# Approximate Equivariance SO(3) Needlet Convolution

arXiv: https://arxiv.org/abs/2206.10385 · HTML: https://mlsanity.com/paper/2206.10385/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks](https://mlsanity.com/paper/1810.01483/) (2018)
- [CosmoVAE: Variational Autoencoder for CMB Image Inpainting](https://mlsanity.com/paper/2001.11651/) (2020)

## Built on by (most cited first, 6 of 6)

- [Hypergraph Tversky-Aware Domain Incremental Learning for Brain Tumor Segmentation with Missing Modalities](https://mlsanity.com/paper/2505.16809/) (2025)
- [Spatially Gene Expression Prediction using Dual-Scale Contrastive Learning](https://mlsanity.com/paper/2506.23827/) (2025)
- [Memory-Augmented Incomplete Multimodal Survival Prediction via Cross-Slide and Gene-Attentive Hypergraph Learning](https://mlsanity.com/paper/2506.19324/) (2025)
- [Framelet Message Passing](https://mlsanity.com/paper/2302.14806/) (2023)
- [Graph Representation Learning for Interactive Biomolecule Systems](https://mlsanity.com/paper/2304.02656/) (2023)
- [FOCA: Frequency-Oriented Cross-Domain Forgery Detection, Localization and Explanation via Multi-Modal Large Language Model](https://mlsanity.com/paper/2602.18880/) (2026)

## Abstract (arXiv)

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 mathbbS2 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.