Summary: We study the storing capacity of a neural network with a synapses organized in two clusters, by analysing the maximal volume in interaction space. The cluster organization is introduced through a modified spherical condition on the interactions and also through the requirement of storing together a family of patterns formed by an ‘ancestor’ and one ‘descendant’ that differ on the relative sign of the cluster configurations.
The critical capacity \(\alpha^ c\) is compared with E. Gardner’s [ibid. 21, 257-270 (1988)] result for a uniform system, \(\alpha_ G\), with the result that when good retrieval of only one member of the ‘family’ is required the ratio \(\alpha^ c/\alpha_ G\) coincides with the value obtained by the signal-to-noise method. When we analyse the volume corresponding to joint retrieval of ‘ancestor’ and ‘descendant’ we obtain \(\alpha^ c/\alpha_ G=1/2\) regardless of the cluster modulation.