# Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling

arXiv: https://arxiv.org/abs/1806.00681 · HTML: https://mlsanity.com/paper/1806.00681/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2018.

## Built on by (most cited first, 10 of 10)

- [Is Attention Better Than Matrix Decomposition?](https://mlsanity.com/paper/2109.04553/) (2021)
- [Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network](https://mlsanity.com/paper/2201.02217/) (2022)
- [Visual Attention Methods in Deep Learning: An In-Depth Survey](https://mlsanity.com/paper/2204.07756/) (2022)
- [Nonparametric learning of kernels in nonlocal operators](https://mlsanity.com/paper/2205.11006/) (2022)
- [Interpreting Depression From Question-wise Long-term Video Recording of SDS Evaluation](https://mlsanity.com/paper/2106.13393/) (2021)
- [Unifying Nonlocal Blocks for Neural Networks](https://mlsanity.com/paper/2108.02451/) (2021)
- [Deep Neural Networks and PIDE discretizations](https://mlsanity.com/paper/2108.02430/) (2021)
- [ML-based identification of the interface regions for coupling local and nonlocal models](https://mlsanity.com/paper/2404.15388/) (2024)
- [BrowNNe: Brownian Nonlocal Neurons & Activation Functions](https://mlsanity.com/paper/2406.15617/) (2024)
- [SIEFormer: Spectral-Interpretable and -Enhanced Transformer for Generalized Category Discovery](https://mlsanity.com/paper/2602.13067/) (2026)

## Abstract (arXiv)

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.