Related papers: Neural Sinkhorn Gradient Flow
A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…
Neural Scene Flow Prior (NSFP) and Fast Neural Scene Flow (FNSF) have shown remarkable adaptability in the context of large out-of-distribution autonomous driving. Despite their success, the underlying reasons for their astonishing…
Brain-inspired spiking neural networks (SNNs) are recognized as a promising avenue for achieving efficient, low-energy neuromorphic computing. Direct training of SNNs typically relies on surrogate gradient (SG) learning to estimate…
Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…
Classifier-free guidance (CFG) is a widely used technique for controllable generation in diffusion and flow-based models. Despite its empirical success, CFG relies on a heuristic linear extrapolation that is often sensitive to the guidance…
The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive…
Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…
Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity…
We study the minimization of non-convex functionals over the Wasserstein space. While recent work has showed that perturbed Wasserstein gradient methods can avoid saddle points for benign landscapes, existing approaches remain essentially…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
Sampling from unnormalized densities presents a fundamental challenge with wide-ranging applications, from posterior inference to molecular dynamics simulations. Continuous flow-based neural samplers offer a promising approach, learning a…
We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…
The Wasserstein space of probability measures is known for its intricate Riemannian structure, which underpins the Wasserstein geometry and enables gradient flow algorithms. However, the Wasserstein geometry may not be suitable for certain…
Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…
Learning distance functions between complex objects, such as the Wasserstein distance to compare point sets, is a common goal in machine learning applications. However, functions on such complex objects (e.g., point sets and graphs) are…
Heterogeneous face recognition (HFR) aims to match facial images acquired from different sensing modalities with mission-critical applications in forensics, security and commercial sectors. However, HFR is a much more challenging problem…
Short-term water demand forecasting (StWDF) is the foundation stone in the derivation of an optimal plan for controlling water supply systems. Deep learning (DL) approaches provide the most accurate solutions for this purpose. However, they…
Binary Neural Networks (BNNs) have garnered significant attention due to their immense potential for deployment on edge devices. However, the non-differentiability of the quantization function poses a challenge for the optimization of BNNs,…