Teaching MLP More Graph Information: A Three-stage Multitask Knowledge Distillation Framework

GNN-to-MLP distillation aims to retain the predictive accuracy of a message-passing teacher while deploying a graph-free MLP at inference. Existing methods mainly transfer node-wise predictions or use confidence-based reweighting, but they do not specify where the student should preserve the teacher's graph-induced geometry. We show that this omission leads to two spectral failure modes in the student's representation space. On sparse graphs, the student suffers from spectral underfit, missing high-energy teacher directions concentrated near boundary regions. On dense graphs, it suffers from spectral overfit, retaining spurious directions that the teacher has collapsed through aggregation. Motivated by an energy-weighted teacher-student alignment objective, we propose Graph Geometry-aware MLP (G^2MLP), a training-time distillation framework guided by Ollivier-Ricci curvature. Curvature identifies where the two spectral errors concentrate and is used to allocate supervision between prediction-level and representation-level alignment. The deployed model remains a standard MLP and requires no graph access at inference. Across node-classification benchmarks, G^2MLP consistently improves over graph-free distillation baselines, reduces the teacher-student rank gap in both regimes, and transfers without architectural changes to Graph Transformer teachers and link prediction.

Temporal knowledge graphs (TKGs) support reasoning over time-evolving facts, yet state-of-the-art models are often computationally heavy and costly to deploy. Existing compression and distillation techniques are largely designed for static graphs; directly applying them to temporal settings may overlook time-dependent interactions and lead to performance degradation. We propose an LLM-assisted distillation framework specifically designed for temporal knowledge graph reasoning. Beyond a conventional high-capacity temporal teacher, we incorporate a large language model as an auxiliary instructor to provide enriched supervision. The LLM supplies broad background knowledge and temporally informed signals, enabling a lightweight student to better model event dynamics without increasing inference-time complexity. Training is conducted by jointly optimizing supervised and distillation objectives, using a staged alignment strategy to progressively integrate guidance from both teachers. Extensive experiments on multiple public TKG benchmarks with diverse backbone architectures demonstrate that the proposed approach consistently improves link prediction performance over strong distillation baselines, while maintaining a compact and efficient student model. The results highlight the potential of large language models as effective teachers for transferring temporal reasoning capability to resource-efficient TKG systems.

Hypergraph knowledge distillation aims to retain the predictive performance of a hypergraph neural network (HNN) teacher while reducing inference costs through a lightweight student model. In this work, we observe that HNNs exhibit substantially lower prediction performance on heterophilic nodes connected through semantically diverse hyperedges, indicating that the reliability of teacher knowledge varies across nodes. Motivated by this observation, we propose HADES, a heterophily-aware adaptive distillation method for hypergraph neural networks. HADES quantifies node heterophily and leverages it as an estimate of teacher reliability to modulate the transfer of teacher knowledge during distillation. Experimental results on real-world hypergraphs demonstrate that HADES consistently improves student performance across different HNN teachers and distillation objectives. In many cases, the resulting student models surpass the predictive performance of their teachers while achieving up to 12.3 times faster inference.