On a perceptron-type learning rule for higher order Hopfield neural networks including dilation and translation

In the following, we will introduce a new Perceptron-like learning rule to enhance the recall performance of higher order Hopfield neural networks without significant increase of their complexity. In detail, our approach will lead to a generalized Perceptron learning rule which generates higher order Hopfield neural networks with dilation and translation that perform perfectly on the training set in case that the latter fulfills the so-called conditionally strong Γ-separability condition. In this sense, our learning scheme satisfies a kind of optimality criterion which means that it finds appropriate network parameters in a finite number of learning cycles in case that a solution exists.