We introduce a new analytical framework, developed based on the spatial network calculus, for performance assessment of Low Earth Orbit (LEO) satellite networks. Specifically, we model the satellites' spatial positions as a strong ball-regulated point process on the sphere. Under this model, proximal points in space exhibit a locally repulsive property, reflecting the fact that intersatellite links are protected by a safety distance and would not be arbitrarily close. Subsequently, we derive analytical lower bounds on the conditional coverage probabilities under Nakagami-m and Rayleigh fading, respectively. These expressions have a low computational complexity, enabling efficient numerical evaluations. We validate the effectiveness of our theoretical model by contrasting the coverage probability obtained from our analysis with that estimated from a Starlink constellation. The results show that our analysis provides a tight lower bound on the actual value and, surprisingly, matches the empirical simulations almost perfectly with a 1 dB shift. This demonstrates our framework as an appropriate theoretical model for LEO satellite networks.

Frequent parameter exchanges between clients and the edge server incur substantial communication overhead, posing a critical bottleneck in federated learning (FL). By exploiting the superposition property of wireless waveforms, over-the-air (OTA) computation enables simultaneous analog aggregation of local updates, thereby reducing communication latency and improving spectrum efficiency. However, its scalability is constrained by the limited number of available orthogonal waveform resources, which are typically far fewer than the model dimension. To address this, we propose AgeTop-k, an age-aware gradient sparsification strategy that performs compression through a two-stage selection process. Specifically, the edge server first selects candidate gradient entries based on their magnitudes, and then further prioritizes them according to the Age of Information (AoI), which quantifies the staleness of updates. AoI tracking is achieved efficiently by maintaining an age vector at the edge server. We derive theoretical convergence guarantees for non-convex loss functions and demonstrate the efficacy of AgeTop-k through extensive simulations.

Federated fine-tuning of large language models (LLMs) provides a privacy-preserving approach to deploying pervasive generative AI services, yet the substantial memory overhead of first-order (FO) gradient computation presents significant practical challenges. While zeroth-order (ZO) optimization methods offer memory-efficient alternatives, they remain susceptible to performance degradation brought by data heterogeneity. Specifically, direct ZO-for-FO substitution is incompatible with existing strategies tailored for cross-client discrepancies. In response, we propose a new federated LLM fine-tuning framework, with a holistic revamped design of the entire ZO gradient processing pipeline. Crucially, with our proposed global adaptive optimization and local personalized perturbation, we present a unified solution for incorporating ZO gradients in federated learning, from local personalized perturbation sampling and ZO gradient transmission, to global ZO gradient reconstruction and aggregation with adaptive momentum, thereby directly addressing the challenges of inefficiencies and cross-client discrepancies. Our convergence analysis and experiment results demonstrate the superiority of our proposed framework over diverse heterogeneous data settings, both in terms of generalization and efficiency.

The digital twin edge network (DITEN) is a significant paradigm in the sixth-generation wireless system (6G) that aims to organize well-developed infrastructures to meet the requirements of evolving application scenarios. However, the impact of the interaction between the long-term DITEN maintenance and detailed digital twin tasks, which often entail privacy considerations, is commonly overlooked in current research. This paper addresses this issue by introducing a problem of digital twin association and historical data allocation for a federated learning (FL) task within DITEN. To achieve this goal, we start by introducing a closed-form function to predict the training accuracy of the FL task, referring to it as the data utility. Subsequently, we carry out comprehensive convergence analyses on the proposed FL methodology. Our objective is to jointly optimize the data utility of the digital twin-empowered FL task and the energy costs incurred by the long-term DITEN maintenance, encompassing FL model training, data synchronization, and twin migration. To tackle the aforementioned challenge, we present an optimization-driven learning algorithm that effectively identifies optimized solutions for the formulated problem. Numerical results demonstrate that our proposed algorithm outperforms various baseline approaches.

