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

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.

Wireless physical neural networks (WPNNs) have emerged as a promising paradigm for performing neural computation directly in the physical layer of wireless systems, offering low latency and high energy efficiency. However, most existing WPNN implementations primarily rely on linear physical transformations, which fundamentally limits their expressiveness. In this work, we propose a relay-assisted WPNN architecture based on activation-integrated stacked intelligent metasurfaces (AI-SIMs), where each passive metasurface layer enabling linear wave manipulation is cascaded with an activation metasurface layer that realizes nonlinear processing in the analog domain. By deliberately structuring multi-hop wireless propagation, the relay amplification matrix and the metasurface phase-shift matrices jointly act as trainable network weights, while hardware-implemented activation functions provide essential nonlinearity. Simulation results demonstrate that the proposed architecture achieves high classification accuracy, and that incorporating hardware-based activation functions significantly improves representational capability and performance compared with purely linear physical implementations.

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.