# TINED: GNNs-to-MLPs by Teacher Injection and Dirichlet Energy Distillation

arXiv: https://arxiv.org/abs/2412.11180 · HTML: https://mlsanity.com/paper/2412.11180/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 51 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [DistilHuBERT: Speech Representation Learning by Layer-wise Distillation of Hidden-unit BERT](https://mlsanity.com/paper/2110.01900/) (2021)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Distilling Knowledge from Graph Convolutional Networks](https://mlsanity.com/paper/2003.10477/) (2020)
- [Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks](https://mlsanity.com/paper/2203.00199/) (2022)
- [Less is More: Task-aware Layer-wise Distillation for Language Model Compression](https://mlsanity.com/paper/2210.01351/) (2022)
- [Graph-MLP: Node Classification without Message Passing in Graph](https://mlsanity.com/paper/2106.04051/) (2021)
- [Extract the Knowledge of Graph Neural Networks and Go Beyond it: An Effective Knowledge Distillation Framework](https://mlsanity.com/paper/2103.02885/) (2021)
- [Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoods](https://mlsanity.com/paper/2111.04840/) (2021)
- [Graph-Free Knowledge Distillation for Graph Neural Networks](https://mlsanity.com/paper/2105.07519/) (2021)
- [Knowledge Distillation on Graphs: A Survey](https://mlsanity.com/paper/2302.00219/) (2023)
- [VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs](https://mlsanity.com/paper/2308.02117/) (2023)
- [A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting](https://mlsanity.com/paper/2211.02989/) (2022)
- [Graph-based Knowledge Distillation by Multi-head Attention Network](https://mlsanity.com/paper/1907.02226/) (2019)

## Built on by (most cited first, 5 of 5)

- [Retrieval-Augmented Purifier for Robust LLM-Empowered Recommendation](https://mlsanity.com/paper/2504.02458/) (2025)
- [GLProtein: Global-and-Local Structure Aware Protein Representation Learning](https://mlsanity.com/paper/2506.06294/) (2025)
- [SNAP-KG: Streaming Node Assignment via Projection for Knowledge Graph Entity Integration](https://mlsanity.com/paper/2608.25149/) (2026)
- [Does Graph Compression Preserve Signal Propagation?](https://mlsanity.com/paper/2607.23338/) (2026)
- [More Domains, No Gains? FLO: Fast-Slow Reciprocal Learning for Multi-Domain Graph Pre-training](https://mlsanity.com/paper/2610.14748/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are pivotal in graph-based learning, particularly excelling in node classification. However, their scalability is hindered by the need for multi-hop data during inference, limiting their application in latency-sensitive scenarios. Recent efforts to distill GNNs into multi-layer perceptrons (MLPs) for faster inference often underutilize the layer-level insights of GNNs. In this paper, we present TINED, a novel approach that distills GNNs to MLPs on a layer-by-layer basis using Teacher Injection and Dirichlet Energy Distillation techniques. We focus on two key operations in GNN layers: feature transformation (FT) and graph propagation (GP). We recognize that FT is computationally equivalent to a fully-connected (FC) layer in MLPs. Thus, we propose directly transferring teacher parameters from an FT in a GNN to an FC layer in the student MLP, enhanced by fine-tuning. In TINED, the FC layers in an MLP replicate the sequence of FTs and GPs in the GNN. We also establish a theoretical bound for GP approximation. Furthermore, we note that FT and GP operations in GNN layers often exhibit opposing smoothing effects: GP is aggressive, while FT is conservative. Using Dirichlet energy, we develop a DE ratio to measure these effects and propose Dirichlet Energy Distillation to convey these characteristics from GNN layers to MLP layers. Extensive experiments show that TINED outperforms GNNs and leading distillation methods across various settings and seven datasets. Source code are available at https://github.com/scottjiao/TINED_ICML25/.