Graph Smoothing

Graph smoothing techniques aim to enhance data representations by reducing noise and highlighting underlying structure, primarily within graph-structured data and signals. Current research focuses on developing efficient algorithms, such as those based on graph convolutional networks (GCNs) and transformer-like architectures, that leverage various smoothness priors (e.g., Laplacian regularizers) to achieve this goal. These methods find applications in diverse fields, including natural language processing (e.g., improving sentence embeddings and defending against adversarial attacks on large language models), image processing (e.g., image smoothing and interpolation), and generally improving the performance and interpretability of machine learning models on graph data. The effectiveness and stability of these approaches are actively being investigated, with a particular focus on understanding and mitigating the phenomenon of oversmoothing.