Eur. Phys. J. B 32, 395-399 (2003)
https://doi.org/10.1140/epjb/e2003-00114-7

Efficient Hopfield pattern recognition on a scale-free neural network

¹ School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
² Institute for Theoretical Physics, Cologne University, 50923 Köln, Germany
³ Department of Physics, Technion-IIT, Haifa 32000, Israel
⁴ Cybernetic Vision Research Group, IFSC-USP, Caixa Postal 369, 13560-970 São Carlos, SP, Brazil

Received: 12 January 2003
Published online: 11 April 2003

Abstract

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 N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². 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 Barabási-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 . Although the quality of retrieval decreases for small m, we find good associative memory for . Hence, these networks gain a factor in the computer memory and time.