# Using Random Noise Equivariantly to Boost Graph Neural Networks Universally

arXiv: https://arxiv.org/abs/2502.02479 · HTML: https://mlsanity.com/paper/2502.02479/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 70 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 30 of 59)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [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)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)

## Built on by (most cited first, 2 of 2)

- [On The Expressive Power of GNN Derivatives](https://mlsanity.com/paper/2510.02565/) (2025)
- [Finite-Time Node Separation in Recurrent Graph Neural Networks with Persistent Gaussian Perturbations](https://mlsanity.com/paper/2609.13920/) (2026)

## Abstract (arXiv)

Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures tailored to exploit noise for specific tasks excel yet lack broad applicability. This paper tackles these issues by laying down a theoretical framework that elucidates the increased sample complexity when introducing random noise into GNNs without careful design. We further propose Equivariant Noise GNN (ENGNN), a novel architecture that harnesses the symmetrical properties of noise to mitigate sample complexity and bolster generalization. Our experiments demonstrate that using noise equivariantly significantly enhances performance on node-level, link-level, subgraph, and graph-level tasks and achieves comparable performance to models designed for specific tasks, thereby offering a general method to boost expressivity across various graph tasks.