of-the-art performance. The data is generally represented in the Euclidean space in these domains. Various other domains conform to non-Euclidean space, for which graph is an ideal representation. Graphs are suitable for representing the dependencies and interrelationships between various entities. Traditionally, handcrafted features for graphs are incapable of providing the necessary inference for various tasks from this complex data representation. Recently, there is an emergence of employing various advances in deep learning to graph data-based tasks. This article provides a comprehensive survey of graph neural networks (GNNs) in each learning setting: supervised, unsupervised, semi-supervised, and self-supervised learning. Taxonomy of each graph based learning setting is provided with logical divisions of methods falling in the given learning setting. The approaches for each learning task are analyzed from both theoretical as well as empirical standpoints. Further, we provide general architecture guidelines for building GNNs. Various applications and benchmark datasets are also provided, along with open challenges still plaguing the general applicability of GNNs.

Invariant approaches have been remarkably successful in tackling the problem of domain generalization, where the objective is to perform inference on data distributions different from those used in training. In our work, we investigate whether it is possible to leverage domain information from the unseen test samples themselves. We propose a domain-adaptive approach consisting of two steps: a) we first learn a discriminative domain embedding from unsupervised training examples, and b) use this domain embedding as supplementary information to build a domain-adaptive model, that takes both the input as well as its domain into account while making predictions. For unseen domains, our method simply uses few unlabelled test examples to construct the domain embedding. This enables adaptive classification on any unseen domain. Our approach achieves state-of-the-art performance on various domain generalization benchmarks. In addition, we introduce the first real-world, large-scale domain generalization benchmark, Geo-YFCC, containing 1.1M samples over 40 training, 7 validation, and 15 test domains, orders of magnitude larger than prior work. We show that the existing approaches either do not scale to this dataset or underperform compared to the simple baseline of training a model on the union of data from all training domains. In contrast, our approach achieves a significant improvement.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with an arbitrary depth. Although the primitive graph neural networks have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.

Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.