  Analog arrays are a promising upcoming hardware technology with the potential
to drastically speed up deep learning. Their main advantage is that they
compute matrix-vector products in constant time, irrespective of the size of
the matrix. However, early convolution layers in ConvNets map very unfavorably
onto analog arrays, because kernel matrices are typically small and the
constant time operation needs to be sequentially iterated a large number of
times, reducing the speed up advantage for ConvNets. Here, we propose to
replicate the kernel matrix of a convolution layer on distinct analog arrays,
and randomly divide parts of the compute among them, so that multiple kernel
matrices are trained in parallel. With this modification, analog arrays execute
ConvNets with an acceleration factor that is proportional to the number of
kernel matrices used per layer (here tested 16-128). Despite having more free
parameters, we show analytically and in numerical experiments that this
convolution architecture is self-regularizing and implicitly learns similar
filters across arrays. We also report superior performance on a number of
datasets and increased robustness to adversarial attacks. Our investigation
suggests to revise the notion that mixed analog-digital hardware is not
suitable for ConvNets.
