Abstract
Neural networks with values in multidimensional domains have been intensively studied over the last few years. This paper introduces octonion-valued neural networks, for which the inputs, outputs, weights and biases are all octonions. They represent a generalization of the complex- and quaternion-valued neural networks, that do not fall into the category of Clifford-valued neural networks, because, unlike Clifford algebras, the octonion algebra is not associative. The full deduction of the gradient descent algorithm for training octonion-valued feedforward neural networks is presented. Testing of the proposed network is done using two synthetic function approximation problems and a time series prediction application.
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Popa, CA. (2016). Octonion-Valued Neural Networks. In: Villa, A., Masulli, P., Pons Rivero, A. (eds) Artificial Neural Networks and Machine Learning – ICANN 2016. ICANN 2016. Lecture Notes in Computer Science(), vol 9886. Springer, Cham. https://doi.org/10.1007/978-3-319-44778-0_51
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DOI: https://doi.org/10.1007/978-3-319-44778-0_51
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