# Generalizing Aggregation Functions in GNNs:High-Capacity GNNs via Nonlinear Neighborhood Aggregators

arXiv: https://arxiv.org/abs/2202.09145 · HTML: https://mlsanity.com/paper/2202.09145/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology](https://mlsanity.com/paper/1907.05008/) (2019)
- [Reliable Graph Neural Networks via Robust Aggregation](https://mlsanity.com/paper/2010.15651/) (2020)
- [Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks](https://mlsanity.com/paper/1311.1780/) (2013)
- [Learning Conjoint Attentions for Graph Neural Nets](https://mlsanity.com/paper/2102.03147/) (2021)
- [Rethinking Graph Neural Architecture Search from Message-passing](https://mlsanity.com/paper/2103.14282/) (2021)
- [Signal Recovery from Pooling Representations](https://mlsanity.com/paper/1311.4025/) (2013)

## Built on by (most cited first, 3 of 3)

- [Graph Neural Networks for Financial Fraud Detection: A Review](https://mlsanity.com/paper/2411.05815/) (2024)
- [Generalised f-Mean Aggregation for Graph Neural Networks](https://mlsanity.com/paper/2306.13826/) (2023)
- [Alleviating Over-Smoothing via Aggregation over Compact Manifolds](https://mlsanity.com/paper/2407.19231/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) have achieved great success in many graph learning tasks. The main aspect powering existing GNNs is the multi-layer network architecture to learn the nonlinear graph representations for the specific learning tasks. The core operation in GNNs is message propagation in which each node updates its representation by aggregating its neighbors' representations. Existing GNNs mainly adopt either linear neighborhood aggregation (mean,sum) or max aggregator in their message propagation. (1) For linear aggregators, the whole nonlinearity and network's capacity of GNNs are generally limited due to deeper GNNs usually suffer from over-smoothing issue. (2) For max aggregator, it usually fails to be aware of the detailed information of node representations within neighborhood. To overcome these issues, we re-think the message propagation mechanism in GNNs and aim to develop the general nonlinear aggregators for neighborhood information aggregation in GNNs. One main aspect of our proposed nonlinear aggregators is that they provide the optimally balanced aggregators between max and mean/sum aggregations. Thus, our aggregators can inherit both (i) high nonlinearity that increases network's capacity and (ii) detail-sensitivity that preserves the detailed information of representations together in GNNs' message propagation. Promising experiments on several datasets show the effectiveness of the proposed nonlinear aggregators.