On discrete N-layer heteroassociative memory models

In this paper we investigate computational properties of a new N-layer heteroassociative memory model with respect to information encoding. We describe a technique for encoding a set of m×n matrix patterns where entering one column (row) of a pattern allows the remaining columns (rows) to be recurrently reconstructed. Following are some of the main contributions of this paper: - We show how to transform any given set of patterns to a standard form using a simple procedure. Then we demonstrate that after a competitive initialization among all layers our multilayer network converges in one step to fixed points which are one of the given patterns in its standard form. Due to an increase in the domain of attraction, our architecture becomes more powerful than the previous models. - We analyze the optimal number of layers, as well as their dimensions, based on the cardinality of maximal linearly independent subspaces of the input patterns. - We prove that our proposed model is stable under mild technical assumptions using the discrete Lyapunov energy function.