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Approximate Equivariance SO(3) Needlet Convolution

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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.



Kai Yi is a third-year Ph.D. student majoring in mathematics at the School of Mathematics and Statistics in the University of New South Wales (UNSW) in Sydney, Australia. His research interests lie in geometric deep learning and Bayesian statistics. He has applied geometric deep learning methods to estimating gravitational lensing parameters in cosmology and used VAE for inpainting CMB maps.

This talk is part of the Artificial Intelligence Research Group Talks (Computer Laboratory) series.

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