  We derive a relationship between network representation in energy-efficient
neuromorphic architectures and block Toplitz convolutional matrices. Inspired
by this connection, we develop deep convolutional networks using a family of
structured convolutional matrices and achieve state-of-the-art trade-off
between energy efficiency and classification accuracy for well-known image
recognition tasks. We also put forward a novel method to train binary
convolutional networks by utilising an existing connection between
noisy-rectified linear units and binary activations.
