Convolutional neural networks with fractional order gradient method
This is an incremental improvement for training convolutional neural networks, potentially benefiting researchers and practitioners in deep learning.
The paper tackles the problem of fractional order gradient methods not converging to real extreme points in convolutional neural networks by proposing a simplified fractional order gradient method based on Caputo's definition, which achieves fast convergence, high accuracy, and the ability to escape local optima in experiments.
This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified fractional order gradient method is designed based on Caputo's definition. The parameters within layers are updated by the designed gradient method, but the propagations between layers still use integer order gradients, and thus the complicated derivatives of composite functions are avoided and the chain rule will be kept. By connecting every layers in series and adding loss functions, the proposed convolutional neural networks can be trained smoothly according to various tasks. Some practical experiments are carried out in order to demonstrate fast convergence, high accuracy and ability to escape local optimal point at last.