Global exponential stability of delayed neural ordinary differential equation and its application in text classification

Neural ordinary differential equations (ODEs) enable continuous dynamic modelling and are widely adopted in dynamic system and natural language processing. However, the stability of neural ODEs is essential for stable convergence and favourable generalisation. Existing studies focus on delay-free or single-delay models, limiting their capability to describe multi-delay dynamics. In addition, stability analysis often relies on constructing Lyapunov–Krasovskii functionals (LKFs) with heavy computation. To address these challenges, this paper proposes a neural ODE framework with a dual time-delay structure. First, a direct analysis method based on system solutions is developed to derive a global exponential stability criterion without LKFs construction. Second, the obtained stability condition is further incorporated into the training process as a regularisation term to constrain parameter updates. Finally, the model is verified on text classification, and results show it outperforms CNN, LSTM, and Transformer by 2.93%, 1.19%, and 9.56% in accuracy, respectively.