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1. Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?

   Mao, Haitao; Chen, Zhikai; Jin, Wei; Han, Haoyu; Ma, Yao; Zhao, Tong; Shah, Neil; Tang, Jiliang (December 2023, NeurIPS)

   Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity. However, the analysis of GNN performance with respect to nodes exhibiting different structural patterns, e.g., homophilic nodes in heterophilic graphs, remains rather limited. In the present study, we provide evidence that Graph Neural Networks(GNNs) on node classification typically perform admirably on homophilic nodes within homophilic graphs and heterophilic nodes within heterophilic graphs while struggling on the opposite node set, exhibiting a performance disparity. We theoretically and empirically identify effects of GNNs on testing nodes exhibiting distinct structural patterns. We then propose a rigorous, non-i.i.d PAC-Bayesian generalization bound for GNNs, revealing reasons for the performance disparity, namely the aggregated feature distance and homophily ratio difference between training and testing nodes. Furthermore, we demonstrate the practical implications of our new findings via (1) elucidating the effectiveness of deeper GNNs; and (2) revealing an over-looked distribution shift factor on graph out-of-distribution problem and proposing a new scenario accordingly. 

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2. Neural Collapse in Multi-label Learning with Pick-all-label Loss

   Li, Pengyu; Li, Xiao; Wang, Yutong; Qu, Qing (June 2024, International Conference on Machine Learning)

   We study deep neural networks for the multi-label classification (MLab) task through the lens of neural collapse (NC). Previous works have been restricted to the multi-class classification setting and discovered a prevalent NC phenomenon comprising of the following properties for the last-layer features: (i) the variability of features within every class collapses to zero, (ii) the set of feature means form an equi-angular tight frame (ETF), and (iii) the last layer classifiers collapse to the feature mean upon some scaling. We generalize the study to multi-label learning, and prove for the first time that a generalized NC phenomenon holds with the "pick-all-label'' formulation, which we term as MLab NC. While the ETF geometry remains consistent for features with a single label, multi-label scenarios introduce a unique combinatorial aspect we term the "tag-wise average" property, where the means of features with multiple labels are the scaled averages of means for single-label instances. Theoretically, under proper assumptions on the features, we establish that the only global optimizer of the pick-all-label cross-entropy loss satisfy the multi-label NC. In practice, we demonstrate that our findings can lead to better test performance with more efficient training techniques for MLab learning. 

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3. GNNExplainer: Generating Explanations for Graph Neural Networks

   Ying, R.; Bourgeois, D.; You, J.; Zitnik, M.; Leskovec, J. (December 2019, Advances in neural information processing systems)

   Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs. GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating both graph structure and feature information leads to complex models and explaining predictions made by GNNs remains unsolved. Here we propose GNNEXPLAINER, the first general, model-agnostic approach for providing interpretable explanations for predictions of any GNN-based model on any graph-based machine learning task. Given an instance, GNNEXPLAINER identifies a compact subgraph structure and a small subset of node features that have a crucial role in GNN’s prediction. Further, GNNEXPLAINER can generate consistent and concise explanations for an entire class of instances. We formulate GNNEXPLAINER as an optimization task that maximizes the mutual information between a GNN’s prediction and distribution of possible subgraph structures. Experiments on synthetic and real-world graphs show that our approach can identify important graph structures as well as node features, and outperforms alternative baseline approaches by up to 43.0% in explanation accuracy. GNNEXPLAINER provides a variety of benefits, from the ability to visualize semantically relevant structures to interpretability, to giving insights into errors of faulty GNNs. 

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4. H^2GNN: Graph Neural Networks with Homophilic and Heterophilic Feature Aggregations

   Jing, Shixiong; Chen, Lingwei; Li, Quan; Wu, Dinghao (July 2024, International Conference on Database Systems for Advanced Applications, Springer Nature Singapore)

   Graph neural networks (GNNs) rely on the assumption of graph homophily, which, however, does not hold in some real-world scenarios. Graph heterophily compromises them by smoothing node representations and degrading their discrimination capabilities. To address this limitation, we propose H^2GNN, which implements Homophilic and Heterophilic feature aggregations to advance GNNs in graphs with homophily or heterophily. H^2GNN proceeds by combining local feature separation and adaptive message aggregation, where each node separates local features into similar and dissimilar feature vectors, and aggregates similarities and dissimilarities from neighbors based on connection property. This allows both similar and dissimilar features for each node to be effectively preserved and propagated, and thus mitigates the impact of heterophily on graph learning process. As dual feature aggregations introduce extra model complexity, we also offer a simplified implementation of H^2GNN to reduce training time. Extensive experiments on seven benchmark datasets have demonstrated that H^2GNN can significantly improve node classification performance in graphs with different homophily ratios, which outperforms state-of-the-art GNN models. 

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5. Feature learning in deep classifiers through Intermediate Neural Collapse

   Rangamani, Akshay; Lindegaard, Marius; Galanti, Tomer; Poggio, Tomaso (February 2023, Center for Brains, Minds and Machines (CBMM))

   In this paper, we conduct an empirical study of the feature learning process in deep classifiers. Recent research has identified a training phenomenon called Neural Collapse (NC), in which the top-layer feature embeddings of samples from the same class tend to concentrate around their means, and the top layer’s weights align with those features. Our study aims to investigate if these properties extend to intermediate layers. We empirically study the evolution of the covariance and mean of representations across different layers and show that as we move deeper into a trained neural network, the within-class covariance decreases relative to the between-class covariance. Additionally, we find that in the top layers, where the between-class covariance is dominant, the subspace spanned by the class means aligns with the subspace spanned by the most significant singular vector components of the weight matrix in the corresponding layer. Finally, we discuss the relationship between NC and Associative Memories (Willshaw et al., 1969). 

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