Graph neural networks (GNNs) can efficiently process text-attributed graphs (TAGs) due to their message-passing mechanisms, but their training heavily relies on the human-annotated labels. Moreover, the complex and diverse local topologies of nodes of real-world TAGs make it challenging for a single mechanism to handle. Large language models (LLMs) perform well in zero-/few-shot learning on TAGs but suffer from a scalability challenge. Therefore, we propose a preference-driven knowledge distillation (PKD) framework to synergize the complementary strengths of LLMs and various GNNs for few-shot node classification. Specifically, we develop a GNN-preference-driven node selector that effectively promotes prediction distillation from LLMs to teacher GNNs. To further tackle nodes' intricate local topologies, we develop a node-preference-driven GNN selector that identifies the most suitable teacher GNN for each node, thereby facilitating tailored knowledge distillation from teacher GNNs to the student GNN. Extensive experiments validate the efficacy of our proposed framework in few-shot node classification on real-world TAGs. Our code is be available.

Graph Neural Networks (GNNs) are fundamental to graph-based learning and excel in node classification tasks. However, GNNs suffer from scalability issues due to the need for multi-hop data during inference, limiting their use in latency-sensitive applications. Recent studies attempt to distill GNNs into multi-layer perceptrons (MLPs) for faster inference. They typically treat GNN and MLP models as single units for distillation, insufficiently utilizing the fine-grained knowledge within GNN layers. In this paper, we propose TINED, a novel method that distills GNNs to MLPs layer-wise through Teacher Injection with fine-tuning and Dirichlet Energy Distillation techniques. We analyze key operations in GNN layers, feature transformation (FT) and graph propagation (GP), and identify that an FT performs the same computation as a fully-connected (FC) layer in MLPs. Thus, we propose directly injecting valuable teacher parameters of an FT in a GNN into an FC layer of the student MLP, assisted by fine-tuning. In TINED, FC layers in an MLP mirror the order of the corresponding FTs and GPs in GNN. We provide a theoretical bound on the approximation of GPs. Moreover, we observe that in a GNN layer, FT and GP operations often have opposing smoothing effects: GP is aggressive, while FT is conservative, in smoothing. Using Dirichlet energy, we design a DE ratio to quantify these smoothing effects and propose Dirichlet Energy Distillation to distill these characteristics from GNN layers to MLP layers. Extensive experiments demonstrate that TINED achieves superior performance over GNNs and state-of-the-art distillation methods under various settings across seven datasets. The code is in supplementary material.

To bridge the gaps between powerful Graph Neural Networks (GNNs) and lightweight Multi-Layer Perceptron (MLPs), GNN-to-MLP Knowledge Distillation (KD) proposes to distill knowledge from a well-trained teacher GNN into a student MLP. In this paper, we revisit the knowledge samples (nodes) in teacher GNNs from the perspective of hardness, and identify that hard sample distillation may be a major performance bottleneck of existing graph KD algorithms. The GNN-to-MLP KD involves two different types of hardness, one student-free knowledge hardness describing the inherent complexity of GNN knowledge, and the other student-dependent distillation hardness describing the difficulty of teacher-to-student distillation. However, most of the existing work focuses on only one of these aspects or regards them as one thing. This paper proposes a simple yet effective Hardness-aware GNN-to-MLP Distillation (HGMD) framework, which decouples the two hardnesses and estimates them using a non-parametric approach. Finally, two hardness-aware distillation schemes (i.e., HGMD-weight and HGMD-mixup) are further proposed to distill hardness-aware knowledge from teacher GNNs into the corresponding nodes of student MLPs. As non-parametric distillation, HGMD does not involve any additional learnable parameters beyond the student MLPs, but it still outperforms most of the state-of-the-art competitors. HGMD-mixup improves over the vanilla MLPs by 12.95% and outperforms its teacher GNNs by 2.48% averaged over seven real-world datasets.

Few-shot node classification poses a significant challenge for Graph Neural Networks (GNNs) due to insufficient supervision and potential distribution shifts between labeled and unlabeled nodes. Self-training has emerged as a widely popular framework to leverage the abundance of unlabeled data, which expands the training set by assigning pseudo-labels to selected unlabeled nodes. Efforts have been made to develop various selection strategies based on confidence, information gain, etc. However, none of these methods takes into account the distribution shift between the training and testing node sets. The pseudo-labeling step may amplify this shift and even introduce new ones, hindering the effectiveness of self-training. Therefore, in this work, we explore the potential of explicitly bridging the distribution shift between the expanded training set and test set during self-training. To this end, we propose a novel Distribution-Consistent Graph Self-Training (DC-GST) framework to identify pseudo-labeled nodes that are both informative and capable of redeeming the distribution discrepancy and formulate it as a differentiable optimization task. A distribution-shift-aware edge predictor is further adopted to augment the graph and increase the model's generalizability in assigning pseudo labels. We evaluate our proposed method on four publicly available benchmark datasets and extensive experiments demonstrate that our framework consistently outperforms state-of-the-art baselines.

