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TR97-049 | 22nd October 1997 00:00

On the Complexity of Learning for Spiking Neurons with Temporal Coding


Authors: Michael Schmitt
Publication: 28th October 1997 09:24
Downloads: 1101


Spiking neurons are models for the computational units in
biological neural systems where information is considered to be encoded
mainly in the temporal pattern of their activity. In a network of
spiking neurons a new set of parameters becomes relevant which has no
counterpart in traditional neural network models: the time that a
pulse needs to travel through a connection between two neurons (also
known as delay of a connection). It is known that these delays
are tuned in biological neural systems through a variety of
mechanisms. We investigate the VC-dimension of networks of spiking
neurons where the delays are viewed as programmable parameters
and we prove tight bounds for this VC-dimension. Thus we get
quantitative estimates for the diversity of functions that a network
with fixed architecture can compute with different settings of its
delays. In particular, it turns out that a network of spiking
neurons with $k$ adjustable delays is able to compute a much richer
class of functions than a threshold circuit with $k$ adjustable
weights. The results also yield bounds for the number of training
examples that an algorithm needs for tuning the delays of a network
of spiking neurons. Results about the computational complexity of
such algorithms are also given.

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