# ScaleNet: Scale Invariance Learning in Directed Graphs

arXiv: https://arxiv.org/abs/2411.08758 · HTML: https://mlsanity.com/paper/2411.08758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 38 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [Generalization Error of Invariant Classifiers](https://mlsanity.com/paper/1610.04574/) (2016)
- [Does Invariant Graph Learning via Environment Augmentation Learn Invariance?](https://mlsanity.com/paper/2310.19035/) (2023)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Unleashing the Power of Graph Data Augmentation on Covariate Distribution Shift](https://mlsanity.com/paper/2211.02843/) (2022)
- [MILE: A Multi-Level Framework for Scalable Graph Embedding](https://mlsanity.com/paper/1802.09612/) (2018)
- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [Adaptive Diffusions for Scalable Learning over Graphs](https://mlsanity.com/paper/1804.02081/) (2018)
- [Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs](https://mlsanity.com/paper/2312.17361/) (2023)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have advanced relational data analysis but lack invariance learning techniques common in image classification. In node classification with GNNs, it is actually the ego-graph of the center node that is classified. This research extends the scale invariance concept to node classification by drawing an analogy to image processing: just as scale invariance being used in image classification to capture multi-scale features, we propose the concept of ``scaled ego-graphs''. Scaled ego-graphs generalize traditional ego-graphs by replacing undirected single-edges with ``scaled-edges'', which are ordered sequences of multiple directed edges. We empirically assess the performance of the proposed scale invariance in graphs on seven benchmark datasets, across both homophilic and heterophilic structures. Our scale-invariance-based graph learning outperforms inception models derived from random walks by being simpler, faster, and more accurate. The scale invariance explains inception models' success on homophilic graphs and limitations on heterophilic graphs. To ensure applicability of inception model to heterophilic graphs as well, we further present ScaleNet, an architecture that leverages multi-scaled features. ScaleNet achieves state-of-the-art results on five out of seven datasets (four homophilic and one heterophilic) and matches top performance on the remaining two, demonstrating its excellent applicability. This represents a significant advance in graph learning, offering a unified framework that enhances node classification across various graph types. Our code is available at https://github.com/Qin87/ScaleNet/tree/July25.