# Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph

arXiv: https://arxiv.org/abs/2409.11504 · HTML: https://mlsanity.com/paper/2409.11504/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 83 references that are in the map.
- First posted on arXiv 17 Sep 2024.

## Builds on (most cited first, 30 of 69)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [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)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)

## Built on by (most cited first, 6 of 6)

- [Fixed Aggregation Features Can Rival GNNs](https://mlsanity.com/paper/2601.19449/) (2026)
- [Pretraining Graph Transformers with Atom-in-a-Molecule Quantum Properties for Improved ADMET Modeling](https://mlsanity.com/paper/2410.08024/) (2024)
- [A Theory for Compressibility of Graph Transformers for Transductive Learning](https://mlsanity.com/paper/2411.13028/) (2024)
- [Resolving Oversmoothing with Opinion Dissensus](https://mlsanity.com/paper/2501.19089/) (2025)
- [What Can We Learn From MIMO Graph Convolutions?](https://mlsanity.com/paper/2505.11346/) (2025)
- [Multi-Agent Systems are Mixtures of Experts: Who Becomes an Influencer?](https://mlsanity.com/paper/2605.25929/) (2026)

## Abstract (arXiv)

The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing as a special case. Most approaches to mitigate over-smoothing extend common message-passing schemes, e.g., the graph convolutional network, by utilizing residual connections, gating mechanisms, normalization, or regularization techniques. Our work contrarily proposes to directly tackle the cause of this issue by modifying the message-passing scheme and exchanging different types of messages using multi-relational graphs. We identify a sufficient condition to ensure linearly independent node representations. As one instantion, we show that operating on multiple directed acyclic graphs always satisfies our condition and propose to obtain these by defining a strict partial ordering of the nodes. We conduct comprehensive experiments that confirm the benefits of operating on multi-relational graphs to achieve more informative node representations.