Topological Neural Networks over the Air
This work addresses the challenge of decentralized neural network implementation in noisy wireless environments, representing an incremental advancement in domain-specific applications.
The paper tackles the problem of applying topological neural networks in realistic wireless communication scenarios by proposing a novel design that incorporates channel impairments like fading and noise into the architecture, achieving robustness and superior performance compared to existing methods.
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.