The space of interactions in neural networks with hierarchical cluster organization
Marco Idiart, Alba Theumann · Journal of Physics A Mathematical and General · 1992
The authors study the storing capacity of a neural network with a synapsis 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 Gardner's result (1988) 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 previously by the signal-to-noise method. When the authors analyse the volume corresponding to joint retrieval of 'ancestor' and 'descendant' they obtain alpha c / alpha G =1/2 regardless of the cluster modulation.