Modified pseudo-inverse neural networks storing correlated patterns
Ralf Der, Vladimir Dotsenko, Brunello Tirozzi · Journal of Physics A Mathematical and General · 1992
Neural networks with symmetric couplings which have an intermediate form between the Hebb learning rule and the pseudo-inverse one, storing strongly correlated patterns, are studied. Signal-to-noise analysis is made and replica-symmetric thermodynamic calculations are performed. Both approaches show that both in the Hopfield model limit and in the pseudo-inverse model limit the maximal capacity of the order of (2p/ln(1/p) -1 ) where p<<1 is the average neural activity) can be achieved by appropriate adjustment of the threshold term of the Hamiltonian.