Long Shi
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Long Shi has a total of 216 co-authors. Here are the top co-authors by number of shared publications:
- Jun Li
Southeast University
50 shared publications - Taotao Wang
College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China
22 shared publications - Zhe Wang
School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China
20 shared publications - Ming Ding
CSIRO
16 shared publications - Feng Shu
Hainan University
15 shared publications - Kang Wei
Southeast University
15 shared publications
Latest Publications
- 1 October 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Internet of Things Journal
- Vol. 13  (20) , 47772-47785
Opponent Modeling-Based Dynamic Resource Trading for Multi-UAV Assisted Edge Computing
- 1 October 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Internet of Things Journal
- Vol. 13  (20) , 47772-47785
Opponent Modeling-Based Dynamic Resource Trading for Multi-UAV Assisted Edge Computing
- 1 October 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Vehicular Technology
- Vol. 75  (10) , 25188-25192
Efficient Multimodal Task-Oriented Communication With Dynamic Modality Selection
Task-oriented communication leverages semantic information for efficient transmission by focusing on meanings relevant to downstream tasks rather than exact symbol recovery. In multimodal scenarios, most existing approaches adopt static fusion, where all modalities are always processed jointly. However, this often leads to redundant communication overhead, since some samples can be accurately inferred from a single modality, whereas more ambiguous cases require additional modalities. To address this issue, we propose a multimodal task-oriented communication system based on dynamic modality selection, where conditional mutual information (CMI) is used to assess the incremental value of each modality. A gating network leverages these estimates to select task-relevant modality combinations, achieving adaptive resource allocation. Experiments on movie genre classification and sentiment analysis show that the proposed system sustains competitive accuracy while reducing both computation and transmission costs by over 30%, providing an interpretable and efficient solution for resource-constrained task-oriented communication.
- 1 October 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Vehicular Technology
- Vol. 75  (10) , 25188-25192
Efficient Multimodal Task-Oriented Communication With Dynamic Modality Selection
Task-oriented communication leverages semantic information for efficient transmission by focusing on meanings relevant to downstream tasks rather than exact symbol recovery. In multimodal scenarios, most existing approaches adopt static fusion, where all modalities are always processed jointly. However, this often leads to redundant communication overhead, since some samples can be accurately inferred from a single modality, whereas more ambiguous cases require additional modalities. To address this issue, we propose a multimodal task-oriented communication system based on dynamic modality selection, where conditional mutual information (CMI) is used to assess the incremental value of each modality. A gating network leverages these estimates to select task-relevant modality combinations, achieving adaptive resource allocation. Experiments on movie genre classification and sentiment analysis show that the proposed system sustains competitive accuracy while reducing both computation and transmission costs by over 30%, providing an interpretable and efficient solution for resource-constrained task-oriented communication.
- 19 May 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Wireless Communications
- Vol. 25  (15361276) , 17542-17558
Decision Transformers for RIS-Assisted Systems With Diffusion Model-Based Channel Acquisition
Reconfigurable intelligent surfaces (RISs) have been recognized as a revolutionary technology for future wireless networks. However, RIS-assisted communications have to continuously tune phase-shifts relying on accurate channel state information (CSI) that is generally difficult to obtain due to the large number of RIS channels. The joint design of CSI acquisition and subsection RIS phase-shifts remains a significant challenge in dynamic environments. In this paper, we propose a diffusion-enhanced decision Transformer (DEDT) framework consisting of a diffusion model (DM) designed for efficient CSI acquisition and a decision Transformer (DT) utilized for phase-shift optimizations. Specifically, we first propose a novel DM mechanism, i.e., conditional imputation based on denoising diffusion probabilistic model, for rapidly acquiring real-time full CSI by exploiting the spatial correlations inherent in wireless channels. Then, we optimize beamforming schemes based on the DT architecture, which pre-trains on historical environments to establish a robust policy model. Next, we incorporate a fine-tuning mechanism to ensure rapid beamforming adaptation to new environments, eliminating the retraining process that is imperative in conventional reinforcement learning (RL) methods. Simulation results demonstrate that DEDT can enhance efficiency and adaptability of RIS-aided communications with fluctuating channel conditions compared to state-of-the-art RL methods.
