2014/12/20 by Arnab Paul, Suresh Venkatasubramanian, Paul, Arnab +1 · 1 voice · 13 citations
Computer Science · Mathematics · Psychology · #Adversarial Robustness in Machine Learning #Artificial intelligence #Artificial neural network #Computer science #Connection (principal bundle) #Deep learning #Epistemology #Generative Adversarial Networks and Image Synthesis #Generative grammar #Generative model #Geometry #Group (periodic table) #Mathematics #Neural Networks and Applications #Order (exchange) #Perspective (graphical) #Physics #Process (computing) #Psychology #Representation (politics) #Shadow (psychology) #Simple (philosophy) #Theoretical computer science #cs.LG #cs.NE #stat.ML
paper · pdf · doi:10.48550/arxiv.1412.6621
published in arXiv (Cornell University) (Cornell University) · 13 pages, 5 figures
openalex publication_date 2014/12/20 · arxiv created 2015/02/28 · arxiv updated 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor behind the recent resurgence of the subject is a key algorithmic step called pre-training: first search for a good generative model for the input samples, and repeat the process one layer at a time. We show deeper implications of this simple principle, by establishing a connection with the interplay of orbits and stabilizers of group actions. Although the neural networks themselves may not form groups, we show the existence of \em shadow groups whose elements serve as close approximations. Over the shadow groups, the pre-training step, originally introduced as a mechanism to better initialize a network, becomes equivalent to a search for features with minimal orbits. Intuitively, these features are in a way the \em simplest. Which explains why a deep learning network learns simple features first. Next, we show how the same principle, when repeated in the deeper layers, can capture higher order representations, and why representation complexity increases as the layers get deeper.