Feedback Favors the Generalization of Neural ODEs

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks. A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Stemming from residual neural networks (He et al., 2016), neural ordinary differential equation (neural ODE) (Chen et al., 2018) emerges as a novel learning strategy aiming at learning the latent dynamic model of an unknown system. Recently, neural ODEs have been successfully applied to various scenarios, especially continuous-time missions (Liu & Stacey, 2024; Verma et al., 2024; Greydanus et al., 2019; Cranmer et al., 2020). However, like traditional neural networks, the generalization problem limits the application of neural ODEs in real-world applications. Traditional strategies like model simplification, fit coarsening, data augmentation, and transfer learning have considerably improved the generalization performance of neural networks on unseen tasks (Rohlfs, 2022). However, these strategies usually reduce the Figure 1: Neural network architectures.