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Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation…

Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…

Variational inference with normalizing flows (NFs) is an increasingly popular alternative to MCMC methods. In particular, NFs based on coupling layers (Real NVPs) are frequently used due to their good empirical performance. In theory,…

Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…

We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to…

Reconstructing ghosting-free high dynamic range (HDR) images of dynamic scenes from a set of multi-exposure images is a challenging task, especially with large object motion and occlusions, leading to visible artifacts using existing…

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…

We propose Multiscale Flow, a generative Normalizing Flow that creates samples and models the field-level likelihood of two-dimensional cosmological data such as weak lensing. Multiscale Flow uses hierarchical decomposition of cosmological…

Point cloud upsampling aims to generate dense point clouds from given sparse ones, which is a challenging task due to the irregular and unordered nature of point sets. To address this issue, we present a novel deep learning-based model,…

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…

Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…

While diffusion models generate high-quality images via probability flow, the theoretical understanding of this process remains incomplete. A key question is when probability flow converges to training samples or more general points on the…

In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

Among applications of deep learning (DL) involving low cost sensors, remote image classification involves a physical channel that separates edge sensors and cloud classifiers. Traditional DL models must be divided between an encoder for the…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

When training overparameterized deep networks for classification tasks, it has been widely observed that the learned features exhibit a so-called "neural collapse" phenomenon. More specifically, for the output features of the penultimate…

Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal…