# Over-The-Air Extreme Learning Machines with XL Reception via Nonlinear Cascaded Metasurfaces

arXiv: https://arxiv.org/abs/2601.17749 · HTML: https://mlsanity.com/paper/2601.17749/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [The universal approximation theorem for complex-valued neural networks](https://mlsanity.com/paper/2012.03351/) (2020)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Dynamic Metasurface Antennas for 6G Extreme Massive MIMO Communications](https://mlsanity.com/paper/2006.07838/) (2020)
- [Stacked Intelligent Metasurfaces for Efficient Holographic MIMO Communications in 6G](https://mlsanity.com/paper/2305.08079/) (2023)
- [Over-the-Air Edge Inference via End-to-End Metasurfaces-Integrated Artificial Neural Networks](https://mlsanity.com/paper/2504.00233/) (2025)
- [Implementing Neural Networks Over-the-Air via Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2508.01840/) (2025)
- [Wave-based extreme deep learning based on non-linear time-Floquet entanglement](https://mlsanity.com/paper/2107.08564/) (2021)
- [On the Tacit Linearity Assumption in Common Cascaded Models of RIS-Parametrized Wireless Channels](https://mlsanity.com/paper/2302.04993/) (2023)
- [Universal Approximation with XL MIMO Systems: OTA Classification via Trainable Analog Combining](https://mlsanity.com/paper/2504.12758/) (2025)
- [Over-the-Air Semantic Alignment with Stacked Intelligent Metasurfaces](https://mlsanity.com/paper/2512.05657/) (2025)
- [PhysFad: Physics-Based End-to-End Channel Modeling of RIS-Parametrized Environments with Adjustable Fading](https://mlsanity.com/paper/2202.02673/) (2022)
- [Stacked Intelligent Metasurface Performs a 2D DFT in the Wave Domain for DOA Estimation](https://mlsanity.com/paper/2310.09861/) (2023)
- [Nonlinear Stacked Intelligent Surfaces for Wireless Systems](https://mlsanity.com/paper/2510.23780/) (2025)
- [Nonlinear EM-based Signal Processing](https://mlsanity.com/paper/2512.04595/) (2025)

## Built on by (most cited first, 2 of 2)

- [Metasurfaces-Integrated Wireless Neural Networks for Lightweight Over-The-Air Edge Inference](https://mlsanity.com/paper/2602.19312/) (2026)
- [Relay-Assisted Activation-Integrated SIM for Wireless Physical Neural Networks](https://mlsanity.com/paper/2604.04212/) (2026)

## Abstract (arXiv)

The recently envisioned goal-oriented communications paradigm calls for the application of inference on wirelessly transferred data via Machine Learning (ML) tools. An emerging research direction deals with the realization of inference ML models directly in the physical layer of Multiple-Input Multiple-Output (MIMO) systems, which, however, entails certain significant challenges. In this paper, leveraging the technology of programmable MetaSurfaces (MSs), we present an eXtremely Large (XL) MIMO system that acts as an Extreme Learning Machine (ELM) performing binary classification tasks completely Over-The-Air (OTA), which can be trained in closed form. The proposed system comprises a receiver architecture consisting of densely parallel placed diffractive layers of XL MSs, also known as Stacked Intelligent Metasurfaces (SIM), followed by a single reception radio-frequency chain. The front layer facing the XL MIMO channel consists of identical unit cells of a fixed NonLinear (NL) response, whereas the remaining layers of elements of tunable linear responses are utilized to approximate OTA the trained ELM weights. Our numerical investigations showcase that, in the XL regime of MS elements, the proposed XL-MIMO-ELM system achieves performance comparable to that of digital and idealized ML models across diverse datasets and wireless scenarios, thereby demonstrating the feasibility of embedding OTA learning capabilities into future wireless systems.