Related papers: Geometric Generative Models based on Morphological…

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

Ensuring proper generalization is a critical challenge in applying data-driven methods for solving inverse problems in imaging, as neural networks reconstructing an image must perform well across varied datasets and acquisition geometries.…

Graph Convolutional Networks (GCNs) have already demonstrated their powerful ability to model the irregular data, e.g., skeletal data in human action recognition, providing an exciting new way to fuse rich structural information for nodes…

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Current generative frameworks use end-to-end learning and generate images by sampling from uniform noise distribution. However, these approaches ignore the most basic principle of image formation: images are product of: (a) Structure: the…

Among the wide variety of image generative models, two models stand out: Variational Auto Encoders (VAE) and Generative Adversarial Networks (GAN). GANs can produce realistic images, but they suffer from mode collapse and do not provide…

$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, thereby facilitating…

Quantum generative modeling is among the promising candidates for achieving a practical advantage in data analysis. Nevertheless, one key challenge is to generate large-size images comparable to those generated by their classical…

Facial recognition using deep convolutional neural networks relies on the availability of large datasets of face images. Many examples of identities are needed, and for each identity, a large variety of images are needed in order for the…

Generative Adversarial Networks (GANs) have shown impressive performance in generating photo-realistic images. They fit generative models by minimizing certain distance measure between the real image distribution and the generated data…

We propose, implement, and compare with competitors a new architecture of equivariant neural networks based on geometric (Clifford) algebras: Generalized Lipschitz Group Equivariant Neural Networks (GLGENN). These networks are equivariant…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

A deep generative model is developed for representation and analysis of images, based on a hierarchical convolutional dictionary-learning framework. Stochastic {\em unpooling} is employed to link consecutive layers in the model, yielding…

A class of recent approaches for generating images, called Generative Adversarial Networks (GAN), have been used to generate impressively realistic images of objects, bedrooms, handwritten digits and a variety of other image modalities.…

Recent breakthroughs and rapid integration of generative models (GMs) have sparked interest in the problem of model attribution and their fingerprints. For instance, service providers need reliable methods of authenticating their models to…

While GAN is a powerful model for generating images, its inability to infer a latent space directly limits its use in applications requiring an encoder. Our paper presents a simple architectural setup that combines the generative…

In this paper, an image recognition algorithm based on the combination of deep learning and generative adversarial network (GAN) is studied, and compared with traditional image recognition methods. The purpose of this study is to evaluate…

This paper introduces a novel generative encoder (GE) model for generative imaging and image processing with applications in compressed sensing and imaging, image compression, denoising, inpainting, deblurring, and super-resolution. The GE…

There has been much recent interest in designing neural networks (NNs) with relaxed equivariance, which interpolate between exact equivariance and full flexibility for consistent performance gains. In a separate line of work, structured…