  Analog crossbar arrays comprising programmable nonvolatile resistors are
under intense investigation for acceleration of deep neural network training.
However, the ubiquitous asymmetric conductance modulation of practical
resistive devices critically degrades the classification performance of
networks trained with conventional algorithms. Here, we describe and
experimentally demonstrate an alternative fully-parallel training algorithm:
Stochastic Hamiltonian Descent. Instead of conventionally tuning weights in the
direction of the error function gradient, this method programs the network
parameters to successfully minimize the total energy (Hamiltonian) of the
system that incorporates the effects of device asymmetry. We provide critical
intuition on why device asymmetry is fundamentally incompatible with
conventional training algorithms and how the new approach exploits it as a
useful feature instead. Our technique enables immediate realization of analog
deep learning accelerators based on readily available device technologies.
