Michael Schmitt

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 ...
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Michael Schmitt

A neural network is said to be nonoverlapping if there is at most one

edge outgoing from each node. We investigate the number of examples

that a learning algorithm needs when using nonoverlapping neural

networks as hypotheses. We derive bounds for this sample complexity

in terms of the Vapnik-Chervonenkis dimension. ...
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Michael Schmitt

We calculate lower bounds on the size of sigmoidal neural networks

that approximate continuous functions. In particular, we show that

for the approximation of polynomials the network size has to grow

as $\Omega((\log k)^{1/4})$ where $k$ is the degree of the polynomials.

This bound is ...
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Michael Schmitt

In a great variety of neuron models neural inputs are

combined using the summing operation. We introduce the concept of

multiplicative neural networks which contain units that multiply

their inputs instead of summing them and, thus, allow inputs to

interact nonlinearly. The class of multiplicative networks

comprises such widely known ...
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Michael Schmitt

We study networks of spiking neurons that use the timing of pulses

to encode information. Nonlinear interactions model the spatial

groupings of synapses on the dendrites and describe the computations

performed at local branches. We analyze the question of how many

examples these networks must ...
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