# Topological Neural Networks over the Air

arXiv: https://arxiv.org/abs/2502.10070 · HTML: https://mlsanity.com/paper/2502.10070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Builds on (most cited first, 17 of 17)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Over the Air Deep Learning Based Radio Signal Classification](https://mlsanity.com/paper/1712.04578/) (2017)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Deep Learning-Based Communication Over the Air](https://mlsanity.com/paper/1707.03384/) (2017)
- [HodgeNet: Graph Neural Networks for Edge Data](https://mlsanity.com/paper/1912.02354/) (2019)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Signal Processing on Cell Complexes](https://mlsanity.com/paper/2110.05614/) (2021)
- [Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2303.11323/) (2023)
- [Simplicial Attention Neural Networks](https://mlsanity.com/paper/2203.07485/) (2022)
- [Simplicial Convolutional Filters](https://mlsanity.com/paper/2201.11720/) (2022)
- [Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2210.15058/) (2022)
- [Unsupervised Representation Learning of Structured Radio Communication Signals](https://mlsanity.com/paper/1604.07078/) (2016)
- [Detection Algorithms for Communication Systems Using Deep Learning](https://mlsanity.com/paper/1705.08044/) (2017)

## Abstract (arXiv)

Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized communications over different neighborhoods. Existing TNN architectures have not yet been considered in realistic communication scenarios, where channel effects typically introduce disturbances such as fading and noise. This paper aims to propose a novel TNN design, operating on regular cell complexes, that performs over-the-air computation, incorporating the wireless communication model into its architecture. Specifically, during training and inference, the proposed method considers channel impairments such as fading and noise in the topological convolutional filtering operation, which takes place over different signal orders and neighborhoods. Numerical results illustrate the architecture's robustness to channel impairments during testing and the superior performance with respect to existing architectures, which are either communication-agnostic or graph-based.