Over-the-Air Semantic Alignment Framework

• Over-the-Air Semantic Alignment Framework is a system that uses programmable metasurfaces and RISs to directly synchronize latent representations between transmitter and receiver models.
• It employs trainable analog operators and innovative optimization techniques—such as gradient-based phase optimization, ODE-inspired neural blocks, and split-learning—to mitigate model misalignment.
• The framework achieves robust semantic fidelity with high task accuracy and reduced digital processing, offering significant efficiency gains in distributed communication scenarios.

Over-the-air semantic alignment frameworks enable the direct alignment of latent or semantic representations between heterogeneous transmitter and receiver models via physical-layer mechanisms rather than (or in addition to) conventional digital post-processing. These frameworks leverage the propagation medium—often with the support of programmable metasurfaces or other analog computational elements—to implement semantic equalization, alignment, or transformation, mitigating misalignment due to architectural, training, or data differences in upstream models. Seminal approaches encompass stacked intelligent metasurfaces (SIMs) for linear semantic mapping (Pandolfo et al., 5 Dec 2025), over-the-air ODE-inspired neural blocks using distributed RISs (Liu et al., 8 May 2025), split-learning and partial fine-tuning for neural codec alignment (Choi et al., 2023), and adversarial imitation learning targeting implicit semantic agreement (Xiao et al., 2023). These architectures deliver reductions in communication and computation overhead while supporting robustness and high semantic fidelity in distributed task-oriented communication scenarios.

1. Formal Models and System Architectures

Over-the-air semantic alignment frameworks are architected as cascades of trainable analog (or partially analog) operators within the transmission chain, frequently combined with digital semantic encoders/decoders.

• Stacked Intelligent Metasurfaces (SIM): A SIM consists of $K$ cascaded layers, each described by a linear map $M_k \in \mathbb{C}^{n \times n}$. The metasurface’s transfer function is $G = M = \prod_{k=1}^K M_k$, with each $M_k = \Upsilon_k W_k$, where $\Upsilon_k$ is a trainable diagonal phase-shift matrix and $W_k$ is the known free-space propagation matrix. The SIM is trained so $G$ emulates a desired semantic aligner $A$ (see Section 2) (Pandolfo et al., 5 Dec 2025).
• Over-the-Air ODE-Inspired Neural Networks: Air-ODE blocks employ cascaded groups of distributed RISs, each physically realizing an ODE-inspired convolutional operation. Feature segments from a DeepSC encoder are transmitted directionally to RIS groups, whose phase-shift matrices $\Phi_{p,k}$ approximate trainable weights $w_{p,k}$. The propagation medium thus physically computes a high-order feature transformation aligned to the semantic intent (e.g., for joint image reconstruction and semantic tagging) (Liu et al., 8 May 2025).
• Split-Learning Fine-Tuning: This framework applies distributed split-learning (SL) with partial layer freezing. Each transmitter downloads decoder weights from the receiver, locally fine-tunes a fraction $f$ of decoder layers using its own data (with measured channel impairments), and uploads the fine-tuned parameters. Semantic alignment is achieved by dynamically adapting the decoder on the transmitter side to match the partner’s semantic decoder (Choi et al., 2023).
• Reasoning-Based Implicit Semantic Alignment: The architecture projects detected explicit semantic graphs into a low-dimensional semantic constellation, then uses a generative adversarial imitation learning (G-RML) protocol to align implicit semantic reasoning mechanisms over the air, ensuring the receiver infers implicit meanings congruent with the transmitter's reasoning policy (Xiao et al., 2023).

2. Semantic Alignment Mechanisms

Distinct mathematical tools support over-the-air semantic alignment depending on the domain and use case:

