Construction of high‐dimensional neural networks by linear connections of matrices

Abstract

Abstract High‐dimensional neural networks, such as complex neural networks and three‐dimensional neural networks, have been proposed. They are capable of learning high‐dimensional motions, which cannot be done by real‐valued neural networks. In this paper, high‐dimensional neurons are defined as vectors, and certain high‐dimensional neural networks, such as complex neural networks, quaternary neural networks, and three‐dimensional exterior neural networks, are unified in terms of a vector representation. It is shown that all of these types have the common feature of alternating matrices. The inverse quaternion neural network has the ability to learn rotations. In addition, it is shown that the proposed model cannot represent all rotations in neural networks that are higher than three‐dimensional, and that the inverse quaternary neural network has a partial ability to learn rotations. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(11): 38–45, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjc.10072