Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space
This paper proposes sampling in feature space for group-convolutional neural networks (GCNNs), replacing geometrically dense samples with representative samples selected by feature similarity to decouple geometric resolution from memory and processing costs. Empirical results show that coarse feature-space sampling preserves classification accuracy well, enabling substantial acceleration of equivariant 3D classifier training.
[2605.15368] Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space
[Submitted on 14 May 2026]
Title:Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space
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Abstract:Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.
Comments: 11 pages, 7 figures, 2 tables
Subjects:
Computer Vision and Pattern Recognition (cs.CV); Graphics (cs.GR); Machine Learning (cs.LG)
Cite as: arXiv:2605.15368 [cs.CV]
(or arXiv:2605.15368v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2605.15368
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Daniel Franzen [view email] [v1] Thu, 14 May 2026 19:47:43 UTC (3,466 KB)
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