WirelessMathBench: A Mathematical Modeling Benchmark for LLMs in Wireless Communications

Large Language Models (LLMs) have achieved impressive results across a broad array of tasks, yet their capacity for complex, domain-specific mathematical reasoning-particularly in wireless communications-remains underexplored. In this work, we introduce WirelessMathBench, a novel benchmark specifically designed to evaluate LLMs on mathematical modeling challenges to wireless communications engineering. Our benchmark consists of 587 meticulously curated questions sourced from 40 state-of-the-art research papers, encompassing a diverse spectrum of tasks ranging from basic multiple-choice questions to complex equation completion tasks, including both partial and full completions, all of which rigorously adhere to physical and dimensional constraints. Through extensive experimentation with leading LLMs, we observe that while many models excel in basic recall tasks, their performance degrades significantly when reconstructing partially or fully obscured equations, exposing fundamental limitations in current LLMs. Even DeepSeek-R1, the best performer on our benchmark, achieves an average accuracy of only 38.05%, with a mere 7.83% success rate in full equation completion. By publicly releasing WirelessMathBench along with the evaluation toolkit, we aim to advance the development of more robust, domain-aware LLMs for wireless system analysis and broader engineering applications.

Over-the-Air ODE-Inspired Neural Network for Dual Task-Oriented Semantic Communications

Analog machine-learning hardware platforms promise greater speed and energy efficiency than their digital counterparts. Specifically, over-the-air analog computation allows offloading computation to the wireless propagation through carefully constructed transmitted signals. In addition, reconfigurable intelligent surface (RIS) is emerging as a promising solution for next-generation wireless networks, offering the ability to tailor the communication environment. Leveraging the advantages of RIS, we design and implement the ordinary differential equation (ODE) neural network using over-the-air computation (AirComp) and demonstrate its effectiveness for dual tasks. We engineer the ambient wireless propagation environment through distributed RISs to create an architecture termed the over-the-air ordinary differential equation (Air-ODE) network. Unlike the conventional digital ODE-inspired neural network, the Air-ODE block utilizes the physics of wave reflection and the reconfigurable phase shifts of RISs to implement an ODE block in the analog domain, enhancing spectrum efficiency. Moreover, the advantages of Air-ODE are demonstrated in a deep learning-based semantic communication (DeepSC) system by extracting effective semantic information to reduce the data transmission load, while achieving the dual functions of image reconstruction and semantic tagging simultaneously at the receiver. Simulation results show that the analog Air-ODE network can achieve similar performance to the digital ODE-inspired network. Specifically, for the image reconstruction and semantic tagging task, compared with the analog network without the Air-ODE block, the Air-ODE block can achieve around 2 times gain in both reconstruction quality and tagging accuracy.

Beamforming Design and Association Scheme for Multi-RIS Multi-User mmWave Systems Through Graph Neural Networks

Reconfigurable intelligent surface (RIS) is emerging as a promising technology for next-generation wireless communication networks, offering a variety of merits such as the ability to tailor the communication environment. Moreover, deploying multiple RISs helps mitigate severe signal blocking between the base station (BS) and users, providing a practical and efficient solution to enhance the service coverage. However, fully reaping the potential of a multi-RIS aided communication system requires solving a non-convex optimization problem. This challenge motivates the adoption of learning-based methods for determining the optimal policy. In this paper, we introduce a novel heterogeneous graph neural network (GNN) to effectively leverage the graph topology of a wireless communication environment. Specifically, we design an association scheme that selects a suitable RIS for each user. Then, we maximize the weighted sum rate (WSR) of all the users by iteratively optimizing the RIS association scheme, and beamforming designs until the considered heterogeneous GNN converges. Based on the proposed approach, each user is associated with the best RIS, which is shown to significantly improve the system capacity in multi-RIS multi-user millimeter wave (mmWave) communications. Specifically, simulation results demonstrate that the proposed heterogeneous GNN closely approaches the performance of the high-complexity alternating optimization (AO) algorithm in the considered multi-RIS aided communication system, and it outperforms other benchmark schemes. Moreover, the performance improvement achieved through the RIS association scheme is shown to be of the order of 30%.

Cooperative Beamforming and RISs Association for Multi-RISs Aided Multi-Users MmWave MIMO Systems through Graph Neural Networks

Reconfigurable intelligent surface (RIS) is considered as a promising solution for next-generation wireless communication networks due to a variety of merits, e.g., customizing the communication environment. Therefore, deploying multiple RISs helps overcome severe signal blocking between the base station (BS) and users, which is also a practical and effective solution to achieve better service coverage. However, reaping the full benefits of a multi-RISs aided communication system requires solving a non-convex, infinite-dimensional optimization problem, which motivates the use of learning-based methods to configure the optimal policy. This paper adopts a novel heterogeneous graph neural network (GNN) to effectively exploit the graph topology in the wireless communication optimization problem. First, we characterize all communication link features and interference relations in our system with a heterogeneous graph structure. Then, we endeavor to maximize the weighted sum rate (WSR) of all users by jointly optimizing the active beamforming at the BS, the passive beamforming vector of the RIS elements, as well as the RISs association strategy. Unlike most existing work, we consider a more general scenario where the cascaded link for each user is not fixed but dynamically selected by maximizing the WSR. Simulation results show that our proposed heterogeneous GNNs perform about 10 times better than other benchmarks, and a suitable RISs association strategy is also validated to be effective in improving the quality services of users by 30%.