# Two-level domain-decomposition AdaGrad method for scalable training of graph neural networks

arXiv: https://arxiv.org/abs/2608.22575 · HTML: https://mlsanity.com/paper/2608.22575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 60 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 30 of 40)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1911.07323/) (2019)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models](https://mlsanity.com/paper/2104.07788/) (2021)
- [GNNAdvisor: An Adaptive and Efficient Runtime System for GNN Acceleration on GPUs](https://mlsanity.com/paper/2006.06608/) (2020)
- [PipeGCN: Efficient Full-Graph Training of Graph Convolutional Networks with Pipelined Feature Communication](https://mlsanity.com/paper/2203.10428/) (2022)
- [BNS-GCN: Efficient Full-Graph Training of Graph Convolutional Networks with Partition-Parallelism and Random Boundary Node Sampling](https://mlsanity.com/paper/2203.10983/) (2022)
- [Distributed Graph Neural Network Training: A Survey](https://mlsanity.com/paper/2211.00216/) (2022)
- [Learn Locally, Correct Globally: A Distributed Algorithm for Training Graph Neural Networks](https://mlsanity.com/paper/2111.08202/) (2021)
- [Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies](https://mlsanity.com/paper/2306.17648/) (2023)
- [Machine learning and domain decomposition methods -- a survey](https://mlsanity.com/paper/2312.14050/) (2023)
- [Globally Convergent Multilevel Training of Deep Residual Networks](https://mlsanity.com/paper/2107.07572/) (2021)
- [Trust-Region Algorithms for Training Responses: Machine Learning Methods Using Indefinite Hessian Approximations](https://mlsanity.com/paper/1807.00251/) (2018)

## Abstract (arXiv)

Graph neural networks (GNNs) have emerged as a powerful framework for learning from graph-structured data. However, their efficient training remains challenging, particularly in distributed computing environments. This challenge arises from the use of message passing, which couples all graph nodes, leading to expensive optimization steps, high memory requirements, and substantial communication overhead. To alleviate these limitations, we propose a novel domain-decomposition (DD) variant of AG2m, an AdaGrad method enhanced with second-order curvature information and momentum, denoted by DD-AG2m. The proposed DD-AG2m alternates between AG2m optimization on the original (global) graph and AG2m optimization on the partitioned graphs. To incorporate global information at reduced cost, we further introduce a two-level variant (2DD-AG2m) that performs global optimization steps on a coarse graph obtained by randomly subsampling nodes within each subdomain. Numerical experiments spanning graph classification, node-level regression, and spatiotemporal forecasting tasks demonstrate that the proposed DD methods reduce the computational cost required to achieve the same predictive performance by a factor of 4-8. Moreover, for the fixed computational cost, they improve the predictive performance of GNNs by up to 22% compared with the baseline AG2m.