# Simplifying Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1902.07153 · HTML: https://mlsanity.com/paper/1902.07153/

## Key facts

- Cited by 1,477 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2019.

## Built on by (most cited first, 30 of 1477)

- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [Language is All a Graph Needs](https://mlsanity.com/paper/2308.07134/) (2023)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [MedCPT: Contrastive Pre-trained Transformers with Large-scale PubMed Search Logs for Zero-shot Biomedical Information Retrieval](https://mlsanity.com/paper/2307.00589/) (2023)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [The Values Encoded in Machine Learning Research](https://mlsanity.com/paper/2106.15590/) (2021)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers](https://mlsanity.com/paper/2406.10163/) (2024)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.