Next-generation wireless networks are characterized by two essential features: ubiquitous connectivity and high-speed data transmission. The realization of these features hinges on the development of rational resource allocation strategies to optimize the utilization of radio resources. This study addresses the beamforming design problem for downlink transmission in multi-cell cellular networks, with a focus on maximizing user data rates while adhering to stringent power constraints. To tackle this challenge, we propose a novel graph learning-based optimization framework that learns the mapping from channel states to beamforming vectors in an unsupervised manner. At the core of this framework is an attention-based graph neural network (GNN), which efficiently captures complex inter-node relationships by dynamically computing the importance of neighboring nodes. Furthermore, a jumping knowledge network is integrated to enhance structural representation learning, enabling the model to adaptively capture diverse neighborhood ranges for each node and mitigate the issue of over-smoothing. Extensive simulations demonstrate that the proposed algorithm significantly outperforms existing benchmark methods, exhibiting robust performance and strong generalization capabilities across a wide range of system parameter configurations. © 2025 Elsevier B.V., All rights reserved.