A recurring movement within neural network learning research which tries to render the learning of prediction functions tractable by considering them as dynamical systems, and using the theory of stability in the context of Hamiltonians, optimal control and/or ODE solvers, to make it all work.
Convnets/Resnets as discrete ODE approximations
Arguing that neural networks are in the limit approximants to quadrature solutions of certain ODES, work and gain insights and new tricks into neural nets by using ODE tricks. This is mostly what Haber and Rhutthoto et al do. “Stability of training” is a useful outcome here. Related, but not quite the same, notion of stability, as in input-stability in learning. (Haber and Ruthotto 2018; Haber et al. 2017; Chang, Meng, Haber, Ruthotto, et al. 2018; Ruthotto and Haber 2018)
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