Neural ordinary differential equations (Neural ODEs) is a family of continuous-depth neural networks where the evolution of hidden states is governed by learnable temporal derivatives. We identify a significant limitation in applying traditional Batch Normalization (BN) to Neural ODEs, due to a fundamental mismatch --- BN was initially designed for discrete neural networks with no temporal dimension, whereas Neural ODEs operate continuously over time. To bridge this gap, we introduce temporal adaptive Batch Normalization (TA-BN), a novel technique that acts as the continuous-time analog to traditional BN. Our empirical findings reveal that TA-BN enables the stacking of more layers within Neural ODEs, enhancing their performance. Moreover, when confined to a model architecture consisting of a single Neural ODE followed by a linear layer, TA-BN achieves 91.1\% test accuracy on CIFAR-10 with 2.2 million parameters, making it the first \texttt{unmixed} Neural ODE architecture to approach MobileNetV2-level parameter efficiency.

Neural Ordinary Differential Equations (ODEs) was recently introduced as a new family of neural network models, which relies on black-box ODE solvers for inference and training. Some ODE solvers called adaptive can adapt their evaluation strategy depending on the complexity of the problem at hand, opening great perspectives in machine learning. However, this paper describes a simple set of experiments to show why adaptive solvers cannot be seamlessly leveraged as a black-box for dynamical systems modelling. By taking the Lorenz'63 system as a showcase, we show that a naive application of the Fehlberg's method does not yield the expected results. Moreover, a simple workaround is proposed that assumes a tighter interaction between the solver and the training strategy.