- 19 May 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Wireless Communications
- Vol. 25  (15361276) , 17542-17558
Decision Transformers for RIS-Assisted Systems With Diffusion Model-Based Channel Acquisition
Reconfigurable intelligent surfaces (RISs) have been recognized as a revolutionary technology for future wireless networks. However, RIS-assisted communications have to continuously tune phase-shifts relying on accurate channel state information (CSI) that is generally difficult to obtain due to the large number of RIS channels. The joint design of CSI acquisition and subsection RIS phase-shifts remains a significant challenge in dynamic environments. In this paper, we propose a diffusion-enhanced decision Transformer (DEDT) framework consisting of a diffusion model (DM) designed for efficient CSI acquisition and a decision Transformer (DT) utilized for phase-shift optimizations. Specifically, we first propose a novel DM mechanism, i.e., conditional imputation based on denoising diffusion probabilistic model, for rapidly acquiring real-time full CSI by exploiting the spatial correlations inherent in wireless channels. Then, we optimize beamforming schemes based on the DT architecture, which pre-trains on historical environments to establish a robust policy model. Next, we incorporate a fine-tuning mechanism to ensure rapid beamforming adaptation to new environments, eliminating the retraining process that is imperative in conventional reinforcement learning (RL) methods. Simulation results demonstrate that DEDT can enhance efficiency and adaptability of RIS-aided communications with fluctuating channel conditions compared to state-of-the-art RL methods.
- 5 May 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 74  (00906778) , 8375-8389
Energy-Efficient Data Offloading for Ultra-Dense Heterogeneous Vehicular Networks: A Multi-Population Mean-Field Reinforcement Learning Approach
For ultra-dense vehicular networks, dynamic resource optimization among a large number of heterogeneous agents is rather challenging. This paper proposes a learning-based resource allocation scheme in a vehicle-assisted mobile edge computing (MEC) network, where the uncrewed aerial vehicles (UAVs) and uncrewed ground vehicles (UGVs) are equipped with the MEC servers to provide the computational offloading services to the ground users with time-varying computing demands. Each self-interested vehicle jointly optimizes its trajectory planning and data offloading policies to maximize the expectation of its locally cumulative energy efficiency under the collision and energy constraints. We model the non-cooperative interactions among the massive co-channel vehicles as a multi-population mean-field game (MPMFG), where each vehicle constructs two types of mean-field terms to model the UAVs’ and UGVs’ population distributions, respectively. We propose a multi-population mean-field parameterized deep Q network (MPMF-PDQN) algorithm to solve the equilibrium among the vehicular servers in a discrete-continuous hybrid action space. The simulation results demonstrate that the proposed algorithm significantly enhances the average energy efficiency of the vehicles compared with the baseline algorithms.
- 5 May 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 74  (00906778) , 8375-8389
Energy-Efficient Data Offloading for Ultra-Dense Heterogeneous Vehicular Networks: A Multi-Population Mean-Field Reinforcement Learning Approach
For ultra-dense vehicular networks, dynamic resource optimization among a large number of heterogeneous agents is rather challenging. This paper proposes a learning-based resource allocation scheme in a vehicle-assisted mobile edge computing (MEC) network, where the uncrewed aerial vehicles (UAVs) and uncrewed ground vehicles (UGVs) are equipped with the MEC servers to provide the computational offloading services to the ground users with time-varying computing demands. Each self-interested vehicle jointly optimizes its trajectory planning and data offloading policies to maximize the expectation of its locally cumulative energy efficiency under the collision and energy constraints. We model the non-cooperative interactions among the massive co-channel vehicles as a multi-population mean-field game (MPMFG), where each vehicle constructs two types of mean-field terms to model the UAVs’ and UGVs’ population distributions, respectively. We propose a multi-population mean-field parameterized deep Q network (MPMF-PDQN) algorithm to solve the equilibrium among the vehicular servers in a discrete-continuous hybrid action space. The simulation results demonstrate that the proposed algorithm significantly enhances the average energy efficiency of the vehicles compared with the baseline algorithms.
