eess.SPAug 27, 2026

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

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

Organizations: 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

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Abstract

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.

Figures & tables

Fig. 1 : The proposed XL MIMO system for implementing the proposed OTA - ELM framework using linear and NL MSs . The channel and MS responses are used as components of the ELM algorithm to realize OTA inference. The flow of computation during the forward pass is also sketched in this figure.
Fig. 2 : Classification accuracy the proposed OTA - ELM approaches 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.
Fig. 3 : Classification accuracy of the OTA - ELM approaches over different Ricean factors, considering the WBCD dataset.
Fig. 4 : Performance of the ideal LS benchmark and the approximate SIM solution trained through PGD versus different levels of the measurement SNR , introduced by the observation of the received signals to compute the LS solution.

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