  Stochastic gradient descent based algorithms are typically used as the
general optimization tools for most deep learning models. A Restricted
Boltzmann Machine (RBM) is a probabilistic generative model that can be stacked
to construct deep architectures. For RBM with Bernoulli inputs, non-Euclidean
algorithm such as stochastic spectral descent (SSD) has been specifically
designed to speed up the convergence with improved use of the gradient
estimation by sampling methods. However, the existing algorithm and
corresponding theoretical justification depend on the assumption that the
possible configurations of inputs are finite, like binary variables. The
purpose of this paper is to generalize SSD for Gaussian RBM being capable of
mod- eling continuous data, regardless of the previous assumption. We propose
the gradient descent methods in non-Euclidean space of parameters, via de-
riving the upper bounds of logarithmic partition function for RBMs based on
Schatten-infinity norm. We empirically show that the advantage and improvement
of SSD over stochastic gradient descent (SGD).
