Related papers: On Linear Interpolation in the Latent Space of Dee…

Do different generative image models secretly learn similar underlying representations? We investigate this by measuring the latent space similarity of four different models: VAEs, GANs, Normalizing Flows (NFs), and Diffusion Models (DMs).…

Deep generative models are becoming widely used across science and industry for a variety of purposes. A common challenge is achieving a precise implicit or explicit representation of the data probability density. Recent proposals have…

Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the…

Foundation models for 3D shape generation have recently shown a remarkable capacity to encode rich geometric priors across both global and local dimensions. However, leveraging these priors for downstream tasks can be challenging as…

This paper will discuss the potential of dimensionality reduction with a web-based use of GANs. Throughout a variety of experiments, we show synthesizing visually-appealing samples, interpolating meaningfully between samples, and performing…

Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…

We suggest ways to enforce given constraints in the output of a Generative Adversarial Network (GAN) generator both for interpolation and extrapolation (prediction). For the case of dynamical systems, given a time series, we wish to train…

The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…

We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…

When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…

We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may…

State of the art deep generative networks are capable of producing images with such incredible realism that they can be suspected of memorizing training images. It is why it is not uncommon to include visualizations of training set nearest…

Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the known molecules seen in training. We find that a key limitation is…

Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…

Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and…

Generative adversarial networks (GANs) are popular for generative tasks; however, they often require careful architecture selection, extensive empirical tuning, and are prone to mode collapse. To overcome these challenges, we propose a…

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…

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…