• Linear Semantic Equalizers: SIMs emulate semantic aligners of the forms $A_\ell$ (supervised linear) and $A_f$ (zero-shot Parseval-frame equalizer) directly in the analog domain. For $A_\ell$, the solution minimizes $\|Y - A_\ell X\|_F^2 + \mu\|A_\ell\|_F^2$, yielding $A_\ell = Y X^\dagger (X X^\dagger + \mu I)^{-1}$. For $A_f$, frame operators $F_T$, $F_R$ constructed from shared semantic anchors define $A_f = F_R^\dagger F_T$ (Pandolfo et al., 5 Dec 2025).
• Gradient-based Phase Optimization: To physically realize $A$ as a metasurface transfer function $G$, phases $\{\xi_{k,m}\}$ are updated by minimizing $\|\beta G - A\|_F^2$ (with a complex gain $\beta$), using backpropagation through the product $G = \Upsilon_K W_K \cdots \Upsilon_1 W_1$ (Pandolfo et al., 5 Dec 2025).
• Discrete Approximation of Conv Weights: Air-ODE blocks constrain trainable convolutional weights $w_{p,k}$ by quantizing to feasible RIS-induced values $$\hat{h}_{p,k} = \arg\min_{n} \|w_{p,k} - \tilde{h}_{p,k}^{(n)}\|$$, where $\tilde{h}$ represents cascaded channel and phase-shift responses. Straight-through estimators are used for backpropagation through non-differentiable quantization steps (Liu et al., 8 May 2025).
• Generative Adversarial Imitation Learning (G-RML): The receiver learns a generative policy $\pi_\theta$ that produces implicit semantic trajectories indistinguishable from the transmitter's expert paths, guided by a discriminator $D_\phi$ and trained via the minimax objective (adversarial loss plus policy gradient updates, with discriminator's output serving as pathwise reward) (Xiao et al., 2023).
• Split-Learning Layer Freezing: The SLF protocol fine-tunes only a user-selected subset of decoder layers, parameterized by the freeze fraction $f = \frac{L - \ell}{L}$, balancing semantic alignment latency, communication overhead (downlink/uploaded model size), computation cost, and semantic performance (MSE, accuracy) (Choi et al., 2023).

3. Physical Layer Embodiments and Practical Realization

• Metasurface Implementation: Each layer in a SIM comprises $n$ meta-atoms with phase-shifted coefficients $v_{k,m} = \alpha_k e^{j \xi_{k,m}}$. These phase shifts are quantized (e.g., 2–6 bit resolution) and set via hardware controls such as varactor capacitances. Physical design parameters include inter-layer spacing, cell area, and operational wavelength, with the total transfer matrix shaped by design and runtime adaptation (Pandolfo et al., 5 Dec 2025).
• RIS-Enabled ODE Blocks: RIS elements implement convolution-type operations by aligning their phase shifts to quantized weight approximations. Pre-equalization and channel state tracking ensure greater fidelity during analog computation. The overall architecture enables the physical mixing of signals to collectively realize ODE neural block computations at the propagation level (Liu et al., 8 May 2025).
• Edge Device Workload Reduction: Digital baseline approaches require storage and application of large alignment matrices on-device, as well as frequent pilot transmission. In contrast, SIM- and RIS-based approaches offload the $O(n^3)$ mixing and semantic processing to physical hardware, leaving edge devices to handle only lightweight digital tasks like complex symbol generation and scalar gain adjustment (Pandolfo et al., 5 Dec 2025, Liu et al., 8 May 2025).

4. Training and Optimization Protocols

• SIM Gradient-Based Training: The metasurface phase-shifts are optimized offline via iterative gradient descent against a target semantic aligner. The loss $\|\beta G - A\|_F^2$ is minimized alternately with respect to phases $\xi_{k,m}$ and gain $\beta$. In practice, Adam or SGD with suitable learning rates yields convergence in reasonable timeframes (Pandolfo et al., 5 Dec 2025).
• Air-ODE Training with Quantization: During digital pretraining, the ODE-inspired neural network's quantized weights are mapped to their nearest implementable RIS counterparts. The overall system is fine-tuned in two stages (reconstruction and dual-task), and the quantization is handled through the straight-through estimator (STE) to preserve gradient flow (Liu et al., 8 May 2025).
• G-RML Joint Training: Policy-generator-discriminator pairs are trained in adversarial rounds. The expert trajectory database, roll-out policy for the generator, and pathwise rewards derived from the discriminator enable training until the Jensen-Shannon divergence plateaus or alignment accuracy saturates (Xiao et al., 2023).
• Split-Learning Alignment: The SLF algorithm involves a download-fine-tune-upload-update cycle, with hyperparameters for batch size, layer freeze index $\ell$, learning rate, and codebook commitment adapting the alignment process for resource-constrained or time-sensitive deployments. The trade-off between semantic alignment fidelity and recovery time is controlled by the layer freeze parameter (Choi et al., 2023).

