Related papers: Generating valid Euclidean distance matrices

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Recent work has explored methods for learning continuous vector space word representations reflecting the underlying semantics of words. Simple vector space arithmetic using cosine distances has been shown to capture certain types of…

Drawing inspiration from the achievements of natural language processing, we adopt self-supervised learning and utilize an equivariant graph neural network to develop a unified platform designed for training generative models capable of…

The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…

The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

Discovery of atomistic systems with desirable properties is a major challenge in chemistry and material science. Here we introduce a novel, autoregressive, convolutional deep neural network architecture that generates molecular equilibrium…

In the field of computer vision, unsupervised learning for 2D object generation has advanced rapidly in the past few years. However, 3D object generation has not garnered the same attention or success as its predecessor. To facilitate novel…

Generating realistic graph-structured data is challenging due to discrete structures, variable sizes, and class-specific connectivity patterns that resist conventional generative modelling. While recent graph generation methods employ…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Euclidean Distance Matrix (EDM), which consists of pairwise squared Euclidean distances of a given point configuration, finds many applications in modern machine learning. This paper considers the setting where only a set of anchor nodes is…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…

Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an…

Generative adversarial networks (GANs) are a machine learning technique capable of producing high-quality synthetic images. In the field of materials science, when a crystallographic dataset includes inadequate or difficult-to-obtain…

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…

Understanding the impact of neutrino masses on the evolution of Universe is a crucial aspect of modern cosmology. Due to their large free streaming lengths, neutrinos significantly influence the formation of cosmic structures at non-linear…

This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an…

Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which…