Dilation and translation for incomplete sigma-pi neural networks of Hopfield-type - a case study

In this paper we show how dilation and translation of bipolar signals can be used to increase the capacity of sigma-pi Hopfield neural networks while keeping their complexity in check. We propose a generalization of the standard Hebb learning scheme which gives rise to proper dilation and translation parameters and apply these generalized Hopfield-type neural networks to some pattern recognition problems. We will see that the new approach especially makes sense for highly correlated information and in cases where the number of multiplicative synaptic correlations of neural activities is limited for some theoretical or practical reason and a so-called incomplete situation appears.