Topological Neural Networks over the Air

2024-04-14

IEEE International Conference on Acoustics, Speech, and Signal Processing

AI Summary

To address the insufficient robustness of Topological Neural Networks (TNNs) under realistic wireless fading and noise, this paper proposes the first channel-aware TNN architecture tailored for Over-the-Air Computation (AirComp). Built on regular cell complexes, the model explicitly incorporates physical channel characteristics—such as channel gains and noise distributions—into topological convolutional filtering operations, enabling joint communication-and-learning modeling. Compared with conventional Graph Neural Networks and communication-agnostic baselines, the proposed method significantly improves accuracy and robustness in distributed signal processing under channel distortion, achieving average error reductions of 32.7%–58.4% across diverse SNR and fading scenarios. This work establishes the first unified framework integrating high-order topological representation, AirComp, and physical-layer communication modeling.

Technology Category

• Machine Learning: Hardware-aware ML
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Social Networks and Social Media: Computational social science

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 con-volutional 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.

Problem

• TNNs in realistic wireless communication scenarios
• Incorporating channel impairments in TNN design
• Over-the-air computation with topological convolutional filtering

Innovation

• Topological Neural Networks
• Over-the-air computation
• Channel impairment robustness