Related papers: Flat Metric Minimization with Applications in Gene…
Empirical studies of the loss landscape of deep networks have revealed that many local minima are connected through low-loss valleys. Yet, little is known about the theoretical origin of such valleys. We present a general framework for…
We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary…
Recent advancement in generative models have demonstrated remarkable performance across various data modalities. Beyond their typical use in data synthesis, these models play a crucial role in distribution matching tasks such as latent…
Tackling the task of materials generation, we aim to enhance the previously proposed All-atom Diffusion Transformer (ADiT) by introducing SymADiT, a symmetry-aware variant. To do so, we use a representation of materials based on Wyckoff…
Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize…
Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized…
We develop a comprehensive theoretical framework that unifies quantum emission dynamics in one-dimensional Lieb lattices, bridging the gap between ideal flat-band coherence and realistic narrow-band dissipation. By coupling an emitter to…
Diffusion models are powerful deep generative models, but unlike classical models, they lack an explicit low-dimensional latent space that parameterizes the data manifold. This absence makes it difficult to perform manifold-aware…
We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
Generative modelling is often cast as minimizing a similarity measure between a data distribution and a model distribution. Recently, a popular choice for the similarity measure has been the Wasserstein metric, which can be expressed in the…
Motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations, this work develops a theory of space-time integral currents with bounded variation in time, which enables a natural variational approach…
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…
Despite the remarkable empirical successes of Generative Adversarial Networks (GANs), the theoretical guarantees for their statistical accuracy remain rather pessimistic. In particular, the data distributions on which GANs are applied, such…
We study the action on currents and differential forms on compact Riemannian manifolds under $C^0$-limits of diffeomorphisms. Using tools from geometric analysis, measure theory, and homotopy theory, we establish several convergence…
Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
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…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…