Related papers: Flat Metric Minimization with Applications in Gene…

Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution.…

This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and…

A physical nonlinear dynamical model of a laser diode is considered. We propose a feed-forward control scheme based on differential flatness for the design of input-current modulations to compensate diode distortions. The goal is to…

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep…

Modern Generative Adversarial Networks are capable of creating artificial, photorealistic images from latent vectors living in a low-dimensional learned latent space. It has been shown that a wide range of images can be projected into this…

Explaining generalizations and preventing over-confident predictions are central goals of studies on the loss landscape of neural networks. Flatness, defined as loss invariability on perturbations of a pre-trained solution, is widely…

Generative Adversarial Networks (GANs) have achieved great success in generating realistic images. Most of these are conditional models, although acquisition of class labels is expensive and time-consuming in practice. To reduce the…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…

A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…

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…

This paper demonstrates the robustness of Lipschitz-regularized $\alpha$-divergences as objective functionals in generative modeling, showing they enable stable learning across a wide range of target distributions with minimal assumptions.…

We consider d-dimensional Riemanian manifolds which admit d-2 commuting space-like Killing vector fields, orthogonal to a surface, containing two one-parametric families of light-like curves. The condition of the Ricci tensor to be zero…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

While standard flow-matching models transport noise to data uniformly, incorporating an explicit generation order - specifically, establishing coarse, low-frequency structure before fine detail - has proven highly effective for synthesizing…

Current density modeling approaches suffer from at least one of the following shortcomings: expensive training, slow inference, approximate likelihood, mode collapse or architectural constraints like bijective mappings. We propose a simple…

In recent years, machine learning (ML) methods have become increasingly popular in wireless communication systems for several applications. A critical bottleneck for designing ML systems for wireless communications is the availability of…

Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be equipped it with a Riemannian metric, pulled back from the…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…