# Robust Graph Structure Learning under Heterophily

arXiv: https://arxiv.org/abs/2403.03659 · HTML: https://mlsanity.com/paper/2403.03659/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 29 of 29)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [With a Little Help from My Friends: Nearest-Neighbor Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2104.14548/) (2021)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Deep Graph Clustering via Dual Correlation Reduction](https://mlsanity.com/paper/2112.14772/) (2021)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [A Mutual Information Maximization Perspective of Language Representation Learning](https://mlsanity.com/paper/1910.08350/) (2019)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [Augmentations in Graph Contrastive Learning: Current Methodological Flaws & Towards Better Practices](https://mlsanity.com/paper/2111.03220/) (2021)
- [Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs](https://mlsanity.com/paper/2103.14187/) (2021)
- [GLAM: Graph Learning by Modeling Affinity to Labeled Nodes for Graph Neural Networks](https://mlsanity.com/paper/2102.10403/) (2021)

## Built on by (most cited first, 11 of 11)

- [Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignment](https://mlsanity.com/paper/2502.02017/) (2025)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [When Heterophily Meets Heterogeneous Graphs: Latent Graphs Guided Unsupervised Representation Learning](https://mlsanity.com/paper/2409.00687/) (2024)
- [Graph Domain Adaptation via Homophily-Agnostic Reconstructing Structure](https://mlsanity.com/paper/2602.07573/) (2026)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [RCDM: Enabling Robustness for Conditional Diffusion Model](https://mlsanity.com/paper/2408.02710/) (2024)
- [Directed Homophily-Aware Graph Neural Network](https://mlsanity.com/paper/2505.22362/) (2025)
- [GLANCE: Graph Logic Attention Network with Cluster Enhancement for Heterophilous Graph Representation Learning](https://mlsanity.com/paper/2507.18521/) (2025)
- [Aggregation-aware MLP: An Unsupervised Approach for Graph Message-passing](https://mlsanity.com/paper/2507.20127/) (2025)
- [Attention Beyond Neighborhoods: Reviving Transformer for Graph Clustering](https://mlsanity.com/paper/2509.15024/) (2025)
- [Robust Learning on Heterogeneous Graphs with Heterophily: A Graph Structure Learning Approach](https://mlsanity.com/paper/2604.27387/) (2026)

## Abstract (arXiv)

Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real data is inevitably noisy and sparse, which will lead to inferior results. Despite the remarkable success of recent graph representation learning methods, they inherently presume that the graph is homophilic, and largely overlook heterophily, where most connected nodes are from different classes. In this regard, we propose a novel robust graph structure learning method to achieve a high-quality graph from heterophilic data for downstream tasks. We first apply a high-pass filter to make each node more distinctive from its neighbors by encoding structure information into the node features. Then, we learn a robust graph with an adaptive norm characterizing different levels of noise. Afterwards, we propose a novel regularizer to further refine the graph structure. Clustering and semi-supervised classification experiments on heterophilic graphs verify the effectiveness of our method.