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.

翻译：Boughammoura (2023) 近期的一篇论文描述了一种称为F-伴随法的替代公式，用以阐述反向传播算法。具体而言，通过F-伴随算法，计算损失相对于网络中每个权重的梯度是直接且易于实现的。在本工作中，我们发展并研究了这一理论框架，以改进前馈神经网络的一些监督学习算法。我们的主要成果是，通过引入结合梯度下降算法的神经动力学模型，我们推导出了一个平衡的F-伴随过程，该过程为深度前馈网络设置产生了一些局部学习规则。在MNIST和Fashion-MNIST数据集上的实验结果表明，所提出的方法相较于标准的反向传播训练过程带来了显著的改进。