# Are Powerful Graph Neural Nets Necessary? A Dissection on Graph Classification

arXiv: https://arxiv.org/abs/1905.04579 · HTML: https://mlsanity.com/paper/1905.04579/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2019.

## Built on by (most cited first, 30 of 39)

- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [SimGRACE: A Simple Framework for Graph Contrastive Learning without Data Augmentation](https://mlsanity.com/paper/2202.03104/) (2022)
- [AutoGCL: Automated Graph Contrastive Learning via Learnable View Generators](https://mlsanity.com/paper/2109.10259/) (2021)
- [Graph Neural Networks with Local Graph Parameters](https://mlsanity.com/paper/2106.06707/) (2021)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Graph Neural Networks are Inherently Good Generalizers: Insights by Bridging GNNs and MLPs](https://mlsanity.com/paper/2212.09034/) (2022)
- [Pooling Architecture Search for Graph Classification](https://mlsanity.com/paper/2108.10587/) (2021)
- [Bringing Your Own View: Graph Contrastive Learning without Prefabricated Data Augmentations](https://mlsanity.com/paper/2201.01702/) (2022)
- [Label-invariant Augmentation for Semi-Supervised Graph Classification](https://mlsanity.com/paper/2205.09802/) (2022)
- [Curvature Filtrations for Graph Generative Model Evaluation](https://mlsanity.com/paper/2301.12906/) (2023)
- [No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasets](https://mlsanity.com/paper/2502.02379/) (2025)
- [Graph Contrastive Learning with Personalized Augmentation](https://mlsanity.com/paper/2209.06560/) (2022)
- [Topology-aware Embedding Memory for Continual Learning on Expanding Networks](https://mlsanity.com/paper/2401.13200/) (2024)
- [Model-Aware Contrastive Learning: Towards Escaping the Dilemmas](https://mlsanity.com/paper/2207.07874/) (2022)
- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [DT+GNN: A Fully Explainable Graph Neural Network using Decision Trees](https://mlsanity.com/paper/2205.13234/) (2022)
- [Evolving to the Future: Unseen Event Adaptive Fake News Detection on Social Media](https://mlsanity.com/paper/2403.00037/) (2024)
- [Multi-Scale Subgraph Contrastive Learning](https://mlsanity.com/paper/2403.02719/) (2024)
- [MuGSI: Distilling GNNs with Multi-Granularity Structural Information for Graph Classification](https://mlsanity.com/paper/2406.19832/) (2024)
- [Graph Structure Refinement with Energy-based Contrastive Learning](https://mlsanity.com/paper/2412.17856/) (2024)
- [Graph Representation Learning with Massive Unlabeled Data for Rumor Detection](https://mlsanity.com/paper/2508.04252/) (2025)
- [Sparsifying the Update Step in Graph Neural Networks](https://mlsanity.com/paper/2109.00909/) (2021)
- [Label Propagation across Graphs: Node Classification using Graph Neural Tangent Kernels](https://mlsanity.com/paper/2110.03763/) (2021)
- [Demystifying Bitcoin Address Behavior via Graph Neural Networks](https://mlsanity.com/paper/2211.14582/) (2022)
- [Calibrate and Boost Logical Expressiveness of GNN Over Multi-Relational and Temporal Graphs](https://mlsanity.com/paper/2311.01647/) (2023)
- [Saliency-Aware Regularized Graph Neural Network](https://mlsanity.com/paper/2401.00755/) (2024)
- [Bridging the Gap Between Hyperdimensional Computing and Kernel Methods via the Nystr"om Method](https://mlsanity.com/paper/2608.06860/) (2026)
- [Multiscale Hodge Scattering Networks for Data Analysis](https://mlsanity.com/paper/2311.10270/) (2023)
- [Conditional Distribution Learning for Graph Classification](https://mlsanity.com/paper/2411.15206/) (2024)
- [Ego-based Entropy Measures for Structural Representations on Graphs](https://mlsanity.com/paper/2102.08735/) (2021)

## Abstract (arXiv)

Graph Neural Nets (GNNs) have received increasing attentions, partially due to their superior performance in many node and graph classification tasks. However, there is a lack of understanding on what they are learning and how sophisticated the learned graph functions are. In this work, we propose a dissection of GNNs on graph classification into two parts: 1) the graph filtering, where graph-based neighbor aggregations are performed, and 2) the set function, where a set of hidden node features are composed for prediction. To study the importance of both parts, we propose to linearize them separately. We first linearize the graph filtering function, resulting Graph Feature Network (GFN), which is a simple lightweight neural net defined on a textitset of graph augmented features. Further linearization of GFN's set function results in Graph Linear Network (GLN), which is a linear function. Empirically we perform evaluations on common graph classification benchmarks. To our surprise, we find that, despite the simplification, GFN could match or exceed the best accuracies produced by recently proposed GNNs (with a fraction of computation cost), while GLN underperforms significantly. Our results demonstrate the importance of non-linear set function, and suggest that linear graph filtering with non-linear set function is an efficient and powerful scheme for modeling existing graph classification benchmarks.