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.

翻译：深层学习在不同任务上如何运作,从理论角度来说,这仍然是个谜。在本文中,我们通过找到其与两个现有几何结构的相似之处,即量数计算几何学和二面形模板匹配的几何学,来绘制深层学习系统的几何结构,包括进化神经网络、残余网络、循环神经网络、循环神经网络和平衡平衡平衡处理框架。我们还可以分析几何结构与不同网络在算法层面的运行情况之间的关系,以便几何框架能够指导深层学习系统的结构和算法的设计。