eess.SPOct 26, 2026

XL MIMO Extreme Learning Machines: Wave-Domain Inference with Stacked Metasurfaces

Authors: Kyriakos Stylianopoulos, Mattia Fabiani, Davide Dardari, George C. Alexandropoulos

Organizations: Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 16122 Athens, Greece · Dipartimento di Ingegneria dell’Energia Elettrica e dell’Informazione “Guglielmo Marconi” (DEI), WiLAB-CNIT, University of Bologna, Cesena Campus, Cesena (FC), Italy

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

The recently envisioned goal-oriented communications paradigm requires machine learning inference to be performed directly on wirelessly transferred data, by splitting neural network computations between the transmitter, the Receiver (RX), and the wireless channel. Such approaches aim to offload large portions of the computation onto the channel itself, which is often controlled by reconfigurable MetaSurfaces (MSs). Typical MS-parametrized systems, however, enable only limited computation offloading in the wave domain, usually corresponding to a single neural network layer, due to adverse channel fading effects and the almost linear operation of the channel and conventional MS models. In this paper, we demonstrate that an eXtremely Large (XL) Multiple-Input Multiple-Output (MIMO) system equipped with Stacked Intelligent MSs (SIM) at the RX side, together with a single antenna and its accompanying radio-frequency chain, may act as a two-layer neural network operating exclusively over the air. The first (uncontrollable) network layer corresponds to the transformations offered by wireless fading, while the second (controllable) layer is implemented via SIM operations. In particular, only the first, front-end MS layer needs to exhibit nonlinear response to serve as an activation function. Leveraging the Extreme Learning Machine (ELM) framework, the proposed XL MIMO system architecture is shown to be a universal approximator, and the optimal linear-SIM-based combining is derived in closed form, allowing for fast training even and partial signal observability. Numerical evaluations across diverse datasets showcase that the proposed XL-MIMO-ELM framework achieves classification accuracy comparable to idealized digital models, thereby, proving the viability of low complexity, wave-domain neural computations.

Figures & tables

Fig. 1 : The proposed XL MIMO system architecture for implementing the devised XL - MIMO - ELM framework using linear and NL MSs . The responses of the channel and MSs are used as components of the ELM algorithm to realize OTA inference.
Fig. 2 : Element-wise bandpass memoryless NL transformation (top) and its corresponding equivalent low-pass scheme (bottom).
Fig. 3 : Classification accuracy the proposed XL - MIMO - ELM approach versus the number of metamaterials NrN_{\rm r} (corresponding to the number of trainable parameters) at the RX ’s NL MS layer, considering three distinct datasets and different sketching values MM .
Fig. 4 : Performance of the XL - MIMO - ELM approach and digital EI benchmark versus different levels of the measurement SNR .
Fig. 5 : Classification accuracy of the XL - MIMO - ELM approach and digital EI benchmark over different Ricean factors.
More in this topic

Reconfigurable Intelligent Surfaces

Reconfigurable intelligent surfaces are programmable electromagnetic panels that steer wireless signals to improve coverage, capacity, energy use, and sensing.

See all 30 papers

Explore similar work

CardsList
Aug 27, 2026

Over-The-Air Extreme Learning Machines with Nonlinear Stacked Intelligent Metasurfaces

The recently envisioned goal-oriented communications paradigm requires machine learning inference to be performed directly on wirelessly transferred data. This paper presents an eXtremely Large (XL) Multiple-Input Multiple-Output (MIMO) system that operates as an Extreme Learning Machine (ELM) to execute Over-The-Air (OTA) binary classification. To reduce hardware complexity, the receiver is equipped with cascaded metasurfaces terminating in a single radio-frequency chain. A front metasurface layer applies a fixed nonlinear response to the incoming signal, acting as the ELM's activation function. Subsequent tunable linear metasurface layers physically approximate the trained network weights directly in the wave domain. Numerical evaluations across diverse datasets showcase that our XL MIMO architecture achieves classification accuracy comparable to idealized digital models, thereby proving the viability of low-complexity, wave-domain OTA learning.

Kyriakos Stylianopoulos, Mattia Fabiani, Giulia Torcolacci +2

Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece · DEI, University of Bologna, Italy · National Laboratory of Wireless Communications (WiLab), CNIT, Italy

Efficient Neural Network InferenceReconfigurable Intelligent Surfaces
AskPDF
Mar 13, 2026

A Learnable SIM Paradigm: Fundamentals, Training Techniques, and Applications

Stacked intelligent metasurfaces (SIMs) represent a breakthrough in wireless hardware by comprising multilayer, programmable metasurfaces capable of analog computing in the electromagnetic (EM) wave domain. By examining their architectural analogies, this article reveals a deeper connection between SIMs and artificial neural networks (ANNs). Leveraging this profound structural similarity, this work introduces a learnable SIM architecture and proposes a learnable SIM-based machine learning (ML) paradigm for sixth-generation (6G)-andbeyond systems. Then, we develop two SIM-empowered wireless signal processing schemes to effectively achieve multi-user signal separation and distinguish communication signals from jamming signals. The use cases highlight that the proposed SIM-enabled signal processing system can significantly enhance spectrum utilization efficiency and anti-jamming capability in a lightweight manner and pave the way for ultra-efficient and intelligent wireless infrastructures.

Hetong Wang, Yashuai Cao, Tiejun Lv

School of Information and Communication Engineering, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China · School of Intelligence Science and Technology, University of Science and Technology Beijing, Beijing 100083, China

Wireless CommunicationsReconfigurable Intelligent Surfaces6G Networks
AskPDF
Feb 22, 2026

Metasurfaces-Integrated Wireless Neural Networks for Lightweight Over-The-Air Edge Inference

The upcoming sixth Generation (6G) of wireless networks envisions ultra-low latency and energy efficient Edge Inference (EI) for diverse Internet of Things (IoT) applications. However, traditional digital hardware for machine learning is power intensive, motivating the need for alternative computation paradigms. Over-The-Air (OTA) computation is regarded as an emerging transformative approach assigning the wireless channel to actively perform computational tasks. This article introduces the concept of Metasurfaces-Integrated Neural Networks (MINNs), a physical-layer-enabled deep learning framework that leverages programmable multi-layer metasurface structures and Multiple-Input Multiple-Output (MIMO) channels to realize computational layers in the wave propagation domain. The MINN system is conceptualized as three modules: Encoder, Channel (uncontrollable propagation features and metasurfaces), and Decoder. The first and last modules, realized respectively at the multi-antenna transmitter and receiver, consist of conventional digital or purposely designed analog Deep Neural Network (DNN) layers, and the metasurfaces responses of the Channel module are optimized alongside all modules as trainable weights. This architecture enables computation offloading into the end-to-end physical layer, flexibly among its constituent modules, achieving performance comparable to fully digital DNNs while significantly reducing power consumption. The training of the MINN framework, two representative variations, and performance results for indicative applications are presented, highlighting the potential of MINNs as a lightweight and sustainable solution for future EI-enabled wireless systems. The article is concluded with a list of open challenges and promising research directions.

Kyriakos Stylianopoulos, Mario Edoardo Pandolfo, Paolo Di Lorenzo +1

Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 16122 Athens, Greece · National Inter-University Consortium for Telecommunications (CNIT), Parma, Italy · DIAG Department, Sapienza University of Rome, via Ariosto 25, Rome, Italy +1

Wireless CommunicationsEdge InferenceEnergy-Efficient MLReconfigurable Intelligent Surfaces
AskPDF