# Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications

arXiv: https://arxiv.org/abs/2204.00323 · HTML: https://mlsanity.com/paper/2204.00323/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 113 references that are in the map.
- First posted on arXiv 1 Apr 2022.

## Builds on (most cited first, 30 of 53)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [Learning Human-Object Interactions by Graph Parsing Neural Networks](https://mlsanity.com/paper/1808.07962/) (2018)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Disease Prediction using Graph Convolutional Networks: Application to Autism Spectrum Disorder and Alzheimer's Disease](https://mlsanity.com/paper/1806.01738/) (2018)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [Learning Dynamic Graph Representation of Brain Connectome with Spatio-Temporal Attention](https://mlsanity.com/paper/2105.13495/) (2021)
- [Differentiable Graph Module (DGM) for Graph Convolutional Networks](https://mlsanity.com/paper/2002.04999/) (2020)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Few-Shot Graph Learning for Molecular Property Prediction](https://mlsanity.com/paper/2102.07916/) (2021)

## Built on by (most cited first, 4 of 4)

- [MM-GTUNets: Unified Multi-Modal Graph Deep Learning for Brain Disorders Prediction](https://mlsanity.com/paper/2406.14455/) (2024)
- [Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes](https://mlsanity.com/paper/2503.08760/) (2025)
- [Rethinking Graph Super-resolution: Dual Frameworks for Topological Fidelity](https://mlsanity.com/paper/2511.08853/) (2025)
- [Incremental Graph Construction Enables Robust Spectral Clustering of Texts](https://mlsanity.com/paper/2603.03056/) (2026)

## Abstract (arXiv)

Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works have shown that considering relationships between input data samples have a positive regularizing effect for the downstream task in healthcare applications. These relationships are naturally modeled by a (possibly unknown) graph structure between input samples. In this work, we propose Graph-in-Graph (GiG), a neural network architecture for protein classification and brain imaging applications that exploits the graph representation of the input data samples and their latent relation. We assume an initially unknown latent-graph structure between graph-valued input data and propose to learn end-to-end a parametric model for message passing within and across input graph samples, along with the latent structure connecting the input graphs. Further, we introduce a degree distribution loss that helps regularize the predicted latent relationships structure. This regularization can significantly improve the downstream task. Moreover, the obtained latent graph can represent patient population models or networks of molecule clusters, providing a level of interpretability and knowledge discovery in the input domain of particular value in healthcare.