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Use github-native math expressions in markdown #7

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Use github-native math expressions in markdown #7

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13 changes: 6 additions & 7 deletions README.md
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Expand Up @@ -11,11 +11,10 @@ Instead, *escnn* supports steerable CNNs equivariant to both 2D and 3D isometrie
For instance, classical convolutional neural networks (*CNN*s) are by design equivariant to translations of their input.
This means that a translation of an image leads to a corresponding translation of the network's feature maps.
This package provides implementations of neural network modules which are equivariant under all *isometries* E(2) of the image plane
![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^2)
and all *isometries* E(3) of the 3D space
![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^3)
$\mathbb{R}^2$
and all *isometries* E(3) of the 3D space $\mathbb{R}^3$
, that is, under *translations*, *rotations* and *reflections* (and can, potentially, be extended to all isometries E(n) of
![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^n)
$\mathbb{R}^n$
).
In contrast to conventional CNNs, E(n)-equivariant models are guaranteed to generalize over such transformations, and are therefore more data efficient.

Expand All @@ -36,10 +35,10 @@ in our [paper](https://openreview.net/forum?id=WE4qe9xlnQw), we generalize the W
[A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels](https://arxiv.org/abs/2010.10952)
from G-homogeneous spaces to more general spaces X carrying a G-action.
In short, our method leverages a G-steerable basis for unconstrained scalar filters over the whole Euclidean space
![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^n)
$\mathbb{R}^n$
to generate steerable kernel spaces with arbitrary input and output field *types*.
For example, the left side of the next image shows two elements of a SO(2)-steerable basis for functions on
![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=X=\mathbb{R}^2) which are used to generate two
$X=\mathbb{R}^2$ which are used to generate two
basis elements for SO(2)-equivariant steerable kernels on the right.
In particular, the steerable kernels considered map a frequency l=1 vector field (2 channels) to a frequency J=2
vector field (2 channels).
Expand Down Expand Up @@ -154,7 +153,7 @@ y = relu(conv(x)) # 15
```

Line 5 specifies the symmetry group action on the image plane
![my equation](https://chart.apis.google.com/chart?cht=tx&chs=19&chl=\mathbb{R}^2)
$\mathbb{R}^2$
under which the network should be equivariant.
We choose the
[*cyclic group*](https://en.wikipedia.org/wiki/Cyclic_group)
Expand Down