5. Performance Metrics and Empirical Results

• Semantic Fidelity: Alignment accuracy, Jensen-Shannon divergence, and semantic symbol error rate directly measure the closeness of aligned representations to ground-truth semantics. For implicit meanings, interpretation accuracy achieves up to 92% with a semantic SER reduction of 30 dB over no-reasoning baselines (Xiao et al., 2023).
• Task Performance: In over-the-air analog Air-ODE systems, dual-task performance under 30 dB SNR reaches PSNR ≈ 30.35 dB, SSIM ≈ 0.958, and semantic tagging accuracy ≈ 82.5%—recovering ≈97% of the fully digital ODE-inspired network's quality (Liu et al., 8 May 2025). Removing ODE alignment halves the performance metrics.
• Alignment Robustness: SIM frameworks provide robust semantic alignment; e.g., for CIFAR-10 classification between heterogeneous ViT encoders, SIM-attained accuracy is 90+% at SNR ≥20 dB and 65% even at –10 dB (Pandolfo et al., 5 Dec 2025).
• Communication and Computation Overhead: Communication is vastly compressed (e.g., transmitting only $n$ constellation points vs. $m \approx 200$ full-attribute vectors per concept). SIM/RIS approaches offload digital overhead, yielding orders-of-magnitude savings in edge device computation (Pandolfo et al., 5 Dec 2025, Liu et al., 8 May 2025).
• Semantic Alignment vs. Layer Freezing: In SLF, reconstructive MSE drops from ≈0.30 to 0.113, and classification accuracy increases from ≈30% to over 97% post-aligning. The layer freeze fraction $f$ tunes the trade-off between recovery latency and semantic precision. For $\ell=2$, recovery time is 2.14s, MSE is 0.113, and accuracy is 97.83% (Choi et al., 2023).

6. Current Limitations and Extensions

• Hardware and Physical Constraints: SIM scalability is limited by the number of meta-atoms and layers for high-dimensional semantic spaces; increased stack depth incurs cost and insertion loss. Narrowband designs require frequency-agile metasurfaces for wideband operation; phase quantization and fabrication tolerances may reduce fidelity (Pandolfo et al., 5 Dec 2025).
• Adaptation and Multi-User Settings: Future directions include real-time joint optimization for semantic mapping and instantaneous channel state, as well as extending over-the-air alignment to multi-user scenarios via multi-beam mappings or non-linear metasurface elements (Pandolfo et al., 5 Dec 2025).
• Algorithmic Flexibility: Air-ODE frameworks could integrate more flexible ODE architectures, richer semantic feature sets, or online adaptation to channel drifting via in-situ fine-tuning (Liu et al., 8 May 2025). SLF-based approaches suggest generality in aligning diverse NN-based transceivers with controlled communication and computation cost.
• Implicit Semantic Reasoning: Reasoning-driven frameworks (G-RML) show the potential for over-the-air alignment of implicit, higher-order semantics beyond explicit feature alignment, opening avenues for richer intent-aware communication with reduced bandwidth and computation (Xiao et al., 2023).

7. Comparative Summary Table

Framework	Core Principle	Physical Embodiment	Alignment Mechanism
SIM (Pandolfo et al., 5 Dec 2025)	Linear semantic mapping in wave domain	K-layer metasurface stack	Gradient-trained phase optimization for $G \approx A$
Air-ODE (Liu et al., 8 May 2025)	ODE-inspired neural feature alignment	Cascaded RISs	Quantized ODE weights mapped to RIS phase shifts via STE
SLF (Choi et al., 2023)	Distributed partial NN fine-tuning	Standard NN hardware	Download + local fine-tune + upload, controlled freeze
G-RML (Xiao et al., 2023)	Implicit semantic reasoning alignment	Digital + channel transfer	Adversarial policy imitation (G-RML)

A plausible implication is that further integration of metasurface-based analog computation with learning-based digital adaptation can increase the flexibility, efficiency, and robustness of future semantic communication systems, while constraints such as scalability and hardware quantization remain important research challenges.