Related papers: Generating valid Euclidean distance matrices

Unpaired image-to-image translation has been applied successfully to natural images but has received very little attention for manifold-valued data such as in diffusion tensor imaging (DTI). The non-Euclidean nature of DTI prevents current…

Generative Adversarial Networks (GANs) have been successful in producing outstanding results in areas as diverse as image, video, and text generation. Building on these successes, a large number of empirical studies have validated the…

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for…

A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…

Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no model…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Generating molecules with desired chemical properties presents a critical challenge in fields such as chemical synthesis and drug discovery. Recent advancements in artificial intelligence (AI) and deep learning have significantly…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

Learning distance functions between complex objects, such as the Wasserstein distance to compare point sets, is a common goal in machine learning applications. However, functions on such complex objects (e.g., point sets and graphs) are…

Point-clouds are a popular choice for vision and graphics tasks due to their accurate shape description and direct acquisition from range-scanners. This demands the ability to synthesize and reconstruct high-quality point-clouds. Current…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

We present TetGAN, a convolutional neural network designed to generate tetrahedral meshes. We represent shapes using an irregular tetrahedral grid which encodes an occupancy and displacement field. Our formulation enables defining…

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…

While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on…

Generative Adversarial Networks (GANs) are currently the method of choice for generating visual data. Certain GAN architectures and training methods have demonstrated exceptional performance in generating realistic synthetic images (in…

One of the main challenges in the parametrization of geological models is the ability to capture complex geological structures often observed in the subsurface. In recent years, generative adversarial networks (GAN) were proposed as an…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…

Capsule networks offer interesting properties and provide an alternative to today's deep neural network architectures. However, recent approaches have failed to consistently achieve competitive results across different image datasets. We…

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…