Backpropagation and F-adjoint

Ahmed Boughammoura

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arXiv · 2304.13820

Backpropagation and F-adjoint

Ahmed Boughammoura

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Abstract

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.

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Ahmed Boughammoura. 2023-03-29. Backpropagation and F-adjoint. https://arxiv.org/abs/2304.13820

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