Since they were first introduced in [1], Clifford neural networks have shown its utility to enhance the properties of real-valued neural networks. Although the first attempts were not successful, Buchholz [2] formalized the concept of Clifford neuron and defined Clifford neural networks as an extension of real-valued neural networks where the activation function takes full advantage of the properties of the geometric product. This allows us to apply them in many different scenarios. In particular, quaternionic neural networks have shown to be very effective in processing multidimensional input features as single entities [3]. This talk intends to introduce Clifford neural networks as well as their main properties and explore the future research lines based on those networks. Later, we will focus on general quaternionic neural networks, study its main features and see how they can be applied to robotics and computer vision. We will also point out future research lines.
[1] J. K. Pearson (1994). Clifford Networks. PhD thesis, University of Kent.
[2] E. Bayro-Corrochano and S. Buchholz (1997). Geometric neural networks. In G. Sommer and J. J. Koenderink, editors, Algebraic Frames for the Perception-Action
Cycle, Lecture Notes in Computer Science, vol. 1315, pages 379-394, SpringerVerlag,
Berlin, Heidelberg.
[3] T. Parcollet, M. Morchid and G. Linarès (2020). A survey of quaternion neural networks. Artificial Intelligence Review 53, 2957–2982.