Graph Neural Networks (GNNs) have become essential for studying complex data, particularly when represented as graphs. Their value is underpinned by their ability to reflect the intricacies of numerous areas, ranging from social to biological networks. GNNs can grapple with non-linear behaviors, emerging patterns, and complex connections; these are also typical characteristics of complex systems. The renormalization group (RG) theory has emerged as the language for studying complex systems. It is recognized as the preferred lens through which to study complex systems, offering a framework that can untangle their intricate dynamics. Despite the clear benefits of integrating RG theory with GNNs, no existing methods have ventured into this promising territory. This paper proposes a new approach that applies RG theory to devise a novel graph rewiring to improve GNNs' performance on graph-related tasks. We support our proposal with extensive experiments on standard benchmarks and baselines. The results demonstrate the effectiveness of our method and its potential to remedy the current limitations of GNNs. Finally, this paper marks the beginning of a new research direction. This path combines the theoretical foundations of RG, the magnifying glass of complex systems, with the structural capabilities of GNNs. By doing so, we aim to enhance the potential of GNNs in modeling and unraveling the complexities inherent in diverse systems.

翻译：图神经网络（GNN）已成为研究复杂数据（尤其以图形式呈现的数据）的核心工具。其价值在于能够反映从社交网络到生物网络等多个领域的复杂特性。GNN可处理非线性行为、涌现模式及复杂连接——这些也正是复杂系统的典型特征。重整化群（RG）理论已成为研究复杂系统的通用语言，被视为解析复杂系统内在动态机制的首选理论框架。尽管将RG理论与GNN相结合具有显著优势，但现有方法尚未涉足这一前景广阔的研究领域。本文提出了一种基于RG理论的新型图重构方法，旨在提升GNN在图相关任务中的性能。我们在标准基准测试和基线模型上开展了大量实验验证该方法的有效性。结果表明，所提方法不仅性能优异，还具有弥补当前GNN局限性的潜力。最后，本文开创了一个全新的研究方向：将作为复杂系统"放大镜"的RG理论基础与GNN的结构处理能力有机融合，从而增强GNN在建模和解构各类系统固有复杂性方面的能力。