相关论文: Growing hyperbolic networks beyond two dimensions:…

Deep Convolutional Networks (ConvNets) are fundamental to, besides large-scale visual recognition, a lot of vision tasks. As the primary goal of the ConvNets is to characterize complex boundaries of thousands of classes in a…

Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…

We study typical distances in a geometric random graph on the hyperbolic plane. Introduced by Krioukov et al.~\cite{ar:Krioukov} as a model for complex networks, $N$ vertices are drawn randomly within a bounded subset of the hyperbolic…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden…

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…

The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…

The search for the model or ingredients that describe the current vision of our cosmos has led to the creation of a set of highly favorable experiments, and therefore a great flow of information. Due to this torrent of information and the…

We revisit the topic of self-organized criticality (SOC) in simple statistical graph models, with the purpose of capturing essential processes leading to the emergence of macroscopic spacetime from the microscopic dynamics in loop quantum…

Hyperbolicity is a graph parameter related to how much a graph resembles a tree with respect to distances. Its computation is challenging as the main approaches consist in scanning all quadruples of the graph or using fast matrix…

Learning models of complex spatial density functions, representing the steady-state density of mobile nodes moving on a two-dimensional terrain, can assist in network design and optimization problems, e.g., by accelerating the computation…

We study the link structure of on-line social networks (OSNs), and introduce a new model for such networks which may help infer their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs nodes are identified with points in…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…

The Self-Optimization (SO) model is a useful computational model for investigating self-organization in "soft" Artificial life (ALife) as it has been shown to be general enough to model various complex adaptive systems. So far, existing…

Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…

Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks.…