Operator-learning-inspired Modeling of Neural Ordinary Differential Equations
This work addresses a key bottleneck in NODEs for researchers and practitioners in deep learning, offering a novel approach to improve performance in tasks like image classification and time series analysis.
The paper tackles the modeling of the time-derivative term in neural ordinary differential equations (NODEs) by proposing a branched Fourier neural operator (BFNO) method, which significantly outperforms existing methods in general downstream tasks.
Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for various downstream tasks, e.g., image classification, time series classification, image generation, etc. Its key part is how to model the time-derivative of the hidden state, denoted dh(t)/dt. People have habitually used conventional neural network architectures, e.g., fully-connected layers followed by non-linear activations. In this paper, however, we present a neural operator-based method to define the time-derivative term. Neural operators were initially proposed to model the differential operator of partial differential equations (PDEs). Since the time-derivative of NODEs can be understood as a special type of the differential operator, our proposed method, called branched Fourier neural operator (BFNO), makes sense. In our experiments with general downstream tasks, our method significantly outperforms existing methods.