The capacity of the Hopfield content-addressable neural network subject to a random dilution is investigated by numerical simulations. The sum-of-outer product learning rule is used to generate the synaptic weight matrix for the storage of M random, binary patterns. Randomly selected synaptic connection are then severed while the memory is probed to determine if the original patterns are still fixed. Other dilution methods are investigated such as one that leaves a Hamiltonian cycle, and one that does not allow isolation of nodes. In general, the critical dilution as a function of the loading ratio, (alpha) equals M/N, takes a sigmoid shape. The critical dilution is also a function of the network size and the sum of the effective Hamming distances between all of the fixed patterns.
Victor M. Castillo,
"Dilution in small Hopfield neural networks: computer models", Proc. SPIE 1710, Science of Artificial Neural Networks, (1 July 1992); doi: 10.1117/12.140157; https://doi.org/10.1117/12.140157