The Kernel Dynamics of Convolutional Neural Networks in Manifolds

We propose a novel expression from manifolds to define Convolutional neural network (CNN). The layered structure is proceeded by integration in limited space continuously, with weights adjusted including value and direction in neural manifolds. Status transfer functions are proposed to simulate the kernel dynamics as a control matrix. We theoretically analyze the stability and controllability of kernel-based CNNs, and verify our findings by numerical experiments.