# Differentiable Graph Module (DGM) for Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2002.04999 · HTML: https://mlsanity.com/paper/2002.04999/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 30 of 86)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Mining Latent Structures for Multimedia Recommendation](https://mlsanity.com/paper/2104.09036/) (2021)
- [DiffWire: Inductive Graph Rewiring via the Lov'asz Bound](https://mlsanity.com/paper/2206.07369/) (2022)
- [Message passing all the way up](https://mlsanity.com/paper/2202.11097/) (2022)
- [Robust Training of Graph Neural Networks via Noise Governance](https://mlsanity.com/paper/2211.06614/) (2022)
- [Probabilistically Rewired Message-Passing Neural Networks](https://mlsanity.com/paper/2310.02156/) (2023)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreaching](https://mlsanity.com/paper/2312.16560/) (2023)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [Make Heterophily Graphs Better Fit GNN: A Graph Rewiring Approach](https://mlsanity.com/paper/2209.08264/) (2022)
- [Latent Graph Inference using Product Manifolds](https://mlsanity.com/paper/2211.16199/) (2022)
- [Over-Squashing in Graph Neural Networks: A Comprehensive survey](https://mlsanity.com/paper/2308.15568/) (2023)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifold](https://mlsanity.com/paper/2302.08210/) (2023)
- [Multivariate Time Series Forecasting with Latent Graph Inference](https://mlsanity.com/paper/2203.03423/) (2022)
- [Self-Supervised Graph Structure Refinement for Graph Neural Networks](https://mlsanity.com/paper/2211.06545/) (2022)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)
- [Principled Multimodal Representation Learning](https://mlsanity.com/paper/2507.17343/) (2025)
- [Latent Structure Mining with Contrastive Modality Fusion for Multimedia Recommendation](https://mlsanity.com/paper/2111.00678/) (2021)
- [Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimization](https://mlsanity.com/paper/2309.04810/) (2023)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)

## Abstract (arXiv)

Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications ranging from social science, biomedicine, and particle physics to computer vision, graphics, and chemistry. One of the limitations of the majority of current graph neural network architectures is that they are often restricted to the transductive setting and rely on the assumption that the underlying graph is em known and em fixed. Often, this assumption is not true since the graph may be noisy, or partially and even completely unknown. In such cases, it would be helpful to infer the graph directly from the data, especially in inductive settings where some nodes were not present in the graph at training time. Furthermore, learning a graph may become an end in itself, as the inferred structure may provide complementary insights next to the downstream task. In this paper, we introduce Differentiable Graph Module (DGM), a learnable function that predicts edge probabilities in the graph which are optimal for the downstream task. DGM can be combined with convolutional graph neural network layers and trained in an end-to-end fashion. We provide an extensive evaluation of applications from the domains of healthcare (disease prediction), brain imaging (age prediction), computer graphics (3D point cloud segmentation), and computer vision (zero-shot learning). We show that our model provides a significant improvement over baselines both in transductive and inductive settings and achieves state-of-the-art results.