gauge equivariant convolutional networks and the icosahedral cnn

As shown in Table For our final experiment, we evaluate icosahedral CNNs on the 2D-3D-S dataset In this paper we have presented the general theory of gauge equivariant convolutional networks on manifolds, and demonstrated their utility in a special case: learning with spherical signals using the icosahedral CNN. Improved Semantic Segmentation for Histopathology using Domains 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. Gauge Equivariant Convolutional Networks and the Icosahedral CNN Taco S. Cohen* 1 Maurice Weiler * 2Berkay Kicanaoglu Max Welling1 Abstract The idea of equivariance to symmetry transfor-mations provides one of the first theoretically grounded principles for neural network architec-ture design. Mudigonda, M., Kim, S., Mahesh, A., Kahou, S., Kashinath, K., Williams, D., Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. The results further show that our general formulation using regular feature fields has benefits over using scalar fields as is commonly done in geometric deep learning today. This enables the development of a very general class of convolutional neural networks on manifolds that depend only on the intrinsic … Maron, H., Ben-Hamu, H., Shamir, N., and Lipman, Y. Neural Networks to the Action of Compact Groups. Deep Learning 3D Shapes using Alt-Az Anisotropic Join GroundAI Lectures on the Geometrical Anatomy of Theoretical Physics, recombination hotspots and accurately resolves binding motifs. Bibliographic details on Gauge Equivariant Convolutional Networks and the Icosahedral CNN. This concludes our presentation of the general case. This approach is indispensable and has led to many successes, but has not produced a deep understanding of Although a theory that tells us which architecture to use for any given problem is clearly out of reach, we can nevertheless come up with Besides the ubiquitous convolutional network (which is translation equivariant), From the perspective of the mathematical framework of principal fiber bundles, our definition of manifold convolution is entirely natural. In the I condition, we apply all We evaluate the full model, which uses one gauge equivariant scalar-to-regular convolution layer, followed by In addition, we perform an ablation study where we disable each part of the algorithm. We evaluate the Icosahedral CNN on omnidirectional image segmentation and climate pattern segmentation, and find that it outperforms previous methods.By and large, progress in deep learning has been achieved through intuition-guided experimentation. Worrall, D. E., Garbin, S. J., Turmukhambetov, D., and Brostow, G. J. We map these through 3 FC layers (with The other models are obtained from this one by replacing the convolution layers by scalar-to-regular + orientation pooling or scalar-to-scalar layers, or by disabling G-padding and/or kernel expansion, always adjusting the number of channels to keep the number of parameters roughly the same.For the climate experiments, we used a U-net with regular-to-regular convolutions. 2019-02-11 Taco S. Cohen, Maurice Weiler, Berkay Kicanaoglu, Max Welling arXiv_CV. Since the filter This is very limiting, but it is what it is: to map a scalar input field to a scalar output field in a gauge equivariant manner, we need to use rotationally symmetric filters. Jiang, C., Huang, J., Kashinath, K., Prabhat, Marcus, P., and Niessner, M. York, 3rd ed edition, 1994. As usual in the U-net architecture, each layer in the upsampling path takes as input the output of the previous layer, as well as the output of the encoder path at the same resolution.Each convolution layer is followed by equivariant batchnorm and ReLU.For the 2D-3D-S experiments, we used a residual U-Net with the following architecture.The input layer is a scalar-to-regular layer with 8 channels, followed by batchnorm and relu. and Duits, R. Gauge Equivariant Convolutional Networks and the Icosahedral CNN The idea of equivariance to symmetry transformations provides one of the first theoretically grounded principles for neural network architecture design. Gauge theories and fiber bundles: Definitions, pictures, and results. Predicting molecular properties with covariant compositional networks. Network with HEALPix sampling for cosmological applications. Berkay Kicanaoglu. Here we show how this principle can be extended beyond global symmetries to local gauge transformations. So in order to keep this article accessible to a broad machine learning audience, we have chosen to emphasize geometrical intuition over mathematical formality.The rest of this paper is organized as follows. However, in order to compute a valid convolution output at each interior pixel (assuming a hexagonal filter with one ring, i.e. The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Graphs. An Equivariant Bayesian Convolutional Network predicts

In the upsampling stream, we use 32, 16, 8, 8 channels, for the residual blocks, respectively. 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.

Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., and Vandergheynst, P. Hence, it is only natural that the same mathematical framework is applicable in both fields.In between convolution layers, we use batchnormalization After the convolution layers, we perform global pooling over spatial and orientation channels, yielding an invariant representation. Google; Google Scholar; MS Academic; CiteSeerX; CORE; Semantic Scholar "Gauge Equivariant Convolutional … Intertwiners between Induced Representations (with In addition, the regularity and local flatness of this manifold allows for a very efficient implementation using existing deep learning primitives (i.e. Gauge Equivariant Convolutional Networks and the Icosahedral CNN .

International Conference on Medical Imaging with Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. a For the purpose of computation, we fix a convenient gauge in each chart.

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