# Graph Hierarchical Recurrence for Long-Range Generalization

arXiv: https://arxiv.org/abs/2605.18387 · HTML: https://mlsanity.com/paper/2605.18387/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 18 May 2026.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark](https://mlsanity.com/paper/2309.00367/) (2023)
- [DRew: Dynamically Rewired Message Passing with Delay](https://mlsanity.com/paper/2305.08018/) (2023)
- [DiffWire: Inductive Graph Rewiring via the Lov'asz Bound](https://mlsanity.com/paper/2206.07369/) (2022)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs](https://mlsanity.com/paper/2205.15117/) (2022)

## Abstract (arXiv)

Graph Neural Networks and Graph Transformers have become central to graph learning, combining expressive representation learning with sample-efficient inductive biases. Yet they remain fundamentally limited when predictions depend on correlations between distant graph regions. We address this limitation with Graph Hierarchical Recurrence (GHR), a novel framework that jointly operates on the input graph and a pooled hierarchical abstraction. We also show that existing models degrade more sharply under out-of-range generalization, where test instances require interactions across distances exceeding those observed during training. Despite its minimal design, GHR consistently strengthens every tested message-passing backbone, yielding robust performance on long-range dependencies and particularly pronounced gains in out-of-range regimes. Across a broad suite of long-range benchmarks, GHR achieves state-of-the-art or competitive results on multiple tasks, establishing hierarchical recurrence as an effective mechanism for extending graph models beyond their observed interaction range.