Title: Dynamics-inspired Neuromorphic Representation Learning. Abstract: This paper investigates the dynamics-inspired neuromorphic architecture for neural representation and learning following Hamilton's principle. The proposed approach converts weight-based neural structure to its dynamics-based form that consists of finite sub-models, whose mutual relations measured by computing path integrals amongst their dynamic states are equivalent to the typical neural weights. The feedback signals interpreted as stress forces amongst sub-models push them to move based on the entropy-reduction process derived from the Euler-Lagrange equations. We first train a dynamics-based neural model from scratch and observe that this model outperforms its corresponding feedforward neural networks on MNIST dataset. Then we convert several pre-trained neural structures (e.g., DenseNet, ResNet, Transformers, etc.) into dynamics-based forms, followed by fine-tuning via entropy-reduction to obtain the stabilized dynamic states. We observe consistent improvements of these transformed models on the ImageNet dataset in terms of computational complexity, the number of trainable units, testing accuracy, and robustness. Moreover, we demonstrate the correlation between the performance of a neural system and its structural entropy.