Fractional-Order Gradient Descent for Neural Networks¶
Implements Fractional-Order Gradient Descent for Neural Networks, a survey of training methods that replace the integer-order gradient with a fractional derivative.
This is a review article rather than a single algorithm. It surveys how fractional calculus enters neural-network training: the classical weight update is generalized by substituting the ordinary gradient of the loss with a fractional-order derivative (Riemann–Liouville, Caputo, Grünwald–Letnikov, or Atangana–Baleanu), giving the update a tunable memory of past states through the fractional order \(\alpha\). The paper surveys fractional gradient descent and fractional backpropagation alongside classical and metaheuristic trainers, summarizing reported gains in convergence speed and accuracy.
The review presents only the definitions of the underlying fractional derivatives and summaries of prior work; it does not state a single closed-form parameter-update rule of its own, so no update equation is transcribed here.
Reference: E. Viera-Martin, J. F. Gómez-Aguilar, J. E. Solís-Pérez, J. A. Hernández-Pérez, R. F. Escobar-Jiménez, "Artificial neural networks: a practical review of applications involving fractional calculus", The European Physical Journal Special Topics 2022. https://doi.org/10.1140/epjs/s11734-022-00455-3