APPROXIMATE EQUIVARIANCE SO(3) NEEDLET CONVOLUTION

Kai Yi, Jialin Chen, Yu Guang Wang, Bingxin Zhou, Pietro Liò, Yanan Fan, Jan Hamann
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:189-198, 2022.

Abstract

This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\sS^2$ onto the SO(3) group, which decomposes a spherical signal to approximate and detailed spectral coefficients by a set of tight framelet operators. The spherical signal during the decomposition and reconstruction achieves rotation invariance. Based on needlet transforms, we form a Needlet approximate Equivariance Spherical CNN (NES) with multiple SO(3) needlet convolutional layers. The network establishes a powerful tool to extract geometric-invariant features of spherical signals. The model allows sufficient network scalability with multi-resolution representation. A robust signal embedding is learned with wavelet shrinkage activation function, which filters out redundant high-pass representation while maintaining approximate rotation invariance. The NES achieves state-of-the-art performance for quantum chemistry regression and Cosmic Microwave Background (CMB) delensing reconstruction, which shows great potential for solving scientific challenges with high-resolution and multi-scale spherical signal representation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-yi22a, title = {APPROXIMATE EQUIVARIANCE SO(3) NEEDLET CONVOLUTION}, author = {Yi, Kai and Chen, Jialin and Wang, Yu Guang and Zhou, Bingxin and Li\`{o}, Pietro and Fan, Yanan and Hamann, Jan}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {189--198}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/yi22a/yi22a.pdf}, url = {https://proceedings.mlr.press/v196/yi22a.html}, abstract = {This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\sS^2$ onto the SO(3) group, which decomposes a spherical signal to approximate and detailed spectral coefficients by a set of tight framelet operators. The spherical signal during the decomposition and reconstruction achieves rotation invariance. Based on needlet transforms, we form a Needlet approximate Equivariance Spherical CNN (NES) with multiple SO(3) needlet convolutional layers. The network establishes a powerful tool to extract geometric-invariant features of spherical signals. The model allows sufficient network scalability with multi-resolution representation. A robust signal embedding is learned with wavelet shrinkage activation function, which filters out redundant high-pass representation while maintaining approximate rotation invariance. The NES achieves state-of-the-art performance for quantum chemistry regression and Cosmic Microwave Background (CMB) delensing reconstruction, which shows great potential for solving scientific challenges with high-resolution and multi-scale spherical signal representation.} }
Endnote
%0 Conference Paper %T APPROXIMATE EQUIVARIANCE SO(3) NEEDLET CONVOLUTION %A Kai Yi %A Jialin Chen %A Yu Guang Wang %A Bingxin Zhou %A Pietro Liò %A Yanan Fan %A Jan Hamann %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-yi22a %I PMLR %P 189--198 %U https://proceedings.mlr.press/v196/yi22a.html %V 196 %X This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\sS^2$ onto the SO(3) group, which decomposes a spherical signal to approximate and detailed spectral coefficients by a set of tight framelet operators. The spherical signal during the decomposition and reconstruction achieves rotation invariance. Based on needlet transforms, we form a Needlet approximate Equivariance Spherical CNN (NES) with multiple SO(3) needlet convolutional layers. The network establishes a powerful tool to extract geometric-invariant features of spherical signals. The model allows sufficient network scalability with multi-resolution representation. A robust signal embedding is learned with wavelet shrinkage activation function, which filters out redundant high-pass representation while maintaining approximate rotation invariance. The NES achieves state-of-the-art performance for quantum chemistry regression and Cosmic Microwave Background (CMB) delensing reconstruction, which shows great potential for solving scientific challenges with high-resolution and multi-scale spherical signal representation.
APA
Yi, K., Chen, J., Wang, Y.G., Zhou, B., Liò, P., Fan, Y. & Hamann, J.. (2022). APPROXIMATE EQUIVARIANCE SO(3) NEEDLET CONVOLUTION. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:189-198 Available from https://proceedings.mlr.press/v196/yi22a.html.

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