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In this paper we first write a proof of the perceptron convergence algorithm for the complex multivalued neural networks (CMVNNs). Our primary goal is to formulate and prove the perceptron convergence algorithm for the bicomplex multivalued neural networks (BMVNNs) and other important results in the theory of neural networks based on a bicomplex algebra.


This is a pre-peer review, author-produced PDF of an article that later underwent peer review and was accepted for publication in Applied Mathematics and Computation, volume 445, in 2023. This version may not exactly replicate the final publication. The definitive publisher-authenticated version is available online at

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