Related papers: Sinkhorn-Drifting Generative Models
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical…
The recent many-fold increase in the size of deep neural networks makes efficient distributed training challenging. Many proposals exploit the compressibility of the gradients and propose lossy compression techniques to speed up the…
The stratification of entropy and the stratification of angular momentum are closely analogous. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical…
Diffusion models excel at modeling complex and multimodal trajectory distributions for decision-making and control. Reward-gradient guided denoising has been recently proposed to generate trajectories that maximize both a differentiable…
The self-adjoint angular flux and streamline-upwind Petrov-Galerkin transport equations are discretized using reproducing kernels with the collocation method to produce a discretization that is compatible with conservative reproducing…
Supervised learning models are one of the most fundamental classes of models. Viewing supervised learning from a probabilistic perspective, the set of training data to which the model is fitted is usually assumed to follow a stationary…
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to…
The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous…
Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to the marginal…
We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for…
Spiking neural networks (SNNs) have tremendous potential for energy-efficient neuromorphic chips due to their binary and event-driven architecture. SNNs have been primarily used in classification tasks, but limited exploration on image…
We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal or stationary density, not an averaged observable. Our…
We study diffusion processes driven by a Brownian motion with regular drift in a finite dimension setting. The drift has two components on different time scales, a fast conservative component and a slow dissipative component. Using the…
We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating…
Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
The notion of concept drift refers to the phenomenon that the distribution generating the observed data changes over time. If drift is present, machine learning models can become inaccurate and need adjustment. While there do exist methods…
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel. We explore a numerical approximation approach to kernel…
We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…