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Found 3 papers, 2 papers with code
PCF-GAN: generating sequential data via the characteristic function of measures on the path space
Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data.
Gaussian kernels on non-simply-connected closed Riemannian manifolds are never positive definite
We show that the Gaussian kernel $\exp\left\{-\lambda d_g^2(\bullet, \bullet)\right\}$ on any non-simply-connected closed Riemannian manifold $(\mathcal{M}, g)$, where $d_g$ is the geodesic distance, is not positive definite for any $\lambda > 0$, combining analyses in the recent preprint~[9] by Da Costa--Mostajeran--Ortega and classical comparison theorems in Riemannian geometry.
Path Development Network with Finite-dimensional Lie Group Representation
To tackle this problem, we propose a novel, trainable path development layer, which exploits representations of sequential data with the help of finite-dimensional matrix Lie groups.
