Approximate Equivariance SO(3) Needlet Convolution

• URL: http://arxiv.org/abs/2206.10385v1
• Date: Fri, 17 Jun 2022 17:21:56 GMT
• Title: Approximate Equivariance SO(3) Needlet Convolution
• Authors: Kai Yi, Jialin Chen, Yu Guang Wang, Bingxin Zhou, Pietro Li\`o, Yanan Fan, Jan Hamann
• Abstract summary: This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The network establishes a powerful tool to extract geometric-invariant features of spherical signals. The NES achieves state-of-the-art performance for quantum chemistry regression and Cosmic Microwave Background (CMB) delensing reconstruction.
• Score: 3.1050801937854504
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\mathbb{S}^2$ 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.

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