  This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for
training Boltzmann Machines. Similar in spirit to the Hessian-Free method of
Martens [8], our algorithm belongs to the family of truncated Newton methods
and exploits an efficient matrix-vector product to avoid explicitely storing
the natural gradient metric $L$. This metric is shown to be the expected second
derivative of the log-partition function (under the model distribution), or
equivalently, the variance of the vector of partial derivatives of the energy
function. We evaluate our method on the task of joint-training a 3-layer Deep
Boltzmann Machine and show that MFNG does indeed have faster per-epoch
convergence compared to Stochastic Maximum Likelihood with centering, though
wall-clock performance is currently not competitive.
