  Few algorithms for supervised training of spiking neural networks exist that
can deal with patterns of multiple spikes, and their computational properties
are largely unexplored. We demonstrate in a set of simulations that the ReSuMe
learning algorithm can be successfully applied to layered neural networks.
Input and output patterns are encoded as spike trains of multiple precisely
timed spikes, and the network learns to transform the input trains into target
output trains. This is done by combining the ReSuMe learning algorithm with
multiplicative scaling of the connections of downstream neurons.
  We show in particular that layered networks with one hidden layer can learn
the basic logical operations, including Exclusive-Or, while networks without
hidden layer cannot, mirroring an analogous result for layered networks of rate
neurons.
  While supervised learning in spiking neural networks is not yet fit for
technical purposes, exploring computational properties of spiking neural
networks advances our understanding of how computations can be done with spike
trains.
