Synthesization of Multi-valued Associative High-Capacity Memory Based on Continuous Networks with a Class of Non-smooth Linear Nondecreasing Activation Functions

Abstract

This paper presents a novel design method for multi-valued auto-associative and hetero-associative memories based on a continuous neural network (CNN) with a class of non-smooth linear nondecreasing activation functions. The proposed CNN is robust in terms of the design parameter selection, which is dependent on a set of inequalities rather than the learning procedure. Some globally exponentially stable criteria are obtained to ensure multi-valued associative patterns to be retrieved accurately. The methodology, by generating CNN where the input data are fed via external inputs, avoids spurious memory patterns and achieves $$(2r)^n$$ storage capacity. These analytic results are applied to the associative memory of images. The fault-tolerant capability and the effectiveness are validated by illustrative experiments.