On the Forward Invariance of Neural ODEs

Wei Xiao, Tsun-Hsuan Wang, Ramin Hasani, Mathias Lechner, Yutong Ban, Chuang Gan, Daniela Rus
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:38100-38124, 2023.

Abstract

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system’s parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-xiao23d, title = {On the Forward Invariance of Neural {ODE}s}, author = {Xiao, Wei and Wang, Tsun-Hsuan and Hasani, Ramin and Lechner, Mathias and Ban, Yutong and Gan, Chuang and Rus, Daniela}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {38100--38124}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/xiao23d/xiao23d.pdf}, url = {https://proceedings.mlr.press/v202/xiao23d.html}, abstract = {We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system’s parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.} }
Endnote
%0 Conference Paper %T On the Forward Invariance of Neural ODEs %A Wei Xiao %A Tsun-Hsuan Wang %A Ramin Hasani %A Mathias Lechner %A Yutong Ban %A Chuang Gan %A Daniela Rus %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-xiao23d %I PMLR %P 38100--38124 %U https://proceedings.mlr.press/v202/xiao23d.html %V 202 %X We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system’s parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.
APA
Xiao, W., Wang, T., Hasani, R., Lechner, M., Ban, Y., Gan, C. & Rus, D.. (2023). On the Forward Invariance of Neural ODEs. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:38100-38124 Available from https://proceedings.mlr.press/v202/xiao23d.html.

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