bougham-sn-article.pdf (435.6 kB)

Backpropagation and F-adjoint

Download (435.6 kB)
posted on 2023-04-25, 13:12 authored by Ahmed BoughammouraAhmed Boughammoura

This paper presents a concise mathematical framework for investigating both feed-forward and backward process, during the training to learn model weights, of an artificial neural network (ANN). Inspired from the idea of the two-step rule for backpropagation, we define a notion of F-adjoint which is aimed at a better description of the backpropagation algorithm. In particular, by introducing the notions of F-propagation and F-adjoint through a deep neural network architecture, the backpropagation associated to a cost/loss function is proven to be completely characterized by the F-adjoint of the corresponding F-propagation relatively to the partial derivative, with respect to the inputs, of the cost function.


Email Address of Submitting Author

Submitting Author's Institution

Higher Institute of Informatics and Mathematics, Monastir, Tunisia

Submitting Author's Country

  • Tunisia

Usage metrics