A Forward Learning Algorithm for Neural Memory Ordinary Differential Equations

The deep neural network, based on the backpropagation learning algorithm, has achieved tremendous success. However, the backpropagation algorithm is consistently considered biologically implausible. Many efforts have recently been made to address these biological implausibility issues, nevertheless, these methods are tailored to discrete neural network structures. Continuous neural networks are crucial for investigating novel neural network models with more biologically dynamic characteristics and for interpretability of large language models. The neural memory ordinary differential equation (nmODE) is a recently proposed continuous neural network model that exhibits several intriguing properties. In this study, we present a forward-learning algorithm, called nmForwardLA, for nmODE. This algorithm boasts lower computational dimensions and greater efficiency. Compared with the other learning algorithms, experimental results on MNIST, CIFAR10, and CIFAR100 demonstrate its potency.