Related papers: Geometric deep learning approach to knot theory
In recent years, with the rapid development of computer information technology, the development of artificial intelligence has been accelerating. The traditional geometry recognition technology is relatively backward and the recognition…
In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
We test the efficiency of applying Geometric Deep Learning to the problems in low-dimensional topology in a certain simple setting. Specifically, we consider the class of 3-manifolds described by plumbing graphs and use Graph Neural…
Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large…
In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of…
In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast…
Geometric deep learning provides a principled and versatile manner for the integration of imaging and non-imaging modalities in the medical domain. Graph Convolutional Networks (GCNs) in particular have been explored on a wide variety of…
Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…
This paper investigates the feasibility of using Graph Neural Networks (GNNs) for classical motion planning problems. We propose guiding both continuous and discrete planning algorithms using GNNs' ability to robustly encode the topology of…
Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…
Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been…
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…
Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
Graph-structured data provide a comprehensive description of complex systems, encompassing not only the interactions among nodes but also the intrinsic features that characterize these nodes. These features play a fundamental role in the…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…
We review recent efforts to machine learn relations between knot invariants. Because these knot invariants have meaning in physics, we explore aspects of Chern-Simons theory and higher dimensional gauge theories. The goal of this work is to…
Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral…