  Spiking Neural Networks (SNNs) are being explored for their potential energy
efficiency benefits due to sparse, event-driven computation. Non-spiking
artificial neural networks are typically trained with stochastic gradient
descent using backpropagation. The calculation of true gradients for
backpropagation in spiking neural networks is impeded by the non-differentiable
firing events of spiking neurons. On the other hand, using approximate
gradients is effective, but computationally expensive over many time steps. One
common technique, then, for training a spiking neural network is to train a
topologically-equivalent non-spiking network, and then convert it to an spiking
network, replacing real-valued inputs with proportionally rate-encoded Poisson
spike trains. Converted SNNs function sufficiently well because the mean
pre-firing membrane potential of a spiking neuron is proportional to the dot
product of the input rate vector and the neuron weight vector, similar to the
functionality of a non-spiking network. However, this conversion only considers
the mean and not the temporal variance of the membrane potential. As the
standard deviation of the pre-firing membrane potential is proportional to the
L4-norm of the neuron weight vector, we propose a weight adjustment based on
the L4-norm during the conversion process in order to improve classification
accuracy of the converted network.
