  Significant success has been reported recently using deep neural networks for
classification. Such large networks can be computationally intensive, even
after training is over. Implementing these trained networks in hardware chips
with a limited precision of synaptic weights may improve their speed and energy
efficiency by several orders of magnitude, thus enabling their integration into
small and low-power electronic devices. With this motivation, we develop a
computationally efficient learning algorithm for multilayer neural networks
with binary weights, assuming all the hidden neurons have a fan-out of one.
This algorithm, derived within a Bayesian probabilistic online setting, is
shown to work well for both synthetic and real-world problems, performing
comparably to algorithms with real-valued weights, while retaining
computational tractability.