- Top Cited PapersOpen Access
- 13 April 2026
- Published by Springer Nature in Artificial Intelligence Review
- Vol. 59  (7)
A survey of zero-knowledge proof based verifiable machine learning
As machine learning technologies advance rapidly across various domains, concerns over data privacy and model security have grown significantly. These challenges are particularly pronounced when models are trained and deployed on cloud platforms or third-party servers due to the computational resource limitations of users’ end devices. In response, zero-knowledge proof (ZKP) technology has emerged as a promising solution, enabling effective validation of model performance and authenticity in both training and inference processes without disclosing sensitive data. Thus, ZKP ensures the verifiability and security of machine learning models, making it a valuable tool for privacy-preserving AI. Although some research has explored the verifiable machine learning solutions that exploit ZKP, a comprehensive survey and summary of these efforts remains absent. This survey paper aims to bridge this gap by reviewing and analyzing all the existing Zero-Knowledge Machine Learning (ZKML) research from June 2017 to August 2025. We begin by introducing the concept of ZKML and outlining its ZKP algorithmic setups under three key categories: verifiable training, verifiable inference, and verifiable testing. Next, we provide a comprehensive categorization of existing ZKML research within these categories and analyze the works in detail. Furthermore, we explore the implementation challenges faced in this field and discuss the improvement works to address these obstacles. Additionally, we highlight several commercial applications of ZKML technology. Finally, we propose promising directions for future advancements in this domain.
- 13 April 2026
- Published by Springer Nature in Artificial Intelligence Review
- Vol. 59  (7)
Top Cited PapersOpen AccessA survey of zero-knowledge proof based verifiable machine learning
As machine learning technologies advance rapidly across various domains, concerns over data privacy and model security have grown significantly. These challenges are particularly pronounced when models are trained and deployed on cloud platforms or third-party servers due to the computational resource limitations of users’ end devices. In response, zero-knowledge proof (ZKP) technology has emerged as a promising solution, enabling effective validation of model performance and authenticity in both training and inference processes without disclosing sensitive data. Thus, ZKP ensures the verifiability and security of machine learning models, making it a valuable tool for privacy-preserving AI. Although some research has explored the verifiable machine learning solutions that exploit ZKP, a comprehensive survey and summary of these efforts remains absent. This survey paper aims to bridge this gap by reviewing and analyzing all the existing Zero-Knowledge Machine Learning (ZKML) research from June 2017 to August 2025. We begin by introducing the concept of ZKML and outlining its ZKP algorithmic setups under three key categories: verifiable training, verifiable inference, and verifiable testing. Next, we provide a comprehensive categorization of existing ZKML research within these categories and analyze the works in detail. Furthermore, we explore the implementation challenges faced in this field and discuss the improvement works to address these obstacles. Additionally, we highlight several commercial applications of ZKML technology. Finally, we propose promising directions for future advancements in this domain.
- 23 March 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Vehicular Technology
- Vol. PP  (00189545) , 1-5
Stable-MoE: Lyapunov-based Token Routing for Distributed Mixture-of-Experts Training over Edge Networks
The sparse activation mechanism of mixture of experts (MoE) model empowers edge intelligence with enhanced training efficiency and reduced computational resource consumption. However, traditional token routing in distributed MoE training faces significant challenges in resource-constrained edge net works characterized by heterogeneous computing capabilities and stochastic token arrivals, which inevitably suffer from workload backlog, resource inefficiency, and performance degradation. To address this issue, we propose a novel Lyapunov-based token routing framework for distributed MoE training over resource heterogeneous edge networks, termed Stable-MoE. Specifically, we formulate a stochastic optimization problem to maximize both system throughput and gating consistency via optimizing the token routing strategy and computational resource allocation, while ensuring long-term stability of both token and energy queues at the edge devices. Using the Lyapunov optimization, we transform the intractable long-term optimization problem into tractable per-slot subproblems by enabling online decision-making of token routing and computation frequency utilization without the knowledge of future system states. Experimental results on the SVHN and CIFAR-100 datasets demonstrate that Stable-MoE outperforms the baselines with at least 40% and 5% gains in system throughput and test accuracy, respectively.