Industrial Internet of Things (IIoT) systems are inherently dynamic, deeply embedded in physical environments, and often embodied in autonomous agents. These characteristics demand an AI paradigm that can continuously adapt and generalize across heterogeneous data and tasks. Unlike existing surveys that focus on "IIoT for foundation models" - e.g., how IIoT infrastructure supports data collection or distributed training for large models - this work reverses the perspective by investigating "foundation models for IIoT." We explore how large pre-trained foundation models (FMs) can be leveraged as a service to empower general industrial intelligence in IIoT. We propose a four-dimensional SCCE framework (Sensing-Computing-Connectivity-Evolution) that systematically examines the deployment of FMs in IIoT along the data processing pipeline and system lifecycle. Within this framework, we survey key IIoT tasks and discuss how state-of-the-art FMs (in vision, language, multimodal learning, etc.) can address challenges in noisy sensor data modeling, edge computing constraints, device connectivity and collaboration, and long-term model evolution. Our survey offers a unified, FM-centric perspective on enabling intelligent IIoT services, highlighting critical open challenges and future directions for integrating foundation model capabilities into industrial applications.

In this paper, we introduce a novel mathematical framework for assessing the performance of joint communication and sensing (JCAS) in wireless networks, employing stochastic geometry as an analytical tool. We focus on deriving the meta distribution of the signal-to-interference ratio (SIR) for JCAS networks. This approach enables a fine-grained quantification of individual user or radar performance intrinsic to these networks. Our work involves the modeling of JCAS networks and the derivation of mathematical expressions for the JCAS SIR meta distribution. Through simulations, we validate both our theoretical analysis and illustrate how the JCAS SIR meta distribution varies with the network deployment density.

Federated learning (FL) and split learning (SL) are two effective distributed learning paradigms in wireless networks, enabling collaborative model training across mobile devices without sharing raw data. While FL supports low-latency parallel training, it may converge to less accurate model. In contrast, SL achieves higher accuracy through sequential training but suffers from increased delay. To leverage the advantages of both, hybrid split and federated learning (HSFL) allows some devices to operate in FL mode and others in SL mode. This paper aims to accelerate HSFL by addressing three key questions: 1) How does learning mode selection affect overall learning performance? 2) How does it interact with batch size? 3) How can these hyperparameters be jointly optimized alongside communication and computational resources to reduce overall learning delay? We first analyze convergence, revealing the interplay between learning mode and batch size. Next, we formulate a delay minimization problem and propose a two-stage solution: a block coordinate descent method for a relaxed problem to obtain a locally optimal solution, followed by a rounding algorithm to recover integer batch sizes with near-optimal performance. Experimental results demonstrate that our approach significantly accelerates convergence to the target accuracy compared to existing methods.

We investigate the role of channel access schemes in enhancing the timeliness of status updates in sensor networks. Specifically, we model the large-scale sensor network as a Poisson cellular network and derive the network average age of information (AoI) under five different channel access schemes: slotted ALOHA, frame slotted ALOHA, random scheduling, round robin, and channel-aware. These schemes are categorized based on random vs. scheduled access and non-channel-aware vs. channel-aware. Our goal is to investigate when the additional overhead and complexity introduced by scheduling and channel state information (CSI) are beneficial, enabling better decisions in network design. Our findings reveal that the effectiveness of these schemes is influenced by the signal-to-interference ratio (SIR) decoding threshold, which often reflects the length of communication data. For short-packet communications, the performance differences among various channel access strategies are minimal, and the gains from scheduling are limited. Additionally, the inclusion of extra CSI does not yield performance improvements; in fact, some simple scheduling strategies, along with channelaware strategy that leverage CSI, may not outperform basic random access methods. Among the protocols we examined, the round robin scheme achieves the best performance. In contrast, scheduled access schemes exhibit a clear performance advantage in long-packet communications. Furthermore, the channel-aware scheme significantly enhances the network AoI performance, particularly in networks with higher transmitter competition.

