# Performance Analysis of Fractional Learning Algorithms

arXiv: https://arxiv.org/abs/2110.05201 · HTML: https://mlsanity.com/paper/2110.05201/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 69 references that are in the map.
- First posted on arXiv 11 Oct 2021.

## Builds on (most cited first, 6 of 6)

- [Convolutional neural networks with fractional order gradient method](https://mlsanity.com/paper/1905.05336/) (2019)
- [Lyapunov functions for nabla discrete fractional order systems](https://mlsanity.com/paper/1812.11368/) (2018)
- [Comments on "Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach"](https://mlsanity.com/paper/1802.09211/) (2018)
- [Comments on "A new computing approach for power signal modeling using fractional adaptive algorithms"](https://mlsanity.com/paper/2003.09597/) (2020)
- [Comments on "Generalization of the gradient method with fractional order gradient direction"](https://mlsanity.com/paper/2009.05221/) (2020)
- [Comments on "Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model"](https://mlsanity.com/paper/2009.07076/) (2020)

## Built on by (most cited first, 1 of 1)

- [Fractional-order Jacobian Matrix Differentiation and Its Application in Artificial Neural Networks](https://mlsanity.com/paper/2506.07408/) (2025)

## Abstract (arXiv)

Fractional learning algorithms are trending in signal processing and adaptive filtering recently. However, it is unclear whether the proclaimed superiority over conventional algorithms is well-grounded or is a myth as their performance has never been extensively analyzed. In this article, a rigorous analysis of fractional variants of the least mean squares and steepest descent algorithms is performed. Some critical schematic kinks in fractional learning algorithms are identified. Their origins and consequences on the performance of the learning algorithms are discussed and swift ready-witted remedies are proposed. Apposite numerical experiments are conducted to discuss the convergence and efficiency of the fractional learning algorithms in stochastic environments.