Butterfly Factorization and Butterfly-Net: from Numerical Linear Algebra to Machine Learning
Surprisingly, these sparse matrices in Butterfly Factorization can be viewed as convolutions! Therefore we can construct a simplified structured Convolutional Neural Network (CNN) based on it. This new algorithm, which we named Butterfly-Net, Inherits the advantages of CNN and reduces the computational effort. Together with Butterfly Initialization, which means simply using the elements in Butterfly Factorization matrices to initialize the neural networks, we can complete multiple tasks better and faster.