# Convolutional neural networks with fractional order gradient method

## TL;DR

This paper introduces a novel fractional order gradient method for training convolutional neural networks, improving convergence speed and accuracy while avoiding local minima by combining fractional and integer order gradients.

## Contribution

A simplified fractional order gradient method based on Caputo's definition is proposed, enabling effective training of CNNs with improved convergence and accuracy.

## Key findings

- Demonstrates fast convergence in experiments
- Achieves high accuracy on various tasks
- Shows ability to escape local optima

## Abstract

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.