# Graph Size-imbalanced Learning with Energy-guided Structural Smoothing

arXiv: https://arxiv.org/abs/2412.17591 · HTML: https://mlsanity.com/paper/2412.17591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks](https://mlsanity.com/paper/2106.02817/) (2021)
- [SizeShiftReg: a Regularization Method for Improving Size-Generalization in Graph Neural Networks](https://mlsanity.com/paper/2207.07888/) (2022)
- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [LTE4G: Long-Tail Experts for Graph Neural Networks](https://mlsanity.com/paper/2208.10205/) (2022)
- [Robust Unsupervised Domain Adaptation for Neural Networks via Moment Alignment](https://mlsanity.com/paper/1711.06114/) (2017)
- [Imbalanced Graph Classification via Graph-of-Graph Neural Networks](https://mlsanity.com/paper/2112.00238/) (2021)
- [GraphSHA: Synthesizing Harder Samples for Class-Imbalanced Node Classification](https://mlsanity.com/paper/2306.09612/) (2023)
- [CenGCN: Centralized Convolutional Networks with Vertex Imbalance for Scale-Free Graphs](https://mlsanity.com/paper/2202.07826/) (2022)
- [Meta-Learning with Graph Neural Networks: Methods and Applications](https://mlsanity.com/paper/2103.00137/) (2021)

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

- [SamGoG: A Sampling-Based Graph-of-Graphs Framework for Imbalanced Graph Classification](https://mlsanity.com/paper/2507.13741/) (2025)

## Abstract (arXiv)

Graph is a prevalent data structure employed to represent the relationships between entities, frequently serving as a tool to depict and simulate numerous systems, such as molecules and social networks. However, real-world graphs usually suffer from the size-imbalanced problem in the multi-graph classification, i.e., a long-tailed distribution with respect to the number of nodes. Recent studies find that off-the-shelf Graph Neural Networks (GNNs) would compromise model performance under the long-tailed settings. We investigate this phenomenon and discover that the long-tailed graph distribution greatly exacerbates the discrepancies in structural features. To alleviate this problem, we propose a novel energy-based size-imbalanced learning framework named SIMBA, which smooths the features between head and tail graphs and re-weights them based on the energy propagation. Specifically, we construct a higher-level graph abstraction named textitGraphs-to-Graph according to the correlations between graphs to link independent graphs and smooths the structural discrepancies. We further devise an energy-based message-passing belief propagation method for re-weighting lower compatible graphs in the training process and further smooth local feature discrepancies. Extensive experimental results over five public size-imbalanced datasets demonstrate the superior effectiveness of the model for size-imbalanced graph classification tasks.