How deep learning works --The geometry of deep learning
This foundational work addresses a core theoretical problem in AI for researchers, though it appears incremental as it builds on existing geometric structures.
The paper tackles the theoretical mystery of why deep learning works by proposing a geometric framework that analogizes deep learning systems with quantum computations and diffeomorphic template matching, analyzing structures like CNNs and RNNs to potentially guide network design.
Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric structures, the geometry of quantum computations and the geometry of the diffeomorphic template matching. In this framework, we give the geometric structures of different deep learning systems including convolutional neural networks, residual networks, recursive neural networks, recurrent neural networks and the equilibrium prapagation framework. We can also analysis the relationship between the geometrical structures and their performance of different networks in an algorithmic level so that the geometric framework may guide the design of the structures and algorithms of deep learning systems.