# Renormalized Graph Representations for Node Classification

arXiv: https://arxiv.org/abs/2306.00707 · HTML: https://mlsanity.com/paper/2306.00707/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification](https://mlsanity.com/paper/1802.08888/) (2018)
- [Clique pooling for graph classification](https://mlsanity.com/paper/1904.00374/) (2019)
- [A Multiscale Graph Convolutional Network Using Hierarchical Clustering](https://mlsanity.com/paper/2006.12542/) (2020)
- [Learning low-rank latent mesoscale structures in networks](https://mlsanity.com/paper/2102.06984/) (2021)
- [Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems](https://mlsanity.com/paper/1408.2925/) (2014)
- [Laplacian paths in complex networks: information core emerges from entropic transitions](https://mlsanity.com/paper/2202.06669/) (2022)

## Built on by (most cited first, 1 of 1)

- [Symmetry and Generalisation in Neural Approximations of Renormalisation Transformations](https://mlsanity.com/paper/2510.16591/) (2025)

## Abstract (arXiv)

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node classification tasks. At the theory's core is grouping nodes connected by significant information flow at a given time scale. Representations of the graph at different scales encode interaction information at different ranges. We specifically experiment using representations at the characteristic scale of the graph's mesoscopic structures. We provide the models with the original graph and the graph represented at the characteristic resolution scale and compare them to models that can only access the original graph. Our results showed that models with access to both the original graph and the characteristic scale graph can achieve statistically significant improvements in test accuracy.