layers difference help

[zhujiem]

Hi, I am very interested in your work and want to try their applications. I have figured out the usage of "monarch_linear.py". But I am still confused about other layers with similar names.

• blockdiag_linear.py
• blocksparse_linear.py
• fastlinear.py -- There are several alternative linear layers here
• structured_linear.py -- I know structured_linear is a base class.

Could you please briefly introduce them to help me better understand your code? Thx in advance.

[zhujiem]

I found that monarch_linear is a pure pytorch implementation, but some others are based on huggingface / trion backend. Which one is faster?

[tridao]

These are just various kinds of weight matrices that we've tried / played with over several projects.

• monarch_linear.py implements Monarch matrices as described in the Monarch paper, with 2 block-diagonal matrices and 2 permutations.
• blockdiag_linear.py implements a linear layer whose weight matrix is just a block-diagonal matrix. This is simpler than Monarch.
• blocksparse_linear.py implements a linear layer whose weight matrices are block-sparse. This is more general than blockdiag_linear, and requires fast block-sparse multiply from either huggingface or triton.
• fastlinear.py: a bunch of different things we tried at some point. Experimental and should not be used.
• structured_linear.py: this is the base class, it takes care of some common steps (converting from sparse to dense, etc.).

[zhujiem]

Hi Tri. Thank you very much for your introduction! It is much more clear for me now. But it did not point out to pixelatedbutterfly linear layer. I even thought blocksparse_linear is for pixelfly. Could you also give me the quick link? I'd like to compare Monarch and Pixelfly.

[tridao]

Pixelfly is blocksparse_linear.py with a specific sparsity pattern (FlatBlockButterflySparsityConfig). You can check the config here to see an example.

[zhujiem]

Many thanks!