Efficient Learning Using Spiking Neural Networks Equipped With Affine
  Encoders and Decoders
A. Martina Neuman Philipp Christian Petersen
We study the learning problem associated with spiking neural networks.
Specifically, we consider hypothesis sets of spiking neural networks with
affine temporal encoders and decoders and simple spiking neurons having only
positive synaptic weights. We demonstrate that the positivity of the weights
continues to enable a wide range of expressivity results, including
rate-optimal approximation of smooth functions or approximation without the
curse of dimensionality. Moreover, positive-weight spiking neural networks are
shown to depend continuously on their parameters which facilitates classical
covering number-based generalization statements. Finally, we observe that from
a generalization perspective, contrary to feedforward neural networks or
previous results for general spiking neural networks, the depth has little to
no adverse effect on the generalization capabilities.