Deep neural networks on diffeomorphism groups for optimal shape reparametrization

Author:

Celledoni Elena,Glöckner Helge,Riseth Jørgen N.ORCID,Schmeding Alexander

Funder

Horizon 2020

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Computer Networks and Communications,Software

Reference39 articles.

1. Agrachev, A., Caponigro, M.: Controllability on the group of diffeomorphisms. Annales de l’Institut Henri Poincaré C, Analyse non linéaire 26(6), 2503–2509 (2009). https://doi.org/10.1016/j.anihpc.2009.07.003

2. Agrachev, A., Sarychev, A.: Control on the manifolds of mappings with a view to the deep learning. Journal of Dynamical and Control Systems (2021). https://doi.org/10.1007/s10883-021-09561-2

3. Bauer, M., Bruveris, M., Marsland, S., Michor, P.W.: Constructing reparameterization invariant metrics on spaces of plane curves. Differential Geometry and its Applications 34, 139–165 (2014). https://doi.org/10.1016/j.difgeo.2014.04.008

4. Behrmann, J., Grathwohl, W., Chen, R.T.Q., Duvenaud, D., Jacobsen, J.H.: Invertible residual networks. In: K. Chaudhuri, R. Salakhutdinov (eds.) Proceedings of the $$36^{{\rm th}}$$ International Conference on Machine Learning, Proceedings of Machine Learning Research, vol. 97, pp. 573–582. PMLR, Long Beach, California, USA (2019). URL https://proceedings.mlr.press/v97/behrmann19a.html

5. Behrmann, J., Vicol, P., Wang, K.C., Grosse, R., Jacobsen, J.H.: Understanding and mitigating exploding inverses in invertible neural networks. In: A. Banerjee, K. Fukumizu (eds.) Proceedings of The $$24^{{\rm th}}$$ International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, vol. 130, pp. 1792–1800. PMLR, Virtual (2021). URL https://proceedings.mlr.press/v130/behrmann21a.html

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