Recent work by Xia et al. leveraged the continuous-limit of the classical momentum accelerated gradient descent and proposed heavy-ball neural ODEs. While this model offers computational efficiency and high utility over vanilla neural ODEs, this approach often causes the overshooting of internal dynamics, leading to unstable training of a model. Prior work addresses this issue by using ad-hoc approaches, e.g., bounding the internal dynamics using specific activation functions, but the resulting models do not satisfy the exact heavy-ball ODE. In this work, we propose adaptive momentum estimation neural ODEs (AdamNODEs) that adaptively control the acceleration of the classical momentum-based approach. We find that its adjoint states also satisfy AdamODE and do not require ad-hoc solutions that the prior work employs. In evaluation, we show that AdamNODEs achieve the lowest training loss and efficacy over existing neural ODEs. We also show that AdamNODEs have better training stability than classical momentum-based neural ODEs. This result sheds some light on adapting the techniques proposed in the optimization community to improving the training and inference of neural ODEs further. Our code is available at https://github.com/pmcsh04/AdamNODE.

提出一种新的模型AdamNODEs，用来控制时间步中加速度的变化，从而提高neural ODEs的训练效果和稳定性，该模型比传统的基于动量的neural ODEs和其他方法具有更好的性能。

AdamNODEs：当神经常微分方程遇到自适应矩时估计