# Studying and Improving Graph Neural Network-based Motif Estimation

arXiv: https://arxiv.org/abs/2506.15709 · HTML: https://mlsanity.com/paper/2506.15709/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 69 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 30 of 33)

- [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)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Relational Pooling for Graph Representations](https://mlsanity.com/paper/1903.02541/) (2019)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries](https://mlsanity.com/paper/2206.11140/) (2022)
- [Breaking the Limits of Message Passing Graph Neural Networks](https://mlsanity.com/paper/2106.04319/) (2021)
- [A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests](https://mlsanity.com/paper/2302.07090/) (2023)
- [Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNs](https://mlsanity.com/paper/2210.13978/) (2022)
- [TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discovery](https://mlsanity.com/paper/2310.19324/) (2023)
- [Molecular Representation Learning via Heterogeneous Motif Graph Neural Networks](https://mlsanity.com/paper/2202.00529/) (2022)
- [Motif Prediction with Graph Neural Networks](https://mlsanity.com/paper/2106.00761/) (2021)
- [Improving Expressivity of GNNs with Subgraph-specific Factor Embedded Normalization](https://mlsanity.com/paper/2305.19903/) (2023)
- [Cumulative effects of triadic closure and homophily in social networks](https://mlsanity.com/paper/1809.06057/) (2018)
- [Higher-order Graph Convolutional Networks](https://mlsanity.com/paper/1809.07697/) (2018)
- [motif2vec: Motif Aware Node Representation Learning for Heterogeneous Networks](https://mlsanity.com/paper/1908.08227/) (2019)
- [On the Power of the Weisfeiler-Leman Test for Graph Motif Parameters](https://mlsanity.com/paper/2309.17053/) (2023)
- [DeSCo: Towards Generalizable and Scalable Deep Subgraph Counting](https://mlsanity.com/paper/2308.08198/) (2023)

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

- [GraDE: A Graph Diffusion Estimator for Frequent Subgraph Discovery in Neural Architectures](https://mlsanity.com/paper/2602.03257/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are a predominant method for graph representation learning. However, beyond subgraph frequency estimation, their application to network motif significance-profile (SP) prediction remains under-explored, with no established benchmarks in the literature. We propose to address this problem, framing SP estimation as a task independent of subgraph frequency estimation. Our approach shifts from frequency counting to direct SP estimation and modulates the problem as multitarget regression. The reformulation is optimised for interpretability, stability and scalability on large graphs. We validate our method using a large synthetic dataset and further test it on real-world graphs. Our experiments reveal that 1-WL limited models struggle to make precise estimations of SPs. However, they can generalise to approximate the graph generation processes of networks by comparing their predicted SP with the ones originating from synthetic generators. This first study on GNN-based motif estimation also hints at how using direct SP estimation can help go past the theoretical limitations that motif estimation faces when performed through subgraph counting.