Dai Shi

Zhiqi Shao, Dai Shi, Andi Han et al. · tsinghua

Graph Neural Networks (GNNs) have emerged as one of the leading approaches for machine learning on graph-structured data. Despite their great success, critical computational challenges such as over-smoothing, over-squashing, and limited expressive power continue to impact the performance of GNNs. In this study, inspired from the time-reversal principle commonly utilized in classical and quantum physics, we reverse the time direction of the graph heat equation. The resulted reversing process yields a class of high pass filtering functions that enhance the sharpness of graph node features. Leveraging this concept, we introduce the Multi-Scaled Heat Kernel based GNN (MHKG) by amalgamating diverse filtering functions' effects on node features. To explore more flexible filtering conditions, we further generalize MHKG into a model termed G-MHKG and thoroughly show the roles of each element in controlling over-smoothing, over-squashing and expressive power. Notably, we illustrate that all aforementioned issues can be characterized and analyzed via the properties of the filtering functions, and uncover a trade-off between over-smoothing and over-squashing: enhancing node feature sharpness will make model suffer more from over-squashing, and vice versa. Furthermore, we manipulate the time again to show how G-MHKG can handle both two issues under mild conditions. Our conclusive experiments highlight the effectiveness of proposed models. It surpasses several GNN baseline models in performance across graph datasets characterized by both homophily and heterophily.

Dai Shi, Andi Han, Lequan Lin et al.

Graph-based message-passing neural networks (MPNNs) have achieved remarkable success in both node and graph-level learning tasks. However, several identified problems, including over-smoothing (OSM), limited expressive power, and over-squashing (OSQ), still limit the performance of MPNNs. In particular, OSQ serves as the latest identified problem, where MPNNs gradually lose their learning accuracy when long-range dependencies between graph nodes are required. In this work, we provide an exposition on the OSQ problem by summarizing different formulations of OSQ from current literature, as well as the three different categories of approaches for addressing the OSQ problem. In addition, we also discuss the alignment between OSQ and expressive power and the trade-off between OSQ and OSM. Furthermore, we summarize the empirical methods leveraged from existing works to verify the efficiency of OSQ mitigation approaches, with illustrations of their computational complexities. Lastly, we list some open questions that are of interest for further exploration of the OSQ problem along with potential directions from the best of our knowledge.

Andi Han, Dai Shi, Lequan Lin et al.

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is being iteratively aggregated to central nodes from their neighbourhood. Such a scheme has been found to be intrinsically linked to a physical process known as heat diffusion, where the propagation of GNNs naturally corresponds to the evolution of heat density. Analogizing the process of message passing to the heat dynamics allows to fundamentally understand the power and pitfalls of GNNs and consequently informs better model design. Recently, there emerges a plethora of works that proposes GNNs inspired from the continuous dynamics formulation, in an attempt to mitigate the known limitations of GNNs, such as oversmoothing and oversquashing. In this survey, we provide the first systematic and comprehensive review of studies that leverage the continuous perspective of GNNs. To this end, we introduce foundational ingredients for adapting continuous dynamics to GNNs, along with a general framework for the design of graph neural dynamics. We then review and categorize existing works based on their driven mechanisms and underlying dynamics. We also summarize how the limitations of classic GNNs can be addressed under the continuous framework. We conclude by identifying multiple open research directions.

Dai Shi, Zhiqi Shao, Yi Guo et al.

Knowledge distillation (KD) has shown great potential for transferring knowledge from a complex teacher model to a simple student model in which the heavy learning task can be accomplished efficiently and without losing too much prediction accuracy. Recently, many attempts have been made by applying the KD mechanism to the graph representation learning models such as graph neural networks (GNNs) to accelerate the model's inference speed via student models. However, many existing KD-based GNNs utilize MLP as a universal approximator in the student model to imitate the teacher model's process without considering the graph knowledge from the teacher model. In this work, we provide a KD-based framework on multi-scaled GNNs, known as graph framelet, and prove that by adequately utilizing the graph knowledge in a multi-scaled manner provided by graph framelet decomposition, the student model is capable of adapting both homophilic and heterophilic graphs and has the potential of alleviating the over-squashing issue with a simple yet effectively graph surgery. Furthermore, we show how the graph knowledge supplied by the teacher is learned and digested by the student model via both algebra and geometry. Comprehensive experiments show that our proposed model can generate learning accuracy identical to or even surpass the teacher model while maintaining the high speed of inference.

Jiayu Zhai, Lequan Lin, Dai Shi et al.

Numerous recent research on graph neural networks (GNNs) has focused on formulating GNN architectures as an optimization problem with the smoothness assumption. However, in node classification tasks, the smoothing effect induced by GNNs tends to assimilate representations and over-homogenize labels of connected nodes, leading to adverse effects such as over-smoothing and misclassification. In this paper, we propose a novel bilevel optimization framework for GNNs inspired by the notion of Bregman distance. We demonstrate that the GNN layer proposed accordingly can effectively mitigate the over-smoothing issue by introducing a mechanism reminiscent of the "skip connection". We validate our theoretical results through comprehensive empirical studies in which Bregman-enhanced GNNs outperform their original counterparts in both homophilic and heterophilic graphs. Furthermore, our experiments also show that Bregman GNNs can produce more robust learning accuracy even when the number of layers is high, suggesting the effectiveness of the proposed method in alleviating the over-smoothing issue.

Dai Shi, Luke Thompson, Linhan Luo et al.

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50\% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.