Papers › Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Taco S. Cohen, Maurice Weiler, Berkay Kicanaoglu, Max Welling
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. Here we show how this principle can be extended beyond global symmetries to local gauge transformations. This enables the development of a very general class of convolutional neural networks on manifolds that depend only on the intrinsic geometry, and which includes many popular methods from equivariant and geometric deep learning. We implement gauge equivariant CNNs for signals defined on the surface of the icosahedron, which provides a reasonable approximation of the sphere. By choosing to work with this very regular manifold, we are able to implement the gauge equivariant convolution using a single conv2d call, making it a highly scalable and practical alternative to Spherical CNNs. Using this method, we demonstrate substantial improvements over previous methods on the task of segmenting omnidirectional images and global climate patterns.
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Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Semantic Segmentation | Stanford2D3D Panoramic | GaugeNet (R2R-U-Net) | mAcc | 55.9 | #23 of 25 | Archive leaderboard | report |
| Semantic Segmentation | Stanford2D3D Panoramic | GaugeNet (R2R-U-Net) | mIoU | 39.4% | #23 of 25 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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