- 23 March 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Vehicular Technology
- Vol. PP  (00189545) , 1-5
Stable-MoE: Lyapunov-based Token Routing for Distributed Mixture-of-Experts Training over Edge Networks
The sparse activation mechanism of mixture of experts (MoE) model empowers edge intelligence with enhanced training efficiency and reduced computational resource consumption. However, traditional token routing in distributed MoE training faces significant challenges in resource-constrained edge net works characterized by heterogeneous computing capabilities and stochastic token arrivals, which inevitably suffer from workload backlog, resource inefficiency, and performance degradation. To address this issue, we propose a novel Lyapunov-based token routing framework for distributed MoE training over resource heterogeneous edge networks, termed Stable-MoE. Specifically, we formulate a stochastic optimization problem to maximize both system throughput and gating consistency via optimizing the token routing strategy and computational resource allocation, while ensuring long-term stability of both token and energy queues at the edge devices. Using the Lyapunov optimization, we transform the intractable long-term optimization problem into tractable per-slot subproblems by enabling online decision-making of token routing and computation frequency utilization without the knowledge of future system states. Experimental results on the SVHN and CIFAR-100 datasets demonstrate that Stable-MoE outperforms the baselines with at least 40% and 5% gains in system throughput and test accuracy, respectively.
- 11 March 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Wireless Communications Letters
- Vol. 15  (21622337) , 2179-2183
Low-Latency Federated Fine-Tuning for Large Language Models Over Wireless Networks
Recently, federated large language models (LLMs) have drawn significant attention thanks to coupled capabilities of LLMs and federated learning (FL) that address privacy concerns in collaborative fine-tuning. However, due to large-scale parameters of LLMs, existing federated LLM fine-tuning frameworks incur significant challenges in resource-constrained clients characterized by heterogeneous computing capabilities and random wireless channels. To address this issue, we propose a joint client-specific pruning and bandwidth allocation (JCPBA) framework for federated LLMs to improve the fine-tuning efficiency over the wireless networks. Specifically, we formulate a fine-tuning latency minimization problem by jointly optimizing pruning rates and bandwidth allocations. Furthermore, we solve this optimization problem using a block coordinate descent method. Extensive experiments on the datasets of Yahoo Answers and GSM8K demonstrate that the proposed framework significantly reduces wall-clock fine-tuning time compared with state-of-the-art baselines and gains equal or lower test loss at the cost of lower computation and communication overhead.
- 11 March 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Wireless Communications Letters
- Vol. 15  (21622337) , 2179-2183
Low-Latency Federated Fine-Tuning for Large Language Models Over Wireless Networks
Recently, federated large language models (LLMs) have drawn significant attention thanks to coupled capabilities of LLMs and federated learning (FL) that address privacy concerns in collaborative fine-tuning. However, due to large-scale parameters of LLMs, existing federated LLM fine-tuning frameworks incur significant challenges in resource-constrained clients characterized by heterogeneous computing capabilities and random wireless channels. To address this issue, we propose a joint client-specific pruning and bandwidth allocation (JCPBA) framework for federated LLMs to improve the fine-tuning efficiency over the wireless networks. Specifically, we formulate a fine-tuning latency minimization problem by jointly optimizing pruning rates and bandwidth allocations. Furthermore, we solve this optimization problem using a block coordinate descent method. Extensive experiments on the datasets of Yahoo Answers and GSM8K demonstrate that the proposed framework significantly reduces wall-clock fine-tuning time compared with state-of-the-art baselines and gains equal or lower test loss at the cost of lower computation and communication overhead.