The rapid development of graph neural networks (GNNs) encourages the rising of link prediction, achieving promising performance with various applications. Unfortunately, through a comprehensive analysis, we surprisingly find that current link predictors with dynamic negative samplers (DNSs) suffer from the migration phenomenon between "easy" and "hard" samples, which goes against the preference of DNS of choosing "hard" negatives, thus severely hindering capability. Towards this end, we propose the MeBNS framework, serving as a general plugin that can potentially improve current negative sampling based link predictors. In particular, we elaborately devise a Meta-learning Supported Teacher-student GNN (MST-GNN) that is not only built upon teacher-student architecture for alleviating the migration between "easy" and "hard" samples but also equipped with a meta learning based sample re-weighting module for helping the student GNN distinguish "hard" samples in a fine-grained manner. To effectively guide the learning of MST-GNN, we prepare a Structure enhanced Training Data Generator (STD-Generator) and an Uncertainty based Meta Data Collector (UMD-Collector) for supporting the teacher and student GNN, respectively. Extensive experiments show that the MeBNS achieves remarkable performance across six link prediction benchmark datasets.

Recent studies attempted to utilize multilayer perceptrons (MLPs) to solve semisupervised node classification on graphs, by training a student MLP by knowledge distillation from a teacher graph neural network (GNN). While previous studies have focused mostly on training the student MLP by matching the output probability distributions between the teacher and student models during distillation, it has not been systematically studied how to inject the structural information in an explicit and interpretable manner. Inspired by GNNs that separate feature transformation $T$ and propagation $\Pi$, we re-frame the distillation process as making the student MLP learn both $T$ and $\Pi$. Although this can be achieved by applying the inverse propagation $\Pi^{-1}$ before distillation from the teacher, it still comes with a high computational cost from large matrix multiplications during training. To solve this problem, we propose Propagate & Distill (P&D), which propagates the output of the teacher before distillation, which can be interpreted as an approximate process of the inverse propagation. We demonstrate that P&D can readily improve the performance of the student MLP.

Recent studies attempted to utilize multilayer perceptrons (MLPs) to solve semi-supervised node classification on graphs, by training a student MLP by knowledge distillation (KD) from a teacher graph neural network (GNN). While previous studies have focused mostly on training the student MLP by matching the output probability distributions between the teacher and student models during KD, it has not been systematically studied how to inject the structural information in an explicit and interpretable manner. Inspired by GNNs that separate feature transformation $T$ and propagation $\Pi$, we re-frame the KD process as enabling the student MLP to explicitly learn both $T$ and $\Pi$. Although this can be achieved by applying the inverse propagation $\Pi^{-1}$ before distillation from the teacher GNN, it still comes with a high computational cost from large matrix multiplications during training. To solve this problem, we propose Propagate & Distill (P&D), which propagates the output of the teacher GNN before KD and can be interpreted as an approximate process of the inverse propagation $\Pi^{-1}$. Through comprehensive evaluations using real-world benchmark datasets, we demonstrate the effectiveness of P&D by showing further performance boost of the student MLP.

To bridge the gaps between topology-aware Graph Neural Networks (GNNs) and inference-efficient Multi-Layer Perceptron (MLPs), GLNN proposes to distill knowledge from a well-trained teacher GNN into a student MLP. Despite their great progress, comparatively little work has been done to explore the reliability of different knowledge points (nodes) in GNNs, especially their roles played during distillation. In this paper, we first quantify the knowledge reliability in GNN by measuring the invariance of their information entropy to noise perturbations, from which we observe that different knowledge points (1) show different distillation speeds (temporally); (2) are differentially distributed in the graph (spatially). To achieve reliable distillation, we propose an effective approach, namely Knowledge-inspired Reliable Distillation (KRD), that models the probability of each node being an informative and reliable knowledge point, based on which we sample a set of additional reliable knowledge points as supervision for training student MLPs. Extensive experiments show that KRD improves over the vanilla MLPs by 12.62% and outperforms its corresponding teacher GNNs by 2.16% averaged over 7 datasets and 3 GNN architectures.

Recent years have witnessed the great success of Graph Neural Networks (GNNs) in handling graph-related tasks. However, MLPs remain the primary workhorse for practical industrial applications due to their desirable inference efficiency and scalability. To reduce their gaps, one can directly distill knowledge from a well-designed teacher GNN to a student MLP, which is termed as GNN-to-MLP distillation. However, the process of distillation usually entails a loss of information, and ``which knowledge patterns of GNNs are more likely to be left and distilled into MLPs?" becomes an important question. In this paper, we first factorize the knowledge learned by GNNs into low- and high-frequency components in the spectral domain and then derive their correspondence in the spatial domain. Furthermore, we identified a potential information drowning problem for existing GNN-to-MLP distillation, i.e., the high-frequency knowledge of the pre-trained GNNs may be overwhelmed by the low-frequency knowledge during distillation; we have described in detail what it represents, how it arises, what impact it has, and how to deal with it. In this paper, we propose an efficient Full-Frequency GNN-to-MLP (FF-G2M) distillation framework, which extracts both low-frequency and high-frequency knowledge from GNNs and injects it into MLPs. Extensive experiments show that FF-G2M improves over the vanilla MLPs by 12.6% and outperforms its corresponding teacher GNNs by 2.6% averaged over six graph datasets and three common GNN architectures.