A learning and forgetting algorithm in associative memories: results involving pseudo inverses

The authors develop a design technique for associative memories with learning and forgetting abilities via artificial feedback neural networks. The proposed method utilizes the theory of large-scale dynamical systems, instead of the usual energy methods. Networks synthesized by this design method are capable of learning new patterns as well as forgetting existing patterns without the necessity of recomputing the entire interconnection weights and external inputs. The method employs the properties of pseudo-inverse matrices to iteratively solve systems of linear equations, and provides significant improvements over the outer product method and the projection learning rule. Several specific examples are given to illustrate the strengths and weaknesses of the methodology