Envisioning Future Deep Learning Theories: Some Basic Concepts and Characteristics
This work addresses the need for a comprehensive theoretical foundation in deep learning, which is incremental as it builds on existing efforts to demystify neural networks.
The authors propose a theoretical framework for deep learning, arguing that future theories should incorporate hierarchical architecture, iterative optimization, and compressive data evolution, and they instantiate this with a graphical model called neurashed to explain empirical patterns like implicit regularization.
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 \textit{hierarchically} structured network architecture, parameters \textit{iteratively} optimized using stochastic gradient-based methods, and information from the data that evolves \textit{compressively}. As an instantiation, we integrate these characteristics into a graphical model called \textit{neurashed}. 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.