Related papers: Convex Potential Flows: Universal Probability Dist…
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,…
The goal of this paper is to provide a new perspective on speech modeling by incorporating perceptual invariances such as amplitude scaling and temporal shifts. Conventional generative formulations often treat each dataset sample as a fixed…
We present a short overview on the strongest variational formulation for gradient flows of geodesically $\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures.…
Continuous diffusion models are commonly acknowledged to display a deterministic probability flow, whereas discrete diffusion models do not. In this paper, we aim to establish the fundamental theory for the probability flow of discrete…
In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network…
This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous…
We investigate the distributed DC-Optimal Power Flow (DC-OPF) problem for a dynamic and uncertain environment. The unpredictable supply of renewable resources and varying prices of the electricity market are a few factors responsible for…
In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular,…
Diffusion models have demonstrated strong performance in sampling and editing multi-modal data with high generation quality, yet they suffer from the iterative generation process which is computationally expensive and slow. In addition,…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…
The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
We present a novel, conditional generative probabilistic model of set-valued data with a tractable log density. This model is a continuous normalizing flow governed by permutation equivariant dynamics. These dynamics are driven by a…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing…
This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…