Efficient, Accurate and Stable Gradients for Neural ODEs

• URL: http://arxiv.org/abs/2410.11648v1
• Date: Tue, 15 Oct 2024 14:36:05 GMT
• Title: Efficient, Accurate and Stable Gradients for Neural ODEs
• Authors: Sam McCallum, James Foster,
• Abstract summary: We present a class of algebraically reversible solvers that are both high-order and numerically stable. This construction naturally extends to numerical schemes for Neural CDEs and SDEs.
• Score: 3.79830302036482
• License:
• Abstract: Neural ODEs are a recently developed model class that combine the strong model priors of differential equations with the high-capacity function approximation of neural networks. One advantage of Neural ODEs is the potential for memory-efficient training via the continuous adjoint method. However, memory-efficient training comes at the cost of approximate gradients. Therefore, in practice, gradients are often obtained by simply backpropagating through the internal operations of the forward ODE solve - incurring high memory cost. Interestingly, it is possible to construct algebraically reversible ODE solvers that allow for both exact gradients and the memory-efficiency of the continuous adjoint method. Unfortunately, current reversible solvers are low-order and suffer from poor numerical stability. The use of these methods in practice is therefore limited. In this work, we present a class of algebraically reversible solvers that are both high-order and numerically stable. Moreover, any explicit numerical scheme can be made reversible by our method. This construction naturally extends to numerical schemes for Neural CDEs and SDEs.

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