In this work, we theoretically demonstrate that current graph positional encodings (PEs) are not beneficial and could potentially hurt performance in tasks involving heterophilous graphs, where nodes that are close tend to have different labels. This limitation is critical as many real-world networks exhibit heterophily, and even highly homophilous graphs can contain local regions of strong heterophily. To address this limitation, we propose Learnable Laplacian Positional Encodings (LLPE), a new PE that leverages the full spectrum of the graph Laplacian, enabling them to capture graph structure on both homophilous and heterophilous graphs. Theoretically, we prove LLPE’s ability to approximate a general class of graph distances and demonstrate its generalization properties. Empirically, our evaluation on 12 benchmarks demonstrates that LLPE improves accuracy across a variety of GNNs, including graph transformers, by up to 35% and 14% on synthetic and real-world graphs, respectively. Going forward, our work represents a significant step towards developing PEs that effectively capture complex structures in heterophilous graphs.

Distributed graph neural network (GNN) training facilitates learning on massive graphs that surpass the storage and computational capabilities of a single machine. Traditional distributed frameworks strive for performance parity with centralized training by maximally recovering cross-instance node dependencies, relying either on inter-instance communication or periodic fallback to centralized training. However, these processes create overhead and constrain the scalability of the framework. In this work, we propose a streamlined framework for distributed GNN training that eliminates these costly operations, yielding improved scalability, convergence speed, and performance over state-of-the-art approaches. Our framework (1) comprises independent trainers that asynchronously learn local models from locally available parts of the training graph and (2) synchronizes these local models only through periodic (time-based) model aggregation. Contrary to prevailing belief, our theoretical analysis shows that it is not essential to maximize the recovery of cross-instance node dependencies to achieve performance parity with centralized training. Instead, our framework leverages randomized assignment of nodes or super-nodes (i.e., collections of original nodes) to partition the training graph in order to enhance data uniformity and minimize discrepancies in gradient and loss function across instances. Experiments on social and e-commerce networks with up to 1.3 billion edges show that our proposed framework achieves state-of-the-art performance and 2.31 \(\times\) speedup compared to the fastest baseline despite using less training data.

Heterophily, or the tendency of connected nodes in networks to have different class labels or dissimilar features, has been identified as challenging for many Graph Neural Network (GNN) models. While the challenges of applying GNNs for node classification when class labels display strong heterophily are well understood, it is unclear how heterophily affects GNN performance in other important graph learning tasks where class labels are not available. In this work, we focus on the link prediction task and systematically analyze the impact of heterophily in node features on GNN performance. We first introduce formal definitions of homophilic and heterophilic link prediction tasks, and present a theoretical framework that highlights the different optimizations needed for the respective tasks. We then analyze how different link prediction encoders and decoders adapt to varying levels of feature homophily and introduce designs for improved performance. Based on our definitions, we identify and analyze six real-world benchmarks spanning from homophilic to heterophilic link prediction settings, with graphs containing up to 30M edges. Our empirical analysis on a variety of synthetic and real-world datasets confirms our theoretical insights and highlights the importance of adopting learnable decoders and GNN encoders with ego- and neighbor-embedding separation in message passing for link prediction tasks beyond homophily.

Recent years have witnessed a surge of research interest in graph machine learning. However, the benchmark datasets available to the field are rather limited in both quantity and diversity, an issue particularly notable given the immense potential applications of graph learning. The lack of diverse benchmark datasets may have biased the development of graph machine learning techniques towards narrow directions. By crowdsourcing novel tasks and datasets, this workshop aims to increase the diversity of graph learning benchmarks, identify new demands of graph machine learning in general, and gain a better synergy of how concrete techniques perform on these benchmarks. Moreover, this workshop offers a platform for discussions of best practices in curating graph learning benchmarks and data-centric approaches for graph learning.

We bridge two research directions on graph neural networks (GNNs), by formalizing the relation between heterophily of node labels (i.e., connected nodes tend to have dissimilar labels) and the robustness of GNNs to adversarial attacks. Our theoretical and empirical analyses show that for homophilous graph data, impactful structural attacks always lead to reduced homophily, while for heterophilous graph data the change in the homophily level depends on the node degrees. These insights have practical implications for defending against attacks on real-world graphs: we deduce that separate aggregators for ego- and neighbor-embeddings, a design principle which has been identified to significantly improve prediction for heterophilous graph data, can also offer increased robustness to GNNs. Our comprehensive experiments show that GNNs merely adopting this design achieve improved empirical and certifiable robustness compared to the best-performing unvaccinated model. Additionally, combining this design with explicit defense mechanisms against adversarial attacks leads to an improved robustness with up to 18.33% performance increase under attacks compared to the best-performing vaccinated model.

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar features. Many popular GNNs fail to generalize to this setting, and are even outperformed by models that ignore the graph structure (e.g., multilayer perceptrons). Motivated by this limitation, we identify a set of key designs—ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations—that boost learning from the graph structure under heterophily. We combine them into a graph neural network, H2GCN, which we use as the base method to empirically evaluate the effectiveness of the identified designs. Going beyond the traditional benchmarks with strong homophily, our empirical analysis shows that the identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively, and yield competitive performance under homophily.

Mapping the human brain, or understanding how certain brain regions relate to specific aspects of cognition, has been and remains an active area of neuroscience research. Functional magnetic resonance imaging (fMRI) data---in the form of images, time series or graphs---are central in this research, but pose many challenges in phenotype prediction tasks (e.g., noisy, small training samples). Standardly employed handcrafted models and newly proposed neural network methods pose limitations in the expressive power and interpretability, respectively, in this context. In this work focusing on fMRI-derived brain graphs, a modality that partially handles some challenges of fMRI data, we propose a grouping-based interpretable neural network model, GroupINN, that effectively classifies cognitive performance with 85% fewer model parameters than baseline deep models, while also identifying the most predictive brain subnetworks within several task-specific contexts. Our method incorporates the idea of node grouping into the design of the neural network. That way, unlike other methods that employ clustering as a preprocessing step to reorder nodes, GroupINN learns the node grouping and extracts graph features jointly. Experiments on task-based fMRI datasets show that our method is $2.6-69\times$ faster than other deep models, while achieving comparable or better accuracy and providing interpretability.