Metasurfaces-Integrated Wireless Neural Networks for Lightweight Over-The-Air Edge Inference
Authors: Kyriakos Stylianopoulos, Mario Edoardo Pandolfo, Paolo Di Lorenzo, George C. Alexandropoulos
Organizations: 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 · DIET Department, Sapienza University of Rome, Via Eudossiana 18, Rome, Italy
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.
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Fig. 1: Conceptual architecture of the Metasurfaces-Integrated Neural Network (MINN) framework comprising three core modules. The Encoder and Decoder modules, which may incorporate neural network structures, are collocated respectively at the multi-antenna TX and RX nodes, while the Channel module performs OTA computations leveraging the fading coefficients of the wireless channel, the programmable EM responses of multi-layer MS structures constituting it, as well as the properties of the RX thermal noise. The E2E MIMO system is described as the composition of these three modules, therefore, the chain rule may be applied to compute the respective gradients and, consequently, optimize the heterogeneous DNN weights and constituent MS responses through gradient descent. It is noted that: i ) the physical MS device(s) enabling the reconfigurability of the signal propagation environment may be collocated at either in the TX or RX, instead of being placed in between them (in this case, it is probable that the MS(s) affect only the portion of the signal components impinging on them), or in both; and i ) the Encoder and Decoder DNN components can be implemented either through conventional digital processors or equivalent analog computation units (e.g., liquid state machines, memristors, and multi-layer MS structures, such as Stacked Intelligent Metasurfaces (SIM)).
Fig. 2: Mean accuracy of different MINN versions for MNIST classification, considering fixed SNR during training and inference. All simulated 4×4 MIMO system setups included a SIM positioned close to the TX at a distance corresponding to approximately 7.5% of the total TX-RX distance, with its broadside perpendicular to the TX-RX line of sight, differing on the number of MS layers and the number of metamaterials per layer. A geometric channel with 10 scatterers, yielding static fading conditions, has been considered. Two convolutional layers followed by a linear layer were used at the TX digital DNN, while the RX digital DNN comprised three feedforward layers. The “No SIM” baseline refers to performing inference with only the digital DNNs at the transceivers, i.e., without manipulating the wireless channel through any MS (a simplified MINN variation including only the uncontrollable component of the Channel module). The “Digital DNN” benchmark refers to performing MNIST classification entirely on the TX with the same number of layers, without accounting for channel transmission, and is therefore an upper bound. All networks were trained for 50 epochs irrespective of their size. As observed, by increasing the number of SIM elements and the received SNR level, larger MINNs approach the Digital DNN bound, whereas the removal of the SIM is detrimental to the training process. It is additionally demonstrated that, under lower SNRs, deeper MINN versions are not always more efficient since they suffer from higher signal attenuation through the SIM layers.
Fig. 3: Two variations of the MINN architecture for the example of MNIST handwritten digit classification: (a) An all-MSs MIMO system where all three modules are primarily implemented by MSs. At the TX, the forward network pass initiates through a single antenna illuminating the first layer of the E2E wave-domain-based DNN, which has as many elements as the number of features within the input data (i.e., the number of MNIST image pixels). This data is encoded via the EM responses of this layer’s diffractive metamaterials [ 4 ] . At the RX, the final MS layer, constituting of ten fully absorbing metamaterials each followed by an energy detector (with each representing one of the possible MNIST digits), provides the output inferred digit. Although conceptually regarded as parts of the Channel module handling all OTA computations, the hidden diffractive MS layers may be flexibly distributed at all system physical devices. For example, some can be collocated with the transceiver devices and the remaining installed all together or in groups within the signal propagation environment. Alternatively, those diffractive MSs may be placed at one of the end devices and inside the MIMO channel, or solely within that channel, enabling lightweight transmissions, receptions or both. (b) An XL MIMO system where the Encoder and Decoder modules are respectively carried out by a multi-antenna TX and RX, and the Channel module is devoid of programmable devices. [ 7 ] . At the TX, each pixel of the input data is encoded and fed to a distinct antenna, while, at the RX, the signal received at each antenna is first fed to a nonlinear RF component, then, it is multiplied by a controllable weight, and, finally, all weighted analog outputs are combined to provide the output inferred digit. This XL MIMO system capitalizes on the random transformations imposed by the uncontrollable Channel module on the feature signals before being superimposed at the RX antennas, operating as an OTA ELM.