The proliferation of mobile devices and real-time status updating applications has motivated the optimization of data freshness in the context of age of information (AoI). Meanwhile, increasing computational demands have inspired research on CPU scheduling. Since prior CPU scheduling strategies have ignored data freshness and prior age-minimization strategies have considered only constant CPU speed, we formulate the first CPU scheduling problem as a constrained semi-Markov decision process (SMDP) problem with uncountable space, which aims to minimize the long-term average age of information, subject to an average CPU power constraint. We optimize strategies that specify when the CPU sleeps and adapt the CPU speed (clock frequency) during the execution of update-processing tasks. We consider the age-minimal CPU scheduling problem for both predictable task size (PTS) and unpredictable task size (UTS) cases, where the task size is realized at the start (PTS) or at the completion (UTS) of the task, respectively. To address the non-convex objective, we employ Dinkelbach's fractional programming method to transform our problem into an average cost SMDP. We develop a value-iteration-based algorithm and prove its convergence to obtain optimal policies and structural results for both the PTS and UTS systems. Compared to constant CPU speed, numerical results show that our proposed scheme can reduce the AoI by 50% or more, with increasing benefits under tighter power constraints. Further, for a given AoI target, the age-minimal CPU scheduling policy can reduce the energy consumption by 50% or more, with greater AoI reductions when the task size distribution exhibits higher variance.

With the explosive deployment of non-terrestrial networks (NTNs), the computational complexity of network performance analysis is rapidly escalating. As one of the most suitable mathematical tools for analyzing large-scale network topologies, stochastic geometry (SG) enables the representation of network performance metrics as functions of network parameters, thus offering low-complexity performance analysis solutions. However, choosing between planar and spherical models remains challenging. Planar models neglect Earth's curvature, causing deviations in high-altitude NTN analysis, yet are still often used for simplicity. This paper introduces relative error to quantify the gap between planar and spherical models, helping determine when planar modeling is sufficient. To calculate the relative error, we first propose a point process (PP) generation algorithm that simultaneously generates a pair of homogeneous and asymptotically similar planar and spherical PPs. We then introduce several typical similarity metrics, including topology-related and network-level metrics, and further develop a relative error estimation algorithm based on these metrics. In addition, we derive an analytical expression for the optimal planar altitude, which reduces computational complexity and provides theoretical support for planar approximation. Finally, numerical results investigate how deployment altitude and region affect NTN modeling, with case studies on HAP and LEO satellite constellations.

Federated learning facilitates collaborative model training across multiple clients while preserving data privacy. However, its performance is often constrained by limited communication resources, particularly in systems supporting a large number of clients. To address this challenge, integrating over-the-air computations into the training process has emerged as a promising solution to alleviate communication bottlenecks. The system significantly increases the number of clients it can support in each communication round by transmitting intermediate parameters via analog signals rather than digital ones. This improvement, however, comes at the cost of channel-induced distortions, such as fading and noise, which affect the aggregated global parameters. To elucidate these effects, this paper develops a theoretical framework to analyze the performance of over-the-air federated learning in large-scale client scenarios. Our analysis reveals three key advantages of scaling up the number of participating clients: (1) Enhanced Privacy: The mutual information between a client's local gradient and the server's aggregated gradient diminishes, effectively reducing privacy leakage. (2) Mitigation of Channel Fading: The channel hardening effect eliminates the impact of small-scale fading in the noisy global gradient. (3) Improved Convergence: Reduced thermal noise and gradient estimation errors benefit the convergence rate. These findings solidify over-the-air model training as a viable approach for federated learning in networks with a large number of clients. The theoretical insights are further substantiated through extensive experimental evaluations.

