# FMM-Net: neural network architecture based on the Fast Multipole Method

arXiv: https://arxiv.org/abs/2212.12899 · HTML: https://mlsanity.com/paper/2212.12899/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 25 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)

## Built on by (most cited first, 1 of 1)

- [NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning](https://mlsanity.com/paper/2610.10776/) (2026)

## Abstract (arXiv)

In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into account the sparsity template of the H2 matrix. In numerical comparison with alternative neural networks, including the known H2-based ones, our architecture showed itself as beneficial in terms of performance, memory, and scalability.