SUBMITTED TO ELSEVIER NEUROCOMPUTING Fast Hopfield Neural Networks Using Subspace Projections 1 Daniel Calabuig, Sonia Gimenez, Jose E. Roman, Jose F. Monserrat dacaso@iteam.upv.es, sogico@teleco.upv.es, jroman@itaca.upv.es, jomondel@iteam.upv.es, Abstract – Hopfield Neural Networks are well-suited to the fast solution of complex optimization problems. Their application to real problems usually requires the satisfaction of a set of linear constraints that can be incorporated with an additional violation term. Another option proposed in the literature lies in confining the search space onto the subspace of constraints in such a way that the neuron outputs always satisfy the imposed restrictions. This paper proposes a computationally efficient subspace projection method that also includes variable updating step mechanisms. Some numerical experiments are used to verify the good performance and fast convergence of the new method. Keywords – Hopfield Neural Networks, Linear Constraints, Projection. I. Introduction A Hopfield Neural Network (HNN) is a specific kind of recurrent neural network designed for the minimization of an energy function that contains several terms [9]. From the Hopfield neuron model, any problem that can be written in terms of a second order Lyapunov function can be solved with a quasi-optimal solution using HNNs. These neural networks have gained much relevance in the last decade as a good tool to solve complex optimization problems mainly thanks to their fast response time. Certainly, one of the main advantages of neural techniques is the high computational speed obtained through their hardware implementations, which is even more valuable when considering their usage for industrial applications. Actually, the use of HNNs has 1 NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neurocomputing, vol. 73, no. 10, pp. 1794-1800, 2010, DOI:10.1016/j.neucom.2009.12.031.