A Group Theoretic Perspective on Unsupervised Deep Learning

The modern incarnation of neural networks, now popularly known as Deep Learning (DL), accomplished record-breaking success in processing diverse kinds of signals vision, audio, and text. In parallel, strong interest has ensued towards constructing a theory of DL. This paper opens up a group theory based approach, towards a theoretical understanding of DL, in particular the unsupervised variant. First we establish how a single layer of unsupervised pre-training can be explained in the light of orbit-stabilizer principle, and then we sketch how the same principle can be extended for multiple layers.