  In this work we explore recurrent representations of leaky integrate and fire
neurons operating at a timescale equal to their absolute refractory period. Our
coarse time scale approximation is obtained using a probability distribution
function for spike arrivals that is homogeneously distributed over this time
interval. This leads to a discrete representation that exhibits the same
dynamics as the continuous model, enabling efficient large scale simulations
and backpropagation through the recurrent implementation. We use this approach
to explore the training of deep spiking neural networks including
convolutional, all-to-all connectivity, and maxpool layers directly in Pytorch.
We found that the recurrent model leads to high classification accuracy using
just 4-long spike trains during training. We also observed a good transfer back
to continuous implementations of leaky integrate and fire neurons. Finally, we
applied this approach to some of the standard control problems as a first step
to explore reinforcement learning using neuromorphic chips.
