Hypercomplex-Valued Recurrent Correlation Neural Networks
This work addresses the problem of enhancing associative memory capacity for complex data types like images, though it is incremental as it builds on existing RCNN frameworks.
The authors extended bipolar recurrent correlation neural networks (RCNNs) to handle hypercomplex-valued data, providing mathematical foundations and stability conditions, and demonstrated their application in storing and recalling gray-scale images through computational experiments.
Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield neural network, can be used to implement high-capacity associative memories. In this paper, we extend the bipolar RCNNs for processing hypercomplex-valued data. Precisely, we present the mathematical background for a broad class of hypercomplex-valued RCNNs. Then, we provide the necessary conditions which ensure that a hypercomplex-valued RCNN always settles at an equilibrium using either synchronous or asynchronous update modes. Examples with bipolar, complex, hyperbolic, quaternion, and octonion-valued RCNNs are given to illustrate the theoretical results. Finally, computational experiments confirm the potential application of hypercomplex-valued RCNNs as associative memories designed for the storage and recall of gray-scale images.