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.

I’ve been interested by this since seeing the (Haber and Ruthotto 2018) paper, but it’s got a real kick from the (Chen et al. 2018) won the prize at NeurIPS for learning the ODEs themselves.

## 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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Anil, Cem, James Lucas, and Roger Grosse. 2018. “Sorting Out Lipschitz Function Approximation,” November. https://arxiv.org/abs/1811.05381v1.

Arjovsky, Martin, Amar Shah, and Yoshua Bengio. 2016. “Unitary Evolution Recurrent Neural Networks.” In *Proceedings of the 33rd International Conference on International Conference on Machine Learning - Volume 48*, 1120–8. ICML’16. New York, NY, USA: JMLR.org. http://arxiv.org/abs/1511.06464.

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Chang, Bo, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, and Elliot Holtham. 2018. “Reversible Architectures for Arbitrarily Deep Residual Neural Networks.” In. http://arxiv.org/abs/1709.03698.

Chang, Bo, Lili Meng, Eldad Haber, Frederick Tung, and David Begert. 2018. “Multi-Level Residual Networks from Dynamical Systems View.” In *PRoceedings of ICLR*. http://arxiv.org/abs/1710.10348.

Chen, Tianqi, Ian Goodfellow, and Jonathon Shlens. 2015. “Net2Net: Accelerating Learning via Knowledge Transfer.” November 17, 2015. http://arxiv.org/abs/1511.05641.

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