Envisioning Future Deep Learning Theories: Some Basic Concepts and Characteristics

To advance deep learning methodologies in the next decade, a theoretical framework for reasoning about modern neural networks is needed. While efforts are increasing toward demystifying why deep learning is so effective, a comprehensive picture remains lacking, suggesting that a better theory is possible. We argue that a future deep learning theory should inherit three characteristics: a textithierarchically structured network architecture, parameters textititeratively optimized using stochastic gradient-based methods, and information from the data that evolves textitcompressively. As an instantiation, we integrate these characteristics into a graphical model called textitneurashed. This model effectively explains some common empirical patterns in deep learning. In particular, neurashed enables insights into implicit regularization, information bottleneck, and local elasticity. Finally, we discuss how neurashed can guide the development of deep learning theories.