Implicit Convolutional Kernels for Steerable CNNs
Implicit Convolutional Kernels for Steerable CNNs
Zhdanov, M.; Hoffmann, N.; Cesa, G.
Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group G, such as reflections and rotations. They rely on standard convolutions with G-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group G, implementing a kernel basis does not generalize to other symmetry transformations, complicating the development of general group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize G-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group G for which a G-equivariant MLP can be built. We prove the effectiveness of our method on multiple tasks, including N-body simulations, point cloud classification and molecular property prediction.
Keywords: machine learning; equivariant networks; convolutional neural networks
Involved research facilities
- Data Center
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Contribution to WWW
https://arxiv.org/abs/2212.06096
DOI: 10.48550/arXiv.2212.06096
arXiv: arXiv:2212.06096 -
Poster
NeurIPS 2023, 10.-16.12.2023, New Orleans, USA -
Contribution to proceedings
NeurIPS 2023, 10.-16.12.2023, New Orleans, USA
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Permalink: https://www.hzdr.de/publications/Publ-38090