Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the "standard" Hopfield model, the N "neurons" are connected to each other via N-2 bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N-2. The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabasi-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q(3). Although the quality of retrieval decreases for small m, we find good associative memory for 1 much less than m much less than N. Hence, these networks gain a factor N/m much greater than 1 in the computer memory and time.