Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE

The empirical performance of neural ordinary differential equations (NODEs) is significantly inferior to discrete-layer models on benchmark tasks (e. g. image classification). We demonstrate an explanation is the inaccuracy of existing gradient estimation methods: the adjoint method has numerical errors in reverse-mode integration; the naive method suffers from a redundantly deep computation graph. We propose the Adaptive Checkpoint Adjoint (ACA) method: ACA applies a trajectory checkpoint strategy which records the forward- mode trajectory as the reverse-mode trajectory to guarantee accuracy; ACA deletes redundant components for shallow computation graphs; and ACA supports adaptive solvers. On image classification tasks, compared with the adjoint and naive method, ACA achieves half the error rate in half the training time; NODE trained with ACA outperforms ResNet in both accuracy and test-retest reliability. On time-series modeling, ACA outperforms competing methods. Furthermore, NODE with ACA can incorporate physical knowledge to achieve better accuracy.

Authors

• Juntang Zhuang
• Nicha C. Dvornek
• Xiaoxiao Li
• Sekhar Tatikonda
• Xenophon Papademetris
• James S. Duncan

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