Correcting auto-differentiation in neural-ODE training

• URL: http://arxiv.org/abs/2306.02192v1
• Date: Sat, 3 Jun 2023 20:34:14 GMT
• Title: Correcting auto-differentiation in neural-ODE training
• Authors: Yewei Xu, Shi Chen, Qin Li and Stephen J. Wright
• Abstract summary: We find that when a neural network employs high-order forms to approximate the underlying ODE flows, brute-force computation using auto-differentiation often produces non-converging artificial oscillations. We propose a straightforward post-processing technique that effectively eliminates these oscillations, rectifies the computation and thus respects the updates of the underlying flow.
• Score: 19.472357078065194
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Does the use of auto-differentiation yield reasonable updates to deep neural networks that represent neural ODEs? Through mathematical analysis and numerical evidence, we find that when the neural network employs high-order forms to approximate the underlying ODE flows (such as the Linear Multistep Method (LMM)), brute-force computation using auto-differentiation often produces non-converging artificial oscillations. In the case of Leapfrog, we propose a straightforward post-processing technique that effectively eliminates these oscillations, rectifies the gradient computation and thus respects the updates of the underlying flow.

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