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Neural ODEs demonstrate strong performance in generative and time-seriesmodelling. However, training them via the adjoint method is slow compared todiscrete models due to the requirement of numerically solving ODEs. To speedneural ODEs up, a common approach is to regularise the solutions. However, thisapproach may affect the expressivity of the model; when the trajectory itselfmatters, this is particularly important. In this paper, we propose analternative way to speed up the training of neural ODEs. The key idea is tospeed up the adjoint method by using Gau{\ss}-Legendre quadrature to solveintegrals faster than ODE-based methods while remaining memory efficient. Wealso extend the idea to training SDEs using the Wong-Zakai theorem, by traininga corresponding ODE and transferring the parameters. Our approach leads tofaster training of neural ODEs, especially for large models. It also presents anew way to train SDE-based models.

Faster Training of Neural ODEs Using Gau{\ss}-Legendre Quadrature