Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis

2026-03-18

AI Summary

Existing methods for 3D point clouds struggle to simultaneously achieve strict SE(3) equivariance and scalability to large-scale data. This work proposes the ECKConv architecture, which explicitly constructs continuous SE(3)-equivariant convolutional kernels over double coset spaces and integrates them with an interleaved operator combining coordinate-based neural networks and group convolutions. This design enables efficient and memory-friendly feature extraction while preserving full equivariance. The proposed method substantially enhances model expressiveness and computational efficiency, outperforming existing equivariant approaches across multiple tasks—including point cloud classification, pose registration, part segmentation, and large-scale semantic segmentation—thereby demonstrating a compelling balance among equivariance, scalability, and performance.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

A symmetry on rigid motion is one of the salient factors in efficient learning of 3D point cloud problems. Group convolution has been a representative method to extract equivariant features, but its realizations have struggled to retain both rigorous symmetry and scalability simultaneously. We advocate utilizing the intertwiner framework to resolve this trade-off, but previous works on it, which did not achieve complete SE(3) symmetry or scalability to large-scale problems, necessitate a more advanced kernel architecture. We present Equivariant Coordinate-based Kernel Convolution, or ECKConv. It acquires SE(3) equivariance from the kernel domain defined in a double coset space, and its explicit kernel design using coordinate-based networks enhances its learning capability and memory efficiency. The experiments on diverse point cloud tasks, e.g., classification, pose registration, part segmentation, and large-scale semantic segmentation, validate the rigid equivariance, memory scalability, and outstanding performance of ECKConv compared to state-of-the-art equivariant methods.

Problem

• SE(3) equivariance
• point cloud analysis
• scalability
• group convolution
• symmetry

Innovation

• SE(3) equivariance
• coordinate-based kernel
• double coset space
• point cloud analysis
• memory-efficient convolution