# Hierarchical Neural Networks, p-Adic PDEs, and Applications to Image Processing

arXiv: https://arxiv.org/abs/2406.07790 · HTML: https://mlsanity.com/paper/2406.07790/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 67 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [Small-World Brain Networks Revisited](https://mlsanity.com/paper/1608.05665/) (2016)
- [p-Adic Statistical Field Theory and Deep Belief Networks](https://mlsanity.com/paper/2207.13877/) (2022)
- [Hierarchical Wilson-Cowan Models and Connection Matrices](https://mlsanity.com/paper/2305.00120/) (2023)

## Built on by (most cited first, 3 of 3)

- [v-PuNNs: van der Put Neural Networks for Transparent Ultrametric Representation Learning](https://mlsanity.com/paper/2508.01010/) (2025)
- [p-adic Character Neural Network](https://mlsanity.com/paper/2603.29905/) (2026)
- [Kolmogorov GAM Networks are all you need!](https://mlsanity.com/paper/2501.00704/) (2025)

## Abstract (arXiv)

The first goal of this article is to introduce a new type of p-adic reaction-diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to provide a quick review of the state of the art of p-adic cellular neural networks and their applications to image processing.