# Mitigating Oversmoothing Through Reverse Process of GNNs for Heterophilic Graphs

arXiv: https://arxiv.org/abs/2403.10543 · HTML: https://mlsanity.com/paper/2403.10543/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 28 of 28)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond](https://mlsanity.com/paper/2209.06177/) (2022)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [Model Degradation Hinders Deep Graph Neural Networks](https://mlsanity.com/paper/2206.04361/) (2022)
- [Half-Hop: A graph upsampling approach for slowing down message passing](https://mlsanity.com/paper/2308.09198/) (2023)

## Built on by (most cited first, 10 of 10)

- [Taming Gradient Oversmoothing and Expansion in Graph Neural Networks](https://mlsanity.com/paper/2410.04824/) (2024)
- [The Oversmoothing Fallacy: A Misguided Narrative in GNN Research](https://mlsanity.com/paper/2506.04653/) (2025)
- [Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness-Generalization Perspective](https://mlsanity.com/paper/2412.09805/) (2024)
- [Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning](https://mlsanity.com/paper/2506.17576/) (2025)
- [Reversible Residual Normalization Alleviates Spatio-Temporal Distribution Shift](https://mlsanity.com/paper/2604.15838/) (2026)
- [GOMA: Toward Structure-Driven Multimodal Alignment from a Graph Signal Smoothing Perspective](https://mlsanity.com/paper/2605.15723/) (2026)
- [Graph Transductive Sharpening: Leveraging Unlabeled Predictions in Node Classification](https://mlsanity.com/paper/2605.20248/) (2026)
- [Learn When and Where to Connect: Adaptive Virtual Nodes for Dynamic Message Passing on Graphs](https://mlsanity.com/paper/2606.03068/) (2026)
- [A Spectral Theory of Normalized Corrected GNN Propagation](https://mlsanity.com/paper/2606.23572/) (2026)
- [ProbeMatchDTI: Probe-Driven Multi-Scale Biochemical Pattern Matching for Drug-Target Interaction Prediction](https://mlsanity.com/paper/2609.02549/) (2026)

## Abstract (arXiv)

Graph Neural Network (GNN) resembles the diffusion process, leading to the over-smoothing of learned representations when stacking many layers. Hence, the reverse process of message passing can produce the distinguishable node representations by inverting the forward message propagation. The distinguishable representations can help us to better classify neighboring nodes with different labels, such as in heterophilic graphs. In this work, we apply the design principle of the reverse process to the three variants of the GNNs. Through the experiments on heterophilic graph data, where adjacent nodes need to have different representations for successful classification, we show that the reverse process significantly improves the prediction performance in many cases. Additional analysis reveals that the reverse mechanism can mitigate the over-smoothing over hundreds of layers. Our code is available at https://github.com/ml-postech/reverse-gnn.