# Do We Need Anisotropic Graph Neural Networks?

arXiv: https://arxiv.org/abs/2104.01481 · HTML: https://mlsanity.com/paper/2104.01481/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 59 references that are in the map.
- First posted on arXiv 3 Apr 2021.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [GraphCodeBERT: Pre-training Code Representations with Data Flow](https://mlsanity.com/paper/2009.08366/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Learning to Represent Programs with Graphs](https://mlsanity.com/paper/1711.00740/) (2017)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [Pay Less Attention with Lightweight and Dynamic Convolutions](https://mlsanity.com/paper/1901.10430/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Directional Graph Networks](https://mlsanity.com/paper/2010.02863/) (2020)
- [HyGCN: A GCN Accelerator with Hybrid Architecture](https://mlsanity.com/paper/2001.02514/) (2020)

## Built on by (most cited first, 18 of 18)

- [Expander Graph Propagation](https://mlsanity.com/paper/2210.02997/) (2022)
- [The expressive power of pooling in Graph Neural Networks](https://mlsanity.com/paper/2304.01575/) (2023)
- [MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initialization](https://mlsanity.com/paper/2210.00102/) (2022)
- [How Expressive are Transformers in Spectral Domain for Graphs?](https://mlsanity.com/paper/2201.09332/) (2022)
- [FlowGNN: A Dataflow Architecture for Real-Time Workload-Agnostic Graph Neural Network Inference](https://mlsanity.com/paper/2204.13103/) (2022)
- [Geometric Deep Learning for Molecular Crystal Structure Prediction](https://mlsanity.com/paper/2303.10140/) (2023)
- [Contextualized Messages Boost Graph Representations](https://mlsanity.com/paper/2403.12529/) (2024)
- [Embedding Graphs on Grassmann Manifold](https://mlsanity.com/paper/2205.15068/) (2022)
- [GNNBuilder: An Automated Framework for Generic Graph Neural Network Accelerator Generation, Simulation, and Optimization](https://mlsanity.com/paper/2303.16459/) (2023)
- [Parcel3D: Shape Reconstruction from Single RGB Images for Applications in Transportation Logistics](https://mlsanity.com/paper/2304.08994/) (2023)
- [Introducing Diminutive Causal Structure into Graph Representation Learning](https://mlsanity.com/paper/2406.08709/) (2024)
- [Introduction to Graph Neural Networks for Machine Learning Engineers](https://mlsanity.com/paper/2412.19419/) (2024)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing](https://mlsanity.com/paper/2511.11046/) (2025)
- [Data-Driven Graph Filters via Adaptive Spectral Shaping](https://mlsanity.com/paper/2602.03698/) (2026)
- [EdgeMask-DG*: Learning Domain-Invariant Graph Structures via Adversarial Edge Masking](https://mlsanity.com/paper/2602.05571/) (2026)
- [Electron-Informed Coarse-Graining Molecular Representation Learning for Real-World Molecular Physics](https://mlsanity.com/paper/2602.07087/) (2026)
- [A Comparative Study of Graph Neural Network Layer Selection for Interaction Modelling in Driving Trajectory Prediction](https://mlsanity.com/paper/2606.14956/) (2026)

## Abstract (arXiv)

Common wisdom in the graph neural network (GNN) community dictates that anisotropic models -- in which messages sent between nodes are a function of both the source and target node -- are required to achieve state-of-the-art performance. Benchmarks to date have demonstrated that these models perform better than comparable isotropic models -- where messages are a function of the source node only. In this work we provide empirical evidence challenging this narrative: we propose an isotropic GNN, which we call Efficient Graph Convolution (EGC), that consistently outperforms comparable anisotropic models, including the popular GAT or PNA architectures by using spatially-varying adaptive filters. In addition to raising important questions for the GNN community, our work has significant real-world implications for efficiency. EGC achieves higher model accuracy, with lower memory consumption and latency, along with characteristics suited to accelerator implementation, while being a drop-in replacement for existing architectures. As an isotropic model, it requires memory proportional to the number of vertices in the graph (O(V)); in contrast, anisotropic models require memory proportional to the number of edges (O(E)). We demonstrate that EGC outperforms existing approaches across 6 large and diverse benchmark datasets, and conclude by discussing questions that our work raise for the community going forward. Code and pretrained models for our experiments are provided at https://github.com/shyam196/egc.