Equivariant Deep Dynamical Model for Motion Prediction

Bahar Azari, Deniz Erdogmus
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:11655-11668, 2022.

Abstract

Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction. Most learning tasks have intrinsic symmetries, i.e., the input transformations leave the output unchanged, or the output undergoes a similar transformation. The learning process is, however, usually uninformed of these symmetries. Therefore, the learned representations for individually transformed inputs may not be meaningfully related. In this paper, we propose an SO(3) equivariant deep dynamical model (EqDDM) for motion prediction that learns a structured representation of the input space in the sense that the embedding varies with symmetry transformations. EqDDM is equipped with equivariant networks to parameterize the state-space emission and transition models. We demonstrate the superior predictive performance of the proposed model on various motion data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-azari22a, title = { Equivariant Deep Dynamical Model for Motion Prediction }, author = {Azari, Bahar and Erdogmus, Deniz}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {11655--11668}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/azari22a/azari22a.pdf}, url = {https://proceedings.mlr.press/v151/azari22a.html}, abstract = { Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction. Most learning tasks have intrinsic symmetries, i.e., the input transformations leave the output unchanged, or the output undergoes a similar transformation. The learning process is, however, usually uninformed of these symmetries. Therefore, the learned representations for individually transformed inputs may not be meaningfully related. In this paper, we propose an SO(3) equivariant deep dynamical model (EqDDM) for motion prediction that learns a structured representation of the input space in the sense that the embedding varies with symmetry transformations. EqDDM is equipped with equivariant networks to parameterize the state-space emission and transition models. We demonstrate the superior predictive performance of the proposed model on various motion data. } }
Endnote
%0 Conference Paper %T Equivariant Deep Dynamical Model for Motion Prediction %A Bahar Azari %A Deniz Erdogmus %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-azari22a %I PMLR %P 11655--11668 %U https://proceedings.mlr.press/v151/azari22a.html %V 151 %X Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction. Most learning tasks have intrinsic symmetries, i.e., the input transformations leave the output unchanged, or the output undergoes a similar transformation. The learning process is, however, usually uninformed of these symmetries. Therefore, the learned representations for individually transformed inputs may not be meaningfully related. In this paper, we propose an SO(3) equivariant deep dynamical model (EqDDM) for motion prediction that learns a structured representation of the input space in the sense that the embedding varies with symmetry transformations. EqDDM is equipped with equivariant networks to parameterize the state-space emission and transition models. We demonstrate the superior predictive performance of the proposed model on various motion data.
APA
Azari, B. & Erdogmus, D.. (2022). Equivariant Deep Dynamical Model for Motion Prediction . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:11655-11668 Available from https://proceedings.mlr.press/v151/azari22a.html.

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