Related papers: Shape DNA: Basic Generating Functions for Geometri…

Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep AutoEncoder (AE) network with…

In this paper we investigate the problem of inducing a distribution over three-dimensional structures given two-dimensional views of multiple objects taken from unknown viewpoints. Our approach called "projective generative adversarial…

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing…

Perceptual features (PFs) have been used with great success in tasks such as transfer learning, style transfer, and super-resolution. However, the efficacy of PFs as key source of information for learning generative models is not well…

We propose a method for constructing generative models of 3D objects from a single 3D mesh and improving them through unsupervised low-shot learning from 2D images. Our method produces a 3D morphable model that represents shape and albedo…

Generative models have achieved remarkable performance recently, and thus model hubs have emerged. Existing model hubs typically assume basic text matching is sufficient to search for models. However, in reality, due to different…

In image generation, generative models can be evaluated naturally by visually inspecting model outputs. However, this is not always the case for graph generative models (GGMs), making their evaluation challenging. Currently, the standard…

Feature related particle data analysis plays an important role in many scientific applications such as fluid simulations, cosmology simulations and molecular dynamics. Compared to conventional methods that use hand-crafted feature…

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…

The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based…

The enduring inability of image generative models to recreate intricate geometric features, such as those present in human hands and fingers has been an ongoing problem in image generation for nearly a decade. While strides have been made…

We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…

Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality. We study the 19-dimensional pMSSM, including experimental constraints from all sources and assessing the consistency of potential signals of…

Learning on 3D structures of large biomolecules is emerging as a distinct area in machine learning, but there has yet to emerge a unifying network architecture that simultaneously leverages the graph-structured and geometric aspects of the…

Most earlier 3D structure-based molecular generation approaches follow an atom-wise paradigm, incrementally adding atoms to a partially built molecular fragment within protein pockets. These methods, while effective in designing tightly…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…

The main goal in this paper is to describe the geometric structure of invariant graphs of a certain class of skew products. Our focus is on attracting multi-graphs. An invariant multi-graph is an invariant compact set which is a finite…

A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior…

Physics-inspired Generative Models (GMs), in particular Diffusion Models (DMs) and Poisson Flow Models (PFMs), enhance Bayesian methods and promise great utility in medical imaging. This review examines the transformative role of such…

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear…