Correcting auto-differentiation in neural-ODE training
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.
PDF AbstractTasks
Datasets
Add Datasets
introduced or used in this paper
Results from the Paper
Submit
results from this paper
to get state-of-the-art GitHub badges and help the
community compare results to other papers.
Methods
No methods listed for this paper. Add
relevant methods here