Fig. 4: Mean accuracy of the MINN-ELM variation in Fig. 3b over different binary classification datasets at the received SNR level of 25 dB. XL MIMO system setups with different numbers of TX antenna elements and MS sizes at the RX were simulated under a Rayleigh fading channel, which was treated as the random single hidden layer of the E2E wave-domain-based neural network. Each constituent metamaterial of the last MS-based layer at the RX was designed to realize a cascade of a fixed nonlinear response (thus, acting as an activation function) followed by a tunable linear response (thus, acting as a trainable weight). The MINN-ELM training took place in closed form within each channel coherence block. The number of TX antennas corresponded to the number of input features of the dataset used: 22 for Parkinson’s; 60 (sub-sampled from 784 ) for binary (even/odd) MNIST; 30 for Wisconsin Breast Cancer Diagnosis (WBCD); and 20 (sub-sampled from 590 ) for Semiconductor Manufacturing (SECOM). The MINN-ELM classification performance has been compared with that of a fully digital ELM implementation, considering 200 random initializations over four datasets. As observed, The MINN-ELM performs equally well to its digital counterpart in all scenarios. The performance increases as its approximation power is enhanced by increasing the number of MS elements at the RX, with the exception of the SECOM dataset which suffers from overfitting. In sufficiently XL MIMO conditions, MINN-ELM achieves near-optimal classification for all datasets, approaching their asymptotic theoretical guarantees of universal approximation.
Fig. 5: Mean accuracy of MINN with power control for MNIST classification versus the TX power level, compared with MINN trained under constant power budgets. An 16×8 MIMO system setup with two different sizes of 4 -layer SIM, positioned close to the TX similar to Fig. 2 , operating under a geometric channel with 15 scatterers, was simulated. At each channel realization, the RX position was randomly sampled, resulting overall in dynamic fading conditions. The penalty term γ is a hyper-parameter balancing energy efficiency and classification performance. As depicted, classification with power control yields desired accuracy levels with order of magnitudes lower TX power during inference. This behavior exemplifies this MINN application for low and varying SNR levels.
Fig. 6: Mean accuracy of different MINN versions for the objective of OTA alignment for MNIST classification. Two pairs of Encoder / Decoder modules, corresponding to two distinct TX/RX MIMO links for EI, were first pretrained independently from each other to encode and classify CIFAR-10 images (i.e., learned different encoded spaces that were semantically misaligned). Then, the Channel module was optimized to align those encoded spaces, enabling efficient OTA classification between the Encoder module of the TX of the first pair and the Decoder of the RX of the second pair. This process involved learning a linear transformation that maps the encoding space of the first MIMO pair to the encoding space of the second one. The optimal mapping was first computed digitally, either as a direct linear transformation or by applying Proto Parseval Frame Equalizers (PPFE) onto the encoded data as a pre-processing step. Then, the Channel module controlling a SIM placed at the TX, with different numbers of layers and metamaterials, was optimized to approximate the ideal transformation matrices. The all-MSs MIMO variation of the MINN architecture in Fig. 3 (a) was considered, with the TX’s SIM having a first layer of 768 metamaterials whose responses were designed to correspond to the actual image values, and the RX was equipped with a 384 -element fully absorbing MS comprising the first DNN layer of the Decoder . As observed, when the number of SIM layers and their elements increase, the proposed OTA semantic alignment’s performance approaches that of the simulated fully digital alignment techniques.
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.
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
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.
Meng Hua, Deniz Gündüz
Department of Electrical and Electronic Engineering, Imperial College London, United Kingdom
Wireless physical neural networks (WPNNs) embed neural computation directly into analog hardware, offering lower energy consumption and latency than conventional digital implementations. In this paper, we propose a deep WPNN in which nonlinear activations are realized by a multi-hop multiple-input multiple-output (MIMO) relay network, in which each relay implements a trainable complex linear gain and bias, followed by the power amplifier's intrinsic nonlinearity acting as an activation function. The cascade of multiple relays therefore realizes an over-the-air fully connected network whose parameters can be trained end-to-end. We develop two transceiver designs for different channel state information (CSI) availability scenarios: a least squares (LS)-based scheme requiring only receiver-side CSI, and a singular-value-decomposition (SVD)-based scheme requiring both transmitter-side and receiver-side CSI. Simulation results show that the proposed architecture enables accurate over-the-air inference for image classification. In particular, the results highlight the advantage of exploiting hardware nonlinearity for enhanced inference capability.
Meng Hua, Itsik Bergel, Deniz Gündüz
Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, U.K. · Faculty of Engineering, Bar-Ilan University, Ramat Gan 5290002, Israel