OSR-NET: Ordinary Differential Equation-Based Brain State Recognition Neural Network

Neural ordinary differential equation (ODE) can be approximated by nonlinear mappings by using continuous-times ODEs such that a family of models is formed. Due to their desirable properties, such as invertibility, stability, robustness and parameter efficiency, neural ODEs have attracted increasing attention recently. However, its performance (e.g., stability and robustness) on neuroimaging data has not been explored. To fill this gap, we propose an ODE-based brain state recognition neural network (OSR-Net). It incorporates and ODE block to work jointly with other baseline architectures. We apply the steady neural ODE with time-constant to the perturbed blood oxygen level dependent (BOLD) signals to verify the effectiveness, which outperforms vanilla recurrent neural network (RNN)-based model. The driving force of our OSR-Net is the underlying predefined brain cognition state, which stems from a series of symmetric positive definite (SPD) matrix on Riemannian manifold. Experiments on both simulated and task-based functional neuroimaging data from Human Connectome Project (HCP) have validated that OSR-Net achieved favorable cognition state recognition results than other state-of-the-art methods including vanilla neural ODEs. Our work shows the potential of using neural ODEs as a basic module for building robust deep network models when learning to capture complex functional resonance magnetic imaging (fMRI) time series signals due to their inherent stability. We also furnish an insightful understanding of the superior characteristics of ODE-based model by applying it to neuroimage data.