Unified approach for applications of oscillatory associative-memory networks with error-free retrieval

Given a set of standard binary patterns and a defective pattern, the binary pattern retrieval task is to find the closest pattern to the defective one among these standard patterns. The associative-memory network of Kuramoto oscillators consisting of a Hebbian coupling term and a second-order Fourier term can be applied to this task. When the memorized patterns stored in the Hebbian coupling are mutually orthogonal, recent studies show that the network is capable of distinguishing the memorized patterns from most other patterns. However, the orthogonality usually fails in real situations. In this paper, we present a unified approach for the application of this model in pattern retrieval problems with any general set of standard patterns. By subgrouping the standard patterns and employing an orthogonal lift of each subgroup, this approach makes use of the theory in the case of mutually orthogonal memorized patterns. In particular, the error-free retrieval can be guaranteed, which requires that the retrieved pattern must coincide with one of the standard patterns. As illustrative simulations, pattern retrieval tests for partly sheltered Arabic number symbols are presented.