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Neural-ODE parameterize a differential equation using continuous depth neuralnetwork and solve it using numerical ODE-integrator. These models offer aconstant memory cost compared to models with discrete sequence of hidden layersin which memory cost increases linearly with the number of layers. In additionto memory efficiency, other benefits of neural-ode include adaptability ofevaluation approach to input, and flexibility to choose numerical precision orfast training. However, despite having all these benefits, it still has somelimitations. We identify the ODE-integrator (also called ODE-solver) as theweakest link in the chain as it may have stability, consistency and convergence(CCS) issues and may suffer from slower convergence or may not converge at all.We propose a first-order Nesterov's accelerated gradient (NAG) based ODE-solverwhich is proven to be tuned vis-a-vis CCS conditions. We empiricallydemonstrate the efficacy of our approach by training faster, while achievingbetter or comparable performance against neural-ode employing other fixed-stepexplicit ODE-solvers as well discrete depth models such as ResNet in threedifferent tasks including supervised classification, density estimation, andtime-series modelling.

On Tuning Neural ODE for Stability, Consistency and Faster Convergence