Convert twiddle to corresponding dense matrix

[JCBrouwer]

Hello, thanks for open sourcing this code, it's very interesting work!

I'm wondering how the parameters of the Butterfly layer can be converted to their corresponding dense matrix. Is code for this somewhere in the repository? (I've looked around quite a bit, but might just be missing it). Otherwise could you point me to a resource to learn how to implement this myself?

A little bit of context: I want to use a low rank parameterization of a batch of DxD matrices that have structures that should be well represented by butterfly matrices. However, this BxDxD tensor is used in a tensor product that can't be factored to a single batch matrix multiply (which means using the drop in replacement modules / butterfly_multiply function doesn't work). Therefore I'd like to just convert to a dense matrix and perform the tensor product in the regular way. I understand that this gives up the speedy CUDA implementation, but I'm willing to make this compromise because at least the number of learnable parameters will still be small.

[tridao]

To get the dense matrix from a butterfly you can just multiply the butterfly with an identity matrix:

import torch
import torch.nn.functional as F

from torch_butterfly import Butterfly
b = Butterfly(32, 32, bias=False)
# Need to transpose since we're following nn.Linear convention of multiply input @ weight.t()
dense_matrix = b(torch.eye(32)).t()
# Check that this gives the same answer
x = torch.randn(16, 32)
assert torch.allclose(b(x), F.linear(x, dense_matrix), rtol=1e-5, atol=1e-6)