相关论文: Geometrically Enriched Latent Spaces

Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent being under…

Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a nonlinear function (generator) to map latent samples into the data space.…

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…

Generative adversarial networks (GANs) have proven to be surprisingly efficient for image editing by inverting and manipulating the latent code corresponding to a natural image. This property emerges from the disentangled nature of the…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…

As recent generative models can generate photo-realistic images, people seek to understand the mechanism behind the generation process. Interpretable generation process is beneficial to various image editing applications. In this work, we…

Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and…

Generative adversarial networks (GANs), a class of distribution-learning methods based on a two-player game between a generator and a discriminator, can generally be formulated as a minmax problem based on the variational representation of…

Standard formulations of GANs, where a continuous function deforms a connected latent space, have been shown to be misspecified when fitting different classes of images. In particular, the generator will necessarily sample some low-quality…

The goal of a generative model is to capture the distribution underlying the data, typically through latent variables. After training, these variables are often used as a new representation, more effective than the original features in a…

Recent deep generative models are able to provide photo-realistic images as well as visual or textual content embeddings useful to address various tasks of computer vision and natural language processing. Their usefulness is nevertheless…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

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…

Learning meaningful abstract models of Markov Decision Processes (MDPs) is crucial for improving generalization from limited data. In this work, we show how geometric priors can be imposed on the low-dimensional representation manifold of a…

Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an…

Generative adversarial networks (GANs) have shown remarkable success in generation of unstructured data, such as, natural images. However, discovery and separation of modes in the generated space, essential for several tasks beyond naive…

Variational Autoencoder (VAE) and its variations are classic generative models by learning a low-dimensional latent representation to satisfy some prior distribution (e.g., Gaussian distribution). Their advantages over GAN are that they can…

This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding…

We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework…

Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and…