# RAOA: Alternating-Operator Neural Computation with Programmable Radio Propagation

arXiv: https://arxiv.org/abs/2610.02683 · HTML: https://mlsanity.com/paper/2610.02683/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 22 of 22)

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- [Over-the-Air Edge Inference via End-to-End Metasurfaces-Integrated Artificial Neural Networks](https://mlsanity.com/paper/2504.00233/) (2025)
- [Training all-mechanical neural networks for task learning through in situ backpropagation](https://mlsanity.com/paper/2404.15471/) (2024)
- [Stacked Intelligent Metasurfaces for Wireless Communications: Applications and Challenges](https://mlsanity.com/paper/2407.03566/) (2024)
- [Metasurfaces-Integrated Wireless Neural Networks for Lightweight Over-The-Air Edge Inference](https://mlsanity.com/paper/2602.19312/) (2026)
- [Expressivity of Programmable-Metasurface-Based Physical Neural Networks: Encoding Non-Linearity, Structural Non-Linearity, and Depth](https://mlsanity.com/paper/2603.13602/) (2026)

## Abstract (arXiv)

Can programmable radio propagation serve as computational depth rather than only as a communication channel or one-shot analog transform? We introduce the Radio Alternating Operator Ansatz (RAOA), a recurrent computing architecture that alternates an energy-derived problem update with a mixing update over a persistent latent state. Recomputing the problem field after each mix makes repeated passes compositional even when the same learned controls are reused across depth. We evaluate this idea through exact discrete optimization, constrained programmable-propagation simulation, and pretrained-model adaptation. On discrete objectives, repeated execution can improve solution quality without increasing the learned-control count, and the same formulation handles higher-order interactions directly. A passive phase-only free-space model further shows that the required operators can be approximated by programmable propagation while retaining useful downstream behavior despite realization error. When inserted as a zero-initialized residual adapter, RAOA adapts pretrained language models with WikiText performance close to a matched shallow MLP across three model families, while reasoning-task transfer remains model-dependent. Together, these results connect alternating-operator computation, programmable radio propagation, and neural adaptation within one recurrent framework. The RF realization evidence is simulation-based rather than a hardware demonstration.