Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space
Quick Take
The paper introduces a feature-space sampling method to optimize GCNNs for 3D geometry classification.
Key Points
- GCNNs utilize symmetry as an inductive bias.
- Feature-space sampling reduces computational costs.
- Coarse sampling maintains high classification accuracy.
📖 Reader Mode
~2 min readAbstract: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)
— Originally published at arxiv.org
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