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.
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