backward pass of

class Kernel(torch.nn.Module)

def forward(self, Y, R, n):

def backward(self, grad_K):

\(\displaystyle K^{l_{out}l_{in}}_{ui\;vj} = \sum_{l_f\; k} C^{l_{out}l_{in}l_f}_{ijk} \; Y^{l_f}_k \; R^{l_{out}l_{in}l_f}_{uv} \; n^{l_{out}l_{in}} \)

\(\displaystyle \frac{\partial}{\partial R^{l_{out}l_{in}l_f}_{uv}} = \sum_{i\;j\;k} \frac{\partial}{\partial K^{l_{out}l_{in}}_{ui\;vj}}  C^{l_{out}l_{in}l_f}_{ijk} \; Y^{l_f}_k \; n^{l_{out}l_{in}}\)

\(\displaystyle \frac{\partial}{\partial Y^{l_f}_k} = \sum_{l_{out}\;l_{in}\;ui\;vj} \frac{\partial}{\partial K^{l_{out}l_{in}}_{ui\;vj}}  C^{l_{out}l_{in}l_f}_{ijk} \; R^{l_{out}l_{in}l_f}_{uv} \; n^{l_{out}l_{in}}\)

\(l_{in},l_{out},l_f =\) repr. orders               \(u,v = \) multiplicities               \(i,j =\) repr. components

backward

By Mario Geiger

backward

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