Topological Neural Networks over the Air

TL;DR

This paper introduces a novel topological neural network architecture designed for over-the-air computation in wireless communication scenarios, effectively handling channel impairments like fading and noise, and demonstrating superior robustness and performance.

Contribution

The paper proposes a new TNN architecture operating on regular cell complexes that integrates wireless channel effects into its design, enabling robust over-the-air computation.

Findings

Architecture is robust to channel impairments during testing.

Achieves superior performance compared to existing communication-agnostic or graph-based TNNs.

Effectively incorporates fading and noise into topological convolutional filtering.

Abstract

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.