Interpolated Adjoint Method for Neural ODEs

Talgat Daulbaev, Alexandr Katrutsa, Larisa Markeeva, Julia Gusak, Andrzej Cichocki, Ivan V. Oseledets

Abstract: We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on classification, density estimation, and inference approximation tasks. We also propose a theoretical justification of our approach using logarithmic norm formalism. As a result, our method allows faster model training than the reverse dynamic method that was confirmed and validated by extensive numerical experiments for several standard benchmarks.