  A recent paper by Boughammoura (2023) describes the back-propagation
algorithm in terms of an alternative formulation called the F-adjoint method.
In particular, by the F-adjoint algorithm the computation of the loss gradient,
with respect to each weight within the network, is straightforward and can
simply be done. In this work, we develop and investigate this theoretical
framework to improve some supervised learning algorithm for feed-forward neural
network. Our main result is that by introducing some neural dynamical model
combined by the gradient descent algorithm, we derived an equilibrium F-adjoint
process which yields to some local learning rule for deep feed-forward networks
setting. Experimental results on MNIST and Fashion-MNIST datasets, demonstrate
that the proposed approach provide a significant improvements on the standard
back-propagation training procedure.
