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

• URL: http://arxiv.org/abs/2603.17538v1
• Date: Wed, 18 Mar 2026 09:45:55 GMT
• Title: Learning Coordinate-based Convolutional Kernels for Continuous SE(3) Equivariant and Efficient Point Cloud Analysis
• Abstract summary: A symmetry on rigid motion is one of the salient factors in efficient learning of 3D point cloud problems.<n>Group convolution has been a representative method to extract equivariant features.<n>We present Equivariant Coordinate-based Kernel Convolution, or ECKConv.
• Score: 21.338938947004124
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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