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

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.