Understanding Deep Convolutional Networks
This work provides a theoretical foundation for analyzing deep learning models, which is incremental as it builds on existing knowledge without introducing new methods or applications.
The paper tackles the challenge of understanding deep convolutional networks by introducing a mathematical framework to analyze their properties, focusing on invariants like multiscale contractions and hierarchical symmetries, but does not report specific numerical results.
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.