Ghost Features and Spooky Transfer Learning for Hypercomplex-Valued Neural Networks

Hypercomplex numbers extend the concept of complex numbers by introducing additional imaginary components. Besides increasing dimensionality, operations on the imaginary parts provide algebraic and geometrical properties that can be beneficial for solving machine learning problems. In this paper, we show how to create hypercomplex-valued neural network layers where the real part corresponds to the output of a traditional real-valued layer. The additional imaginary parts of these hypercomplex-valued layers produce what we call ``ghost features,'' which contain enhanced information that is not present in the output of the real-valued layer. Moreover, ghost features can be effectively integrated into a trained neural network through a process we refer to as ``spooky transfer learning.'' This approach allows us to harness the richness of ghost features, leading to more efficient neural networks. The source code and Jupyter Notebook are available at https://github.com/mevalle/v-nets/.