Associative ability of higher order correlation models for sequential patterns

Abstract

This paper describes some results on transition properties and the absolute capacities of higher order correlation and differential correlation associative memories. First, it is shown that the absolute capacities are $\frac{{\mathrm{(}1-\overline{\mathit{s}}\mathrm{)}}^2}{2{\mathrm{(}1-{\overline{\mathit{s}}}^2\mathrm{)}}^{1-\mathit{k}}log\mathit{N}}$ and $\frac{{\{2{\mathrm{(}1-{\overline{\mathit{s}}}^2\mathrm{)}}^{\mathit{k}}-1\}}^2}{2^{\mathit{k}+2}{\mathrm{(}1-{\overline{\mathit{s}}}^2\mathrm{)}}^{1-\mathit{k}}log\mathit{N}}$ for correlation and differential correlation models, respectively, where N is the number of neurons, $\overline{\mathit{s}}$ is the rate of correlation for patterns and k is the dimension. The results show that the absolute capacities approach to 0 rapidly as N increases in both models and they decrease rapidly in the correlation model and slowly in the differential correlation model as $\overline{\mathit{s}}$ increases. Further, it is clarified that the correlation model is superior in storage capacities and inferior in robustness than the differential correlation one.