Latent Time Neural Ordinary Differential Equations

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such Residual networks (ResNets). They provide parameter efficiency and automate the model selection process in some extent. However, they lack much-required uncertainty modelling robustness capabilities which are crucial for their use several real-world applications autonomous driving healthcare. We propose novel unique approach NODE by considering distribution over end-time $T$ of ODE solver. The approach, latent time (LT-NODE), treats variable apply Bayesian obtain posterior from data. In particular, we variational inference learn an approximate parameters. Prediction is done representations different samples can be efficiently using single forward pass. As implicitly defines NODE, would also help NODE. propose, adaptive (ALT-NODE), allow each data point distinct end-times. ALT-NODE uses amortized networks. demonstrate effectiveness approaches through experiments on synthetic image classification