相关论文: On Characterizing the Evolution of Embedding Space…

Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…

Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…

We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…

Topological accuracy in medical image segmentation is a highly important property for downstream applications such as network analysis and flow modeling in vessels or cell counting. Recently, significant methodological advancements have…

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…

Embedding-based neural topic models could explicitly represent words and topics by embedding them to a homogeneous feature space, which shows higher interpretability. However, there are no explicit constraints for the training of…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Recently, it has been shown that the trajectories of iterative…

Graph Neural Networks (GNNs) have excelled in predicting graph properties in various applications ranging from identifying trends in social networks to drug discovery and malware detection. With the abundance of new architectures and…

Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology…

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…

Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise…

In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…

It has been observed that the input space of deep neural network classifiers can exhibit `fragmentation', where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…

Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for…