Large language models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing tasks. Exploiting the heterogeneous capabilities of edge LLMs is crucial for diverse emerging applications, as it enables greater cost-effectiveness and reduced latency. In this work, we introduce Mixture-of-Edge-Experts (MoE2), a novel collaborative inference framework for edge LLMs. We formulate a joint gating and expert selection problem to optimize inference performance under energy and latency constraints. Unlike conventional MoE problems, LLM expert selection becomes significantly more challenging due to the combinatorial nature and the heterogeneity of edge LLMs across various attributes. To this end, we propose a two-level expert selection mechanism through which we uncover an optimality-preserving property of gating parameters across expert selections. This property enables the decomposition of the training and selection processes, significantly reducing complexity. Furthermore, we leverage the objective's monotonicity and design a discrete monotonic optimization algorithm for optimal expert selection. We implement edge servers with NVIDIA Jetson AGX Orins and NVIDIA RTX 4090 GPUs, and perform extensive experiments. Our results validate the performance improvements for various LLM models and show that our MoE2 method can achieve optimal trade-offs among different delay and energy budgets, and outperforms baselines under various system resource constraints. We further demonstrate its strong robustness in dynamic, non-stationary environments and its effectiveness in achieving load balancing.

As 6G evolves, the radio access network must transcend traditional automation to embrace agentic AI capable of perception, reasoning, and evolution. A fundamental cognitive gap persists in current disaggregated architectures, where interfaces force the physical layer to compress high-dimensional states into low-dimensional metrics, trapping reasoning agents behind a semantic bottleneck. This article envisions a shift from interface-bound to memory-centric architectures. We propose a unified memory paradigm that dissolves the boundaries between sensing and reasoning by mapping biological memory hierarchies onto heterogeneous computing fabrics. Enabled by emerging coherent interconnects, this approach creates a cognitive continuum where microsecond-level reflexes, millisecond-level reasoning, and long-term evolution share state across time scales. By replacing message passing with zero-copy observability, we empower AI agents to bridge the gap between real-time responsiveness and long-horizon context for truly autonomous 6G networks.

Given the limited performance and efficiency of on-device Large Language Models (LLMs), the collaborations between multiple LLMs enable desirable performance enhancements, in which data, tokens, and model weights could be shared across LLMs. This process is constrained by task-oriented QoS demands, privacy requirements, and inherent system heterogeneity. In view of the above challenge and to fully exploit the on-device inference capabilities, we present a novel federated inference framework in this position paper, termed federated refinement . This framework presents a new paradigm for heterogeneous LLMs collaboratively performing inference with communicating KV caches in a privacy-preserving manner. Some numerical results are provided to highlight the superiority of . Several interesting topics are also highlighted for future research. By exploring the LLM-native communications, we wish to provide a new paradigm for this broad area.

This is supplementary Table 2.

Joint sensing and communication (JSC) systems aim to leverage the same spectral resources for both communication and sensing tasks within a single system. These systems have the potential to enhance sensing capabilities through advanced communication techniques, while also utilizing precise localization and tracking information from sensing technologies to improve communication. However, the integration of information obtained from sensing and transmitted in communication is not yet fully understood. This paper investigates the challenge of guaranteeing timely delivery of sensing information within JSC systems. We introduce a novel metric, termed as the age of estimation information (AoEI), which integrates radar mutual information (MI) and age of information (AoI). This unified metric effectively captures both the passage of time and the accuracy of estimation information, making it well-suited for the JSC system. Further, we delve into the joint optimization of time and power allocation for a single JSC node with both sensing and communication capabilities. Our objective is to minimize the long-term average AoEI while adhering to a long-term average power constraint. To tackle this problem, we formulate it as an average-reward constrained Markov decision process (CMDP) and propose a model-free constrained deep reinforcement learning (CDRL) algorithm, namely the average policy optimization (APO)-Lagrangian based algorithm. Simulation results demonstrate that our proposed algorithm effectively meets the constraint in dynamic and uncertain environments while achieving a favorable balance between AoEI and power consumption. Additionally, our algorithm outperforms four baseline schemes, showcasing its superior performance.

