# GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction

arXiv: https://arxiv.org/abs/2410.03396 · HTML: https://mlsanity.com/paper/2410.03396/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 30 of 37)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Generating Adversarial Examples with Adversarial Networks](https://mlsanity.com/paper/1801.02610/) (2018)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [AEGNN: Asynchronous Event-based Graph Neural Networks](https://mlsanity.com/paper/2203.17149/) (2022)
- [InfoGCL: Information-Aware Graph Contrastive Learning](https://mlsanity.com/paper/2110.15438/) (2021)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)

## Abstract (arXiv)

Graph-structured data is integral to many applications, prompting the development of various graph representation methods. Graph autoencoders (GAEs), in particular, reconstruct graph structures from node embeddings. Current GAE models primarily utilize self-correlation to represent graph structures and focus on node-level tasks, often overlooking multi-graph scenarios. Our theoretical analysis indicates that self-correlation generally falls short in accurately representing specific graph features such as islands, symmetrical structures, and directional edges, particularly in smaller or multiple graph contexts. To address these limitations, we introduce a cross-correlation mechanism that significantly enhances the GAE representational capabilities. Additionally, we propose GraphCroc, a new GAE that supports flexible encoder architectures tailored for various downstream tasks and ensures robust structural reconstruction, through a mirrored encoding-decoding process. This model also tackles the challenge of representation bias during optimization by implementing a loss-balancing strategy. Both theoretical analysis and numerical evaluations demonstrate that our methodology significantly outperforms existing self-correlation-based GAEs in graph structure reconstruction.