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On the Forward Invariance of Neural ODEs
Wei Xiao · Johnson Tsun-Hsuan Wang · Ramin Hasani · Mathias Lechner · Yutong Ban · Chuang Gan · Daniela Rus

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #419
Event URL: https://weixy21.github.io/invariance/ »

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.

Author Information

Wei Xiao (MIT)

I am a Postdoc Associate at the MIT Computer Science and Artificial Intelligence Laboratory

Johnson Tsun-Hsuan Wang (Massachusetts Institute of Technology)
Ramin Hasani (MIT)
Mathias Lechner (Massachusetts Institute of Technology)
Yutong Ban
Chuang Gan (Umass Amherst/ IBM)
Daniela Rus (MIT CSAIL)

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