Federated Learning (FL) on resource-constrained edge devices faces a critical challenge: The computational energy required for training Deep Neural Networks (DNNs) often dominates communication costs. However, most existing Energy-Harvesting FL (EHFL) strategies fail to account for this reality, resulting in wasted energy due to redundant local computations. For efficient and proactive resource management, algorithms that predict local update contributions must be devised. We propose a lightweight client scheduling framework using the Version Age of Information (VAoI), a semantics-aware metric that quantifies update timeliness and significance. Crucially, we overcome VAoI's typical prohibitive computational cost, which requires statistical distance over the entire parameter space, by introducing a feature-based proxy. This proxy estimates model redundancy using intermediate-layer extraction from a single forward pass, dramatically reducing computational complexity. Experiments conducted under extreme non-IID data distributions and scarce energy availability demonstrate superior learning performance while achieving energy reduction compared to existing baseline selection policies. Our framework establishes semantics-aware scheduling as a practical and vital solution for EHFL in realistic scenarios where training costs dominate transmission costs.

Tumor dissemination is increasingly recognized to begin early in tumor development. Although most of these early disseminated cells are cleared, some survive and persist below clinical detection, acting as reservoirs for metastatic relapse. Metastatic tumor cells often rely on interactions with local stromal cells to support their colonization. In this study, we propose that pericyte-tumor cell interactions promote dormancy induction in the early metastatic lung, enhancing disseminated tumor cell (DTC) persistence. Extravital imaging demonstrated that DTCs interact with pericytes upon extravasation into the lung. Co-culture experiments were used to assess DTC fate after pericyte contact and revealed that transient contact with pericytes reduced the proliferation of metastatic 4T1 breast cancer cells but had no effect on non-metastatic 67NR cells. In vivo , transient pericyte contact resulted in higher lung metastatic burden, driven by small, non-proliferative lesions (<6 cells), 10 days after intracardiac injection. These lesions exhibited reduced KI67 staining and EdU incorporation compared to those from monocultured cells. We further observed that primary lung pericytes transferred lyso-phospholipids (lyso-PLs) specifically to metastatic 4T1 cells through direct contact. Gene expression analysis indicated that transient pericyte contact activated pathways related to syncytium formation in metastatic cells. In normal physiology, pericytes act in a syncytium to regulate blood flow via mechanosensitive channels in response to blood pressure changes. We hypothesize that tumor cells exploit these mechanosensitive responses to trigger lyso-PL transfer from pericytes. Supporting this, calcium imaging showed higher calcium activity in pericytes co-cultured with 4T1 cells, and calcium channel inhibitors significantly reduced lyso-PL transfer. Pharmacological activation of pericyte calcium channels induced lyso-PL release, which was subsequently taken up by tumor cells. Conditioned medium from activated pericytes, containing free lyso-PLs, recapitulated the reduced proliferation observed in transient co-culture. Finally, we found our pericyte-induced dormancy signature to be associated with tumor dormancy and distant metastasis free survival latency in breast cancer patients. Together, these findings suggest that early DTCs may exploit pericyte signaling mechanisms to enter dormancy, facilitating their persistence at metastatic sites and contributing to future relapse.

This paper studies the efficiency of training a statistical model among an edge server and multiple clients via Federated Learning (FL) – a machine learning method that preserves data privacy in the training process – over wireless networks. Due to unreliable wireless channels and constrained communication resources, the server can only choose a handful of clients for parameter updates during each communication round. To address this issue, analytical expressions are derived to characterize the FL convergence rate, accounting for key features from both communication and algorithmic aspects, including transmission reliability, scheduling policies, and momentum method. First, the analysis reveals that either delicately designed user scheduling policies or expanding higher bandwidth to accommodate more clients in each communication round can expedite model training in networks with reliable connections. However, these methods become ineffective when the connection is erratic. Second, it has been verified that incorporating the momentum method into the model training algorithm accelerates the rate of convergence and provides greater resilience against transmission failures. Last, extensive empirical simulations are provided to verify these theoretical discoveries and enhancements in performance.