The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the gene...

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

Abstract The tenfold way provides a strong organizing principle for invertible topological phases of matter. Mathematically, it is intimately connected with K -theory via the fact that there exist exactly ten Morita classes simple real superalgebras. This connection physically unsurprising, since weakly interacting are classified by -theory. We argue when interactions present, care has to be ta...

Several applications in communication, control, and learning require approximating target distributions to within small informational divergence. The additional requirement of invertibility usually leads using encoders that are one-to-one mappings, also known as distribution matchers. However, even the best have divergences grow logarithmically with block length. To overcome this limitation, an...