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

arXiv 2406.07790 ↗First posted 12 Jun 2024cs.NE cs.AI eess.IVcited by 3

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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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 3 of its 67 references that are in the map. First posted on arXiv 12 Jun 2024.

Builds on

3 of 67 references.

References · 3

  1. 2016Small-World Brain Networks Revisitedcited by 16
  2. 2022p-Adic Statistical Field Theory and Deep Belief Networkscited by 2
  3. 2023Hierarchical Wilson-Cowan Models and Connection Matricescited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025v-PuNNs: van der Put Neural Networks for Transparent Ultrametric Representation Learningcited by 5
  2. 2026p-adic Character Neural Networkcited by 2
  3. 2025Kolmogorov GAM Networks are all you need!cited by 1