# pathGCN: Learning General Graph Spatial Operators from Paths

arXiv: https://arxiv.org/abs/2207.07408 · HTML: https://mlsanity.com/paper/2207.07408/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 60 references that are in the map.
- First posted on arXiv 15 Jul 2022.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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 Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)

## Built on by (most cited first, 15 of 15)

- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [Improving Graph Neural Networks with Learnable Propagation Operators](https://mlsanity.com/paper/2210.17224/) (2022)
- [Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes](https://mlsanity.com/paper/2308.06838/) (2023)
- [Are GATs Out of Balance?](https://mlsanity.com/paper/2310.07235/) (2023)
- [Towards Better Generalization with Flexible Representation of Multi-Module Graph Neural Networks](https://mlsanity.com/paper/2209.06589/) (2022)
- [Improving Subgraph-GNNs via Edge-Level Ego-Network Encodings](https://mlsanity.com/paper/2312.05905/) (2023)
- [Global-Local Graph Neural Networks for Node-Classification](https://mlsanity.com/paper/2406.10863/) (2024)
- [Scalable Graph Compressed Convolutions](https://mlsanity.com/paper/2407.18480/) (2024)
- [Every Node Counts: Improving the Training of Graph Neural Networks on Node Classification](https://mlsanity.com/paper/2211.16631/) (2022)
- [Multi-Temporal Relationship Inference in Urban Areas](https://mlsanity.com/paper/2306.08921/) (2023)
- [Learning From Simplicial Data Based on Random Walks and 1D Convolutions](https://mlsanity.com/paper/2404.03434/) (2024)
- [Information propagation dynamics in Deep Graph Networks](https://mlsanity.com/paper/2410.10464/) (2024)
- [LGRPool: Hierarchical Graph Pooling Via Local-Global Regularisation](https://mlsanity.com/paper/2504.08530/) (2025)
- [Learning from Historical Activations in Graph Neural Networks](https://mlsanity.com/paper/2601.01123/) (2026)
- [Diffusion Attention Expert Model for Predicting and Semi-automatic Localizing STAS in Lung Cancer Histopathological Images](https://mlsanity.com/paper/2605.16444/) (2026)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.