Fully tensorial approach to hypercomplex neural networks

Fully tensorial theory of hypercomplex neural networks is given. The key point is to observe that the algebra multiplication can be represented as a rank three tensor. This approach is attractive for neural network libraries that support effective tensorial operations.

KHNNs: hypercomplex neural networks computations via Keras using TensorFlow and PyTorch

Neural networks used in computations with more advanced algebras than real numbers perform better in some applications. However, there is no general framework for constructing hypercomplex neural networks. We propose a library integrated with Keras that can do computations within TensorFlow and PyTorch. It provides Dense and Convolutional 1D, 2D, and 3D layers architectures.