Frequency-guided Structure Learning Advances Graph Neural Networks for Heterophilic Data Challenges

Graph neural networks frequently encounter difficulties when discerning meaningful patterns in complex datasets where connections between nodes often link dissimilar elements, a condition known as heterophily. Ayushman Raghuvanshi, Gonzalo Mateos, and Sundeep Prabhakar Chepuri, from the Indian Institute of Science and the University of Rochester, address this challenge with a new approach to graph structure learning. Their work introduces a method that simultaneously refines both the standard, similar-node connections and the more subtle, dissimilar-node links within a graph, using a technique that analyses the frequencies present in the data. This innovative framework, which incorporates a specialised spectral encoder and a label-based structural loss function, demonstrably improves performance on benchmark heterophilic datasets, offering a significant advance in the ability of graph neural networks to extract useful information from challenging data.

The study pioneers an end-to-end approach, beginning with a fully connected graph and then employing learnable, feature-driven masking functions to generate complementary graphs tailored to capture distinct relational patterns. These resulting graphs are then processed using carefully designed low- and high-pass filter banks, enabling the extraction of relevant frequency components from node features., The team engineered a label-based structural loss function that explicitly encourages the recovery of both homophilic and heterophilic edges, effectively driving task-driven graph structure learning. Rigorous analysis of this loss function yielded stability bounds, ensuring reliable performance and establishing robustness guarantees for the filter banks even with perturbations in the graph structure.

Experiments employing six established heterophilic benchmark datasets allowed for comprehensive evaluation of the method’s capabilities., The technique reveals a significant improvement over existing state-of-the-art graph neural networks and graph rewiring methods, consistently achieving superior performance across all benchmarks. Results demonstrate the benefits of integrating frequency information with supervised topology inference, overcoming limitations of approaches that rely solely on node features, which often prove unreliable in heterophilic settings. The work highlights that feature similarity alone is insufficient to accurately recover graph structures, and that the proposed method effectively addresses this issue by leveraging label information to guide structural inference.,.

Frequency-Guided Learning for Heterophilic Graph Structures

Scientists have achieved a breakthrough in graph structure learning, particularly for heterophilic graphs where connected nodes often exhibit dissimilar labels and weak feature similarity. Their work introduces Frequency-Guided Structure Learning (FgGSL), a framework that simultaneously learns both homophilic and heterophilic graph structures alongside a spectral encoder, addressing limitations found in existing graph neural networks and rewiring methods. The team developed a learnable masking function to infer these complementary graph structures, processing them with specifically designed low- and high-pass filter banks to capture different frequency components within the data., Experiments conducted on six heterophilic benchmarks demonstrate that FgGSL consistently outperforms state-of-the-art graph neural networks and graph rewiring techniques. Results demonstrate the framework’s ability to recover structures closely aligned with actual label-based counterparts, maintaining performance even when testing node labels are unavailable, provided prediction error remains bounded.

The team measured a markedly different similarity distribution between semantically similar and dissimilar node pairs within the learned embeddings, indicating a refined understanding of relationships within the graph., The core of FgGSL lies in a label-aware structural loss function, explicitly promoting the recovery of both homophilic and heterophilic edges, and enabling task-driven structure learning. Scientists derived stability bounds for this structural loss, guaranteeing robustness of the filter banks even with minor data perturbations. By jointly modeling low- and high-frequency modes through complementary spectral filters, FgGSL effectively captures informative relationships that conventional aggregation-based GNNs often miss, representing a significant advancement in task-driven graph structure learning under conditions of heterophily. This work establishes a novel approach to graph inference, combining frequency information with supervised topology inference for improved performance and interpretability.,.

Frequency-Guided Learning Resolves Heterophilic Graph Challenges

This research introduces frequency-guided structure learning, or FgGSL, a new framework designed to improve node classification on graphs where connections often link dissimilar nodes, a challenging scenario known as heterophily. The team successfully developed a method that simultaneously learns both homophilic and heterophilic structures within a graph, employing a feature-driven masking function and combining low- and high-pass spectral filters to capture relevant relationships. By explicitly encouraging the recovery of both types of edges through a label-based structural loss, the model achieves task-driven graph inference with guaranteed stability and robustness., Evaluations on six benchmark datasets demonstrate that FgGSL consistently surpasses the performance of existing graph neural networks and graph rewiring techniques. Analysis of the learned node embeddings reveals a clear separation between node pairs within the same class and those belonging to different classes, confirming the model’s ability to effectively represent heterophilic structures. The authors acknowledge that the performance of individual filter variants highlights the benefit of combining both low- and high-pass filters, suggesting a synergistic effect in capturing diverse graph features. Future work could explore the application of this framework to other graph-based machine learning tasks and investigate the potential for adapting the learned structures to different downstream applications.