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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Prashant Joshi, Eduardo D. Sontag

It had previously been shown that generic cortical microcircuit

models can perform complex real-time computations on continuous

input streams, provided that these computations can be carried out

with a rapidly fading memory. We investigate in this article the

computational capability of such circuits in the ...
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