Fast Algorithms for Quaternion-Valued Convolutional Neural Networks

摘要

In this article, we analyze algorithmic ways to reduce the arithmetic complexity of calculating quaternion-valued linear convolution and also synthesize a new algorithm for calculating this convolution. During the synthesis of the discussed algorithm, we use the fact that quaternion multiplication may be represented as a matrix–vector product. The matrix participating in the product has unique structural properties that allow performing its advantageous decomposition. Namely, this decomposition leads to reducing the multiplicative complexity of computations. In addition, we used the fact that when calculating the elements of the quaternion-valued convolution, the part of the calculations of all matrix–vector products is common. It gives an additional reduction in the number of additions of real numbers and, consequently, a decrease in the additive complexity of calculations. Thus, the use of the proposed algorithm will contribute to the acceleration of calculations in quaternion-valued convolution neural networks.