Related papers: Riemannian Neural Geodesic Interpolant

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…

Global climate projections rely on computationally demanding Earth System Models (ESMs), which are typically limited to coarse spatial resolutions due to their high cost. To obtain high-resolution projections for regions of interest, it is…

Reliable wall-to-wall biomass density estimation from NASA's GEDI mission requires interpolating sparse LIDAR observations across heterogeneous landscapes. While machine learning approaches like Random Forest and XGBoost are widely used,…

For semantic segmentation of remote sensing images (RSI), trade-off between representation power and location accuracy is quite important. How to get the trade-off effectively is an open question,where current approaches of utilizing very…

Existing image generation models face critical challenges regarding the trade-off between computation and fidelity. Specifically, models relying on a pretrained Variational Autoencoder (VAE) suffer from information loss, limited detail, and…

In the recent past, nested structures in Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analysis (PGA) technique, for example, the principal nested…

Combining electroencephalogram (EEG) datasets for supervised machine learning (ML) is challenging due to session, subject, and device variability. ML algorithms typically require identical features at train and test time, complicating…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

Based on Stochastic Gradient Descent (SGD), the paper introduces two optimizers, named Interpolational Accelerating Gradient Descent (IAGD) as well as Noise-Regularized Stochastic Gradient Descent (NRSGD). IAGD leverages second-order Newton…

Stochastic neural networks such as Restricted Boltzmann Machines (RBMs) have been successfully used in applications ranging from speech recognition to image classification. Inference and learning in these algorithms use a Markov Chain Monte…

Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…

Deep neural networks achieve superior performance for learning from independent and identically distributed (i.i.d.) data. However, their performance deteriorates significantly when handling out-of-distribution (OoD) data, where the…

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance…

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…

We propose a generative framework for learning stochastic dynamics from endpoint and intermediate distributional observations. The method formulates generation as a McKean-Vlasov control problem in which terminal and time-marginal laws are…

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…

Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…