GMR-Conv: An Efficient Rotation and Reflection Equivariant Convolution Kernel Using Gaussian Mixture Rings
Authors: Yuexi Du, Jiazhen Zhang, Nicha C. Dvornek, John A. Onofrey
Abstract: Symmetry, where certain features remain invariant under geometric transformations, can often serve as a powerful prior in designing convolutional neural networks (CNNs). While conventional CNNs inherently support translational equivariance, extending this property to rotation and reflection has proven challenging, often forcing a compromise between equivariance, efficiency, and information loss. In this work, we introduce Gaussian Mixture Ring Convolution (GMR-Conv), an efficient convolution kernel that smooths radial symmetry using a mixture of Gaussian-weighted rings. This design mitigates discretization errors of circular kernels, thereby preserving robust rotation and reflection equivariance without incurring computational overhead. We further optimize both the space and speed efficiency of GMR-Conv via a novel parameterization and computation strategy, allowing larger kernels at an acceptable cost. Extensive experiments on eight classification and one segmentation datasets demonstrate that GMR-Conv not only matches conventional CNNs' performance but can also surpass it in applications with orientation-less data. GMR-Conv is also proven to be more robust and efficient than the state-of-the-art equivariant learning methods. Our work provides inspiring empirical evidence that carefully applied radial symmetry can alleviate the challenges of information loss, marking a promising advance in equivariant network architectures. The code is available at https://github.com/XYPB/GMR-Conv.
Explore the paper tree
Click on the tree nodes to be redirected to a given paper and access their summaries and virtual assistant
Look for similar papers (in beta version)
By clicking on the button above, our algorithm will scan all papers in our database to find the closest based on the contents of the full papers and not just on metadata. Please note that it only works for papers that we have generated summaries for and you can rerun it from time to time to get a more accurate result while our database grows.