# Generalised f-Mean Aggregation for Graph Neural Networks

arXiv: https://arxiv.org/abs/2306.13826 · HTML: https://mlsanity.com/paper/2306.13826/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 24 Jun 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks](https://mlsanity.com/paper/1311.1780/) (2013)
- [Learning Aggregation Functions](https://mlsanity.com/paper/2012.08482/) (2020)
- [Generalizing Aggregation Functions in GNNs:High-Capacity GNNs via Nonlinear Neighborhood Aggregators](https://mlsanity.com/paper/2202.09145/) (2022)

## Built on by (most cited first, 5 of 5)

- [Sequential Signal Mixing Aggregation for Message Passing Graph Neural Networks](https://mlsanity.com/paper/2409.19414/) (2024)
- [Detection of False Data Injection Attacks (FDIA) on Power Dynamical Systems With a State Prediction Method](https://mlsanity.com/paper/2409.04609/) (2024)
- [MEGA: Message Passing Neural Networks for Multigraphs with EdGe Attributes](https://mlsanity.com/paper/2412.00241/) (2024)
- [MaxSketch: Robust Distinct Counting in Streams via Random Projections](https://mlsanity.com/paper/2605.15571/) (2026)
- [Geometric Mean Pooling for Equal-Weight Multiplicative Coarse-Graining](https://mlsanity.com/paper/2609.21876/) (2026)

## Abstract (arXiv)

Graph Neural Network (GNN) architectures are defined by their implementations of update and aggregation modules. While many works focus on new ways to parametrise the update modules, the aggregation modules receive comparatively little attention. Because it is difficult to parametrise aggregation functions, currently most methods select a ``standard aggregator'' such as mean, sum, or max. While this selection is often made without any reasoning, it has been shown that the choice in aggregator has a significant impact on performance, and the best choice in aggregator is problem-dependent. Since aggregation is a lossy operation, it is crucial to select the most appropriate aggregator in order to minimise information loss. In this paper, we present GenAgg, a generalised aggregation operator, which parametrises a function space that includes all standard aggregators. In our experiments, we show that GenAgg is able to represent the standard aggregators with much higher accuracy than baseline methods. We also show that using GenAgg as a drop-in replacement for an existing aggregator in a GNN often leads to a significant boost in performance across various tasks.