Related papers: Geometric deep learning approach to knot theory
We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial $J(q)$, and the four-dimensional invariants are the Khovanov…
Graph Neural Networks (GNNs), a generalization of deep neural networks on graph data have been widely used in various domains, ranging from drug discovery to recommender systems. However, GNNs on such applications are limited when there are…
In this paper, we explore a novel model reusing task tailored for graph neural networks (GNNs), termed as "deep graph reprogramming". We strive to reprogram a pre-trained GNN, without amending raw node features nor model parameters, to…
In the last years, deep learning has shown to be a game-changing technology in artificial intelligence thanks to the numerous successes it reached in diverse application fields. Among others, the use of deep learning for the recommendation…
We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…
Deep learning is a group of exciting new technologies for neural networks. Through a combination of advanced training techniques and neural network architectural components, it is now possible to create neural networks that can handle…
The goal of multi-modal learning is to use complimentary information on the relevant task provided by the multiple modalities to achieve reliable and robust performance. Recently, deep learning has led significant improvement in multi-modal…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…
Graphs play an important role in many applications. Recently, Graph Neural Networks (GNNs) have achieved promising results in graph analysis tasks. Some state-of-the-art GNN models have been proposed, e.g., Graph Convolutional Networks…
We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…
Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…
Graph neural network (GNN) has gained increasing popularity in recent years owing to its capability and flexibility in modeling complex graph structure data. Among all graph learning methods, hypergraph learning is a technique for exploring…
In recent years, with the rapid enhancement of computing power, deep learning methods have been widely applied in wireless networks and achieved impressive performance. To effectively exploit the information of graph-structured data as well…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…
We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered…
Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work…
Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…