- Open Access
UAV Swarm Enabled Aerial Movable Antenna System for Low-Altitude Economy: From Far-Field to Near-Field Communication
Unmanned aerial vehicle (UAV) with the intrinsic three-dimensional (3D) mobility provides an ideal platform for implementing aerial movable antenna (AMA) system enabled by UAV swarm cooperation. Besides, AMA system is readily to achieve an extremely large-scale array aperture, rendering the conventional far-field uniform plane wave (UPW) model no longer valid for aerial-to-ground links. This paper studies the UAV swarm enabled near-field AMA communication, by taking into account the non-uniform spherical wave (NUSW) model, where UAV swarm trajectory simultaneously influences the channel amplitude and phase. We formulate a general optimization problem to maximize the minimum average communication rate over user equipments (UEs), by jointly optimizing the 3D UAV swarm trajectory and receive beamforming for all UEs. To draw useful insights, the special case of single UE is first studied, and successive convex approximation (SCA) technique is proposed to efficiently optimize the UAV swarm trajectory. For the special case of placement optimization, the optimal placement positions of UAVs for cases of single UAV and two UAVs are derived in closed-form. Then, for the special case of two UEs, we show that an inter-UE interference (IUI)-free communication can be achieved by symmetrically placing an even number of UAVs along a hyperbola, with its foci corresponding to the locations of the two UEs. Furthermore, for arbitrary number of UEs, an alternating optimization algorithm is proposed to efficiently tackle the non-convex optimization problem. Numerical results validate the significant performance gains over the benchmark schemes.
Open AccessUAV Swarm Enabled Aerial Movable Antenna System for Low-Altitude Economy: From Far-Field to Near-Field Communication
Unmanned aerial vehicle (UAV) with the intrinsic three-dimensional (3D) mobility provides an ideal platform for implementing aerial movable antenna (AMA) system enabled by UAV swarm cooperation. Besides, AMA system is readily to achieve an extremely large-scale array aperture, rendering the conventional far-field uniform plane wave (UPW) model no longer valid for aerial-to-ground links. This paper studies the UAV swarm enabled near-field AMA communication, by taking into account the non-uniform spherical wave (NUSW) model, where UAV swarm trajectory simultaneously influences the channel amplitude and phase. We formulate a general optimization problem to maximize the minimum average communication rate over user equipments (UEs), by jointly optimizing the 3D UAV swarm trajectory and receive beamforming for all UEs. To draw useful insights, the special case of single UE is first studied, and successive convex approximation (SCA) technique is proposed to efficiently optimize the UAV swarm trajectory. For the special case of placement optimization, the optimal placement positions of UAVs for cases of single UAV and two UAVs are derived in closed-form. Then, for the special case of two UEs, we show that an inter-UE interference (IUI)-free communication can be achieved by symmetrically placing an even number of UAVs along a hyperbola, with its foci corresponding to the locations of the two UEs. Furthermore, for arbitrary number of UEs, an alternating optimization algorithm is proposed to efficiently tackle the non-convex optimization problem. Numerical results validate the significant performance gains over the benchmark schemes.
- Open Access
Wireless Streamlet: A Spectrum-Aware and Cognitive Consensus Protocol for Edge IoT
Blockchain offers a decentralized trust framework for the Internet of Things (IoT), yet deploying consensus in spectrum-congested and dynamic wireless edge IoT networks faces fundamental obstacles: traditional BFT protocols are spectrum-ignorant, leading to inefficient resource utilization and fragile progress under time-varying interference. This paper presents \textit{Wireless Streamlet}, a spectrum-aware and cognitive consensus protocol tailored for wireless edge IoT. Building on Streamlet's streamlined structure, we introduce a \textit{Channel-Aware Leader Election (CALE)} mechanism. CALE serves as a verifiable cross-layer cognitive engine that leverages receiver-measured channel state information (CSI) piggybacked in signed votes to derive Byzantine-robust connectivity scores from notarization certificates, and deterministically selects a unique weighted leader per epoch from finalized history, thereby improving proposal dissemination reliability under deep fading. Complementing this cognitive adaptation, Wireless Streamlet exploits the single-hop broadcast medium and a deterministic TDMA voting schedule to achieve linear per-epoch on-air transmissions (slot complexity), ensuring deterministic spectral access. To address the communication-storage trade-off, we further propose a coded dual-chain architecture that decouples header-only consensus (State Chain) from payload data (Data Chain). By employing erasure coding and on-chain integrity commitments, the system minimizes redundant spectrum usage for data retrieval while ensuring availability. Experiments show that Wireless Streamlet achieves higher throughput and lower confirmation latency than representative baselines in lossy environments, while substantially reducing per-node storage, demonstrating the efficacy of integrating cognitive sensing into consensus logic.
