# Propagate & Distill: Towards Effective Graph Learners Using Propagation-Embracing MLPs

arXiv: https://arxiv.org/abs/2311.17781 · HTML: https://mlsanity.com/paper/2311.17781/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Graph neural network distillation, one of 12 directions in Knowledge distillation.
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 29 Nov 2023.

## Placed in

- Knowledge distillation / [Graph neural network distillation](https://mlsanity.com/distill/graph-neural-network-distillation/)

## Builds on (most cited first, 26 of 26)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [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)
- [Extracting Low-/High- Frequency Knowledge from Graph Neural Networks and Injecting it into MLPs: An Effective GNN-to-MLP Distillation Framework](https://mlsanity.com/paper/2305.10758/) (2023)
- [SA-MLP: Distilling Graph Knowledge from GNNs into Structure-Aware MLP](https://mlsanity.com/paper/2210.09609/) (2022)
- [Node Representation Learning in Graph via Node-to-Neighbourhood Mutual Information Maximization](https://mlsanity.com/paper/2203.12265/) (2022)
- [Edge-free but Structure-aware: Prototype-Guided Knowledge Distillation from GNNs to MLPs](https://mlsanity.com/paper/2303.13763/) (2023)

## Built on by (most cited first, 1 of 1)

- [Acceleration Algorithms in GNNs: A Survey](https://mlsanity.com/paper/2405.04114/) (2024)

## Abstract (arXiv)

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.