# Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization

arXiv: https://arxiv.org/abs/1912.04154 · HTML: https://mlsanity.com/paper/1912.04154/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime](https://mlsanity.com/paper/2106.01143/) (2021)
- [Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models](https://mlsanity.com/paper/2408.02866/) (2024)
- [Solving the Wide-band Inverse Scattering Problem via Equivariant Neural Networks](https://mlsanity.com/paper/2212.06068/) (2022)
- [ButterflyNet2D: Bridging Classical Methods and Neural Network Methods in Image Processing](https://mlsanity.com/paper/2211.16578/) (2022)

## Abstract (arXiv)

Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform initialization is proposed for both BNet2 and CNN with guaranteed approximation power to represent the Fourier transform operator. Experimentally, BNet2 and the Fourier transform initialization strategy are tested on various tasks, including approximating Fourier transform operator, end-to-end solvers of linear and nonlinear PDEs, and denoising and deblurring of 1D signals. On all tasks, under the same initialization, BNet2 achieves similar accuracy as CNN but has fewer parameters. And Fourier transform initialized BNet2 and CNN consistently improve the training and testing accuracy over the randomly initialized CNN.