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Use native mathematical support
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README.md

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@@ -11,11 +11,10 @@ Instead, *escnn* supports steerable CNNs equivariant to both 2D and 3D isometrie
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For instance, classical convolutional neural networks (*CNN*s) are by design equivariant to translations of their input.
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This means that a translation of an image leads to a corresponding translation of the network's feature maps.
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This package provides implementations of neural network modules which are equivariant under all *isometries* E(2) of the image plane
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![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^2)
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and all *isometries* E(3) of the 3D space
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![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^3)
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$\mathbb{R}^2$
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and all *isometries* E(3) of the 3D space $\mathbb{R}^3$
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, that is, under *translations*, *rotations* and *reflections* (and can, potentially, be extended to all isometries E(n) of
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![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^n)
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$\mathbb{R}^n$
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).
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In contrast to conventional CNNs, E(n)-equivariant models are guaranteed to generalize over such transformations, and are therefore more data efficient.
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@@ -36,10 +35,10 @@ in our [paper](https://openreview.net/forum?id=WE4qe9xlnQw), we generalize the W
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[A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels](https://arxiv.org/abs/2010.10952)
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from G-homogeneous spaces to more general spaces X carrying a G-action.
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In short, our method leverages a G-steerable basis for unconstrained scalar filters over the whole Euclidean space
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![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^n)
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$\mathbb{R}^n$
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to generate steerable kernel spaces with arbitrary input and output field *types*.
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For example, the left side of the next image shows two elements of a SO(2)-steerable basis for functions on
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![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=X=\mathbb{R}^2) which are used to generate two
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$X=\mathbb{R}^2$ which are used to generate two
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basis elements for SO(2)-equivariant steerable kernels on the right.
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In particular, the steerable kernels considered map a frequency l=1 vector field (2 channels) to a frequency J=2
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vector field (2 channels).
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```
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Line 5 specifies the symmetry group action on the image plane
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![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^2)
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$\mathbb{R}^2$
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under which the network should be equivariant.
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We choose the
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[*cyclic group*](https://en.wikipedia.org/wiki/Cyclic_group)

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