Related papers: Latent Space Optimal Transport for Generative Mode…
We introduce a method to stabilize Generative Adversarial Networks (GANs) by defining the generator objective with respect to an unrolled optimization of the discriminator. This allows training to be adjusted between using the optimal…
Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal…
The latent space of a Generative Adversarial Network (GAN) has been shown to encode rich semantics within some subspaces. To identify these subspaces, researchers typically analyze the statistical information from a collection of…
Generative Adversarial Networks (GANs) are popular and successful generative models. Despite their success, optimization is notoriously challenging. In this work, we explain the success and limitations of GANs by casting them as Bayesian…
Irregular distribution in latent space causes posterior collapse, misalignment between posterior and prior, and ill-sampling problem in Variational Autoencoders (VAEs). In this paper, we introduce a novel adaptable three-stage Uniform…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…
Generative Adversarial Networks (GANs) have achieved remarkable achievements in image synthesis. These successes of GANs rely on large scale datasets, requiring too much cost. With limited training data, how to stable the training process…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
Quantized neural networks typically require smaller memory footprints and lower computation complexity, which is crucial for efficient deployment. However, quantization inevitably leads to a distribution divergence from the original…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
In recent years, Generative Adversarial Networks (GANs) have shown substantial progress in modeling complex distributions of data. These networks have received tremendous attention since they can generate implicit probabilistic models that…
While 3D Gaussian Splatting (3DGS) has revolutionized 3D reconstruction, it suffers from significant overhead due to massive redundant primitives. Existing compression methods typically rely on local sampling or fixed pruning thresholds,…
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…
Generative adversarial networks (GANs) have shown remarkable success in generation of data from natural data manifolds such as images. In several scenarios, it is desirable that generated data is well-clustered, especially when there is…
This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…
Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…
Enforcing distributions of latent variables in neural networks is an active subject. It is vital in all kinds of generative models, where we want to be able to interpolate between points in the latent space, or sample from it. Modern…
Generative AutoEncoders require a chosen probability distribution in latent space, usually multivariate Gaussian. The original Variational AutoEncoder (VAE) uses randomness in encoder - causing problematic distortion, and overlaps in latent…