We introduce a new kind of linear transform named Deformable Butterfly (DeBut) that generalizes the conventional butterfly matrices and can be adapted to various input-output dimensions. It inherits the fine-to-coarse-grained learnable hierarchy of traditional butterflies and when deployed to neural networks, the prominent structures and sparsity in a DeBut layer constitutes a new way for network compression. We apply DeBut as a drop-in replacement of standard fully connected and convolutional layers, and demonstrate its superiority in homogenizing a neural network and rendering it favorable properties such as light weight and low inference complexity, without compromising accuracy. The natural complexity-accuracy tradeoff arising from the myriad deformations of a DeBut layer also opens up new rooms for analytical and practical research. The codes and Appendix are publicly available at: https://github.com/ruilin0212/DeBut.
@article{arxiv.2203.13556,
title = {Deformable Butterfly: A Highly Structured and Sparse Linear Transform},
author = {Rui Lin and Jie Ran and King Hung Chiu and Graziano Chesi and Ngai Wong},
journal= {arXiv preprint arXiv:2203.13556},
year = {2022}
}