Fractional Order Gradient

Fractional order gradient methods extend traditional gradient descent optimization by incorporating fractional-order derivatives, aiming to improve convergence speed and escape local minima. Current research focuses on analyzing the convergence properties of these methods in various settings (convex, non-convex, strongly convex), developing adaptive algorithms to enhance stability and efficiency, and exploring their application in diverse fields like crystal structure prediction and deep learning (e.g., convolutional neural networks). This research is significant because it offers the potential for faster and more robust optimization in numerous applications, impacting areas such as materials science, medical image analysis, and machine learning.

Papers

October 20, 2024

Fractional-order spike-timing-dependent gradient descent for multi-layer spiking neural networks
Yi Yang, Richard M. Voyles, Haiyan H. Zhang, Robert A. Nawrocki
Neural Network Spike Timing Dependent Plasticity Fractional Derivative Loss Gradient Fractional Order Gradient

November 30, 2023

Convergence Analysis of Fractional Gradient Descent
Ashwani Aggarwal
Gradient Descent Convergence Analysis Fractional Derivative Order Derivative Convergence Property Fractional Order Gradient

July 30, 2023

Crystal Structure Prediction by Joint Equivariant Diffusion
Rui Jiao, Wenbing Huang, Peijia Lin, Jiaqi Han, Pin Chen, Yutong Lu, Yang Liu
Crystal Structure Equivariant Diffusion Crystal Structure Prediction Fractional Order Gradient

March 8, 2023

The Novel Adaptive Fractional Order Gradient Decent Algorithms Design via Robust Control
Jiaxu Liu, Song Chen, Shengze Cai, Chao Xu
Gradient Descent Robust Control Linear Convergence Rate Fractional Order Gradient

May 1, 2022

Using a novel fractional-order gradient method for CNN back-propagation
Mundher Mohammed Taresh, Ningbo Zhu, Talal Ahmed Ali Ali, Mohammed Alghaili, Weihua Guo
Back Propagation Fractional Derivative Neural Fractional Fractional Order Gradient

March 20, 2022

Fully Convolutional Fractional Scaling
Michael Soloveitchik, Michael Werman
Convolutional Neural Network Scaling Method Fractional Order Gradient