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

TL;DR

This work presents an over-the-air Extreme Learning Machine implemented with cascaded diffractive metasurfaces (CMS) in an XL-MIMO receiver to perform binary classification directly in the wireless channel. The front CMS layer provides a fixed nonlinear activation, while multiple subsequent CMS layers supply trainable linear weights, enabling a closed-form, two-step training procedure that approximates the digital ELM weights. The authors establish universal approximation properties under rich-scattering and quasi-static fading, analyze computational complexity, and demonstrate via simulations on UCI datasets that OTA CMS-ELM performance approaches digital models as the front-layer element count $N_r$ grows, with some sensitivity to channel richness (e.g., Ricean factor). The framework offers a hardware-efficient path toward embedded, end-to-end wireless inference in future GO-enabled communication networks, leveraging the computation within the propagation medium itself. All mathematical expressions are kept in $...$ to ensure precise representation of the system's parameters and operations.

Abstract

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 followed by a single reception radio-frequency chain. The front layer facing the MIMO channel consists of identical unit cells of a fixed NonLinear (NL) response, while 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 communication systems.

Figures (3)

• Figure 1: The proposed system for implementing the proposed -CMS- framework. Channel and responses are used as components of the algorithm to realize inference. The flow of computational during the forward pass is also sketched.
• Figure 2: Classification accuracy of two -CMS- variations versus the number of elements $N_{\rm r}$ at the 's front layer, which corresponds to the number of trainable parameters for three distinct datasets. The "ideal weights" variation assumes the weights are applied in the digital domain or under idealized analog hardware. The " weights" variation approximates those weights through $L$ cascaded with linear responses for full inference.
• Figure 3: Classification accuracy of two -CMS- variations over different Ricean factors for the WBCD dataset, considering different values $N_{\rm r}$ for the 's front layer.

Theorems & Definitions (3)

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