# Relay-Assisted Activation-Integrated SIM for Wireless Physical Neural Networks

arXiv: https://arxiv.org/abs/2604.04212 · HTML: https://mlsanity.com/paper/2604.04212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Over-the-Air Edge Inference via End-to-End Metasurfaces-Integrated Artificial Neural Networks](https://mlsanity.com/paper/2504.00233/) (2025)
- [CNNs in the Air via Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2510.25389/) (2025)
- [Non-Linear Relay Optimization using Deep-Learning tools](https://mlsanity.com/paper/2308.12413/) (2023)
- [Over-The-Air Extreme Learning Machines with XL Reception via Nonlinear Cascaded Metasurfaces](https://mlsanity.com/paper/2601.17749/) (2026)
- [Wireless Physical Neural Networks (WPNNs): Opportunities and Challenges](https://mlsanity.com/paper/2602.14094/) (2026)
- [Realization of a Fully Connected Neural Layer Over-the-Air through Multi-hop Amplify-and-Forward Relays](https://mlsanity.com/paper/2603.20489/) (2026)

## Abstract (arXiv)

Wireless physical neural networks (WPNNs) have emerged as a promising paradigm for performing neural computation directly in the physical layer of wireless systems, offering low latency and high energy efficiency. However, most existing WPNN implementations primarily rely on linear physical transformations, which fundamentally limits their expressiveness. In this work, we propose a relay-assisted WPNN architecture based on activation-integrated stacked intelligent metasurfaces (AI-SIMs), where each passive metasurface layer enabling linear wave manipulation is cascaded with an activation metasurface layer that realizes nonlinear processing in the analog domain. By deliberately structuring multi-hop wireless propagation, the relay amplification matrix and the metasurface phase-shift matrices jointly act as trainable network weights, while hardware-implemented activation functions provide essential nonlinearity. Simulation results demonstrate that the proposed architecture achieves high classification accuracy, and that incorporating hardware-based activation functions significantly improves representational capability and performance compared with purely linear physical implementations.