Open AccessWireless Streamlet: A Spectrum-Aware and Cognitive Consensus Protocol for Edge IoT
Blockchain offers a decentralized trust framework for the Internet of Things (IoT), yet deploying consensus in spectrum-congested and dynamic wireless edge IoT networks faces fundamental obstacles: traditional BFT protocols are spectrum-ignorant, leading to inefficient resource utilization and fragile progress under time-varying interference. This paper presents \textit{Wireless Streamlet}, a spectrum-aware and cognitive consensus protocol tailored for wireless edge IoT. Building on Streamlet's streamlined structure, we introduce a \textit{Channel-Aware Leader Election (CALE)} mechanism. CALE serves as a verifiable cross-layer cognitive engine that leverages receiver-measured channel state information (CSI) piggybacked in signed votes to derive Byzantine-robust connectivity scores from notarization certificates, and deterministically selects a unique weighted leader per epoch from finalized history, thereby improving proposal dissemination reliability under deep fading. Complementing this cognitive adaptation, Wireless Streamlet exploits the single-hop broadcast medium and a deterministic TDMA voting schedule to achieve linear per-epoch on-air transmissions (slot complexity), ensuring deterministic spectral access. To address the communication-storage trade-off, we further propose a coded dual-chain architecture that decouples header-only consensus (State Chain) from payload data (Data Chain). By employing erasure coding and on-chain integrity commitments, the system minimizes redundant spectrum usage for data retrieval while ensuring availability. Experiments show that Wireless Streamlet achieves higher throughput and lower confirmation latency than representative baselines in lossy environments, while substantially reducing per-node storage, demonstrating the efficacy of integrating cognitive sensing into consensus logic.
- 23 January 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Wireless Communications Letters
- Vol. 15  (21622337) , 1499-1503
Graph Neural Networks via AirComp: Algorithms and Performance Analysis
Graph neural networks (GNNs) over the air (AirGNNs) has shown significant potential for efficiently training distributed GNN models by aggregating the feature representations based on the over the air computation (AirComp) technique. However, devices in existing wireless systems operate in half-duplex mode, the collision issue that devices cannot transmit and receive simultaneously may limit the potential of AirGNNs. To tackle this challenge, we proposed two scheduling methods, i.e., collision-aware graph division (CAGD) and interference-aware graph division (IAGD), which can achieve collision avoidance and interference control, respectively. Furthermore, we derive the convergence bound of AirGNNs that reveals the following three key properties: 1) the convergence bound is a function of the accumulated transmission errors of all devices; 2) there is an optimal transmit power for each device in terms of training performance; and 3) there is a fundamental tradeoff between training performance and transmission efficiency. Extensive experimental results on real-world datasets validate the effectiveness of our proposed methods and insights in the theoretical results.
- 23 January 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Wireless Communications Letters
- Vol. 15  (21622337) , 1499-1503
Graph Neural Networks via AirComp: Algorithms and Performance Analysis
Graph neural networks (GNNs) over the air (AirGNNs) has shown significant potential for efficiently training distributed GNN models by aggregating the feature representations based on the over the air computation (AirComp) technique. However, devices in existing wireless systems operate in half-duplex mode, the collision issue that devices cannot transmit and receive simultaneously may limit the potential of AirGNNs. To tackle this challenge, we proposed two scheduling methods, i.e., collision-aware graph division (CAGD) and interference-aware graph division (IAGD), which can achieve collision avoidance and interference control, respectively. Furthermore, we derive the convergence bound of AirGNNs that reveals the following three key properties: 1) the convergence bound is a function of the accumulated transmission errors of all devices; 2) there is an optimal transmit power for each device in terms of training performance; and 3) there is a fundamental tradeoff between training performance and transmission efficiency. Extensive experimental results on real-world datasets validate the effectiveness of our proposed methods and insights in the theoretical results.