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In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social interactions. Learning embedded representations for nodes involves a process that translates network structures into more simplified spaces, thereby enabling the application of machine learning approaches designed for vector data to be extended to network data. Nevertheless, there remains a need to delve into methods for learning embedded representations that prioritize structural aspects. This research introduces HyperS2V, a node embedding approach that centers on the structural similarity within hyper networks. Initially, we establish the concept of hyper-degrees to capture the structural properties of nodes within hyper networks. Subsequently, a novel function is formulated to measure the structural similarity between different hyper-degree values. Lastly, we generate structural embeddings utilizing a multi-scale random walk framework. Moreover, a series of experiments, both intrinsic and extrinsic, are performed on both toy and real networks. The results underscore the superior performance of HyperS2V in terms of both interpretability and applicability to downstream tasks.

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of deep neural networks remains uncertain. For ReLU (Rectified Linear Unit) networks with piecewise linear activations, the number of linear convex regions serves as a natural metric to gauge the network's expressivity. In this paper, we count the number of linear convex regions in deep neural networks based on ReLU. In particular, we prove that for any one-dimensional input, there exists a minimum threshold for the number of neurons required to express it. We also empirically observe that for the same network, intricate inputs hinder its capacity to express linear regions. Furthermore, we unveil the iterative refinement process of decision boundaries in ReLU networks during training. We aspire for our research to serve as an inspiration for network optimization endeavors and aids in the exploration and analysis of the behaviors exhibited by deep networks.

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this challenge, this paper proposes a deep operator learning-based framework that requires a limited high-fidelity dataset for training. We introduce a novel physics-guided, bi-fidelity, Fourier-featured Deep Operator Network (DeepONet) framework that effectively combines low and high-fidelity datasets, leveraging the strengths of each. In our methodology, we began by designing a physics-guided Fourier-featured DeepONet, drawing inspiration from the intrinsic physical behavior of the target solution. Subsequently, we train this network to primarily learn the low-fidelity solution, utilizing an extensive dataset. This process ensures a comprehensive grasp of the foundational solution patterns. Following this foundational learning, the low-fidelity deep operator network's output is enhanced using a physics-guided Fourier-featured residual deep operator network. This network refines the initial low-fidelity output, achieving the high-fidelity solution by employing a small high-fidelity dataset for training. Notably, in our framework, we employ the Fourier feature network as the Trunk network for the DeepONets, given its proficiency in capturing and learning the oscillatory nature of the target solution with high precision. We validate our approach using a well-known 2D benchmark cylinder problem, which aims to predict the time trajectories of lift and drag coefficients. The results highlight that the physics-guided Fourier-featured deep operator network, serving as a foundational building block of our framework, possesses superior predictive capability for the lift and drag coefficients compared to its data-driven counterparts.

Using model weights pretrained on a high-resource language as a warm start can reduce the need for data and compute to obtain high-quality language models for other, especially low-resource, languages. However, if we want to use a new tokenizer specialized for the target language, we cannot transfer the source model's embedding matrix. In this paper, we propose FOCUS - Fast Overlapping Token Combinations Using Sparsemax, a novel embedding initialization method that initializes the embedding matrix effectively for a new tokenizer based on information in the source model's embedding matrix. FOCUS represents newly added tokens as combinations of tokens in the overlap of the source and target vocabularies. The overlapping tokens are selected based on semantic similarity in an auxiliary static token embedding space. We focus our study on using the multilingual XLM-R as a source model and empirically show that FOCUS outperforms random initialization and previous work in language modeling and on a range of downstream tasks (NLI, QA, and NER).

Many annotation tasks in natural language processing are highly subjective in that there can be different valid and justified perspectives on what is a proper label for a given example. This also applies to the judgment of argument quality, where the assignment of a single ground truth is often questionable. At the same time, there are generally accepted concepts behind argumentation that form a common ground. To best represent the interplay of individual and shared perspectives, we consider a continuum of approaches ranging from models that fully aggregate perspectives into a majority label to "share nothing"-architectures in which each annotator is considered in isolation from all other annotators. In between these extremes, inspired by models used in the field of recommender systems, we investigate the extent to which architectures that include layers to model the relations between different annotators are beneficial for predicting single-annotator labels. By means of two tasks of argument quality classification (argument concreteness and validity/novelty of conclusions), we show that recommender architectures increase the averaged annotator-individual F$_1$-scores up to $43\%$ over a majority label model. Our findings indicate that approaches to subjectivity can benefit from relating individual perspectives.

Adversarial examples in machine learning has emerged as a focal point of research due to their remarkable ability to deceive models with seemingly inconspicuous input perturbations, potentially resulting in severe consequences. In this study, we embark on a comprehensive exploration of adversarial machine learning models, shedding light on their intrinsic complexity and interpretability. Our investigation reveals intriguing links between machine learning model complexity and Einstein's theory of special relativity, all through the lens of entanglement. While our work does not primarily center on quantum entanglement, we instead define the entanglement correlations we have discovered to be computational, and demonstrate that distant feature samples can be entangled, strongly resembling entanglement correlation in the quantum realm. This revelation bestows fresh insights for understanding the phenomenon of emergent adversarial examples in modern machine learning, potentially paving the way for more robust and interpretable models in this rapidly evolving field.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

In contrast to batch learning where all training data is available at once, continual learning represents a family of methods that accumulate knowledge and learn continuously with data available in sequential order. Similar to the human learning process with the ability of learning, fusing, and accumulating new knowledge coming at different time steps, continual learning is considered to have high practical significance. Hence, continual learning has been studied in various artificial intelligence tasks. In this paper, we present a comprehensive review of the recent progress of continual learning in computer vision. In particular, the works are grouped by their representative techniques, including regularization, knowledge distillation, memory, generative replay, parameter isolation, and a combination of the above techniques. For each category of these techniques, both its characteristics and applications in computer vision are presented. At the end of this overview, several subareas, where continuous knowledge accumulation is potentially helpful while continual learning has not been well studied, are discussed.

Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.