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 valid for any input dimension, ... more >>>

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 ... more >>>

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 more realistic case where not ... more >>>