# Learning Aggregation Functions

arXiv: https://arxiv.org/abs/2012.08482 · HTML: https://mlsanity.com/paper/2012.08482/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2020.

## Built on by (most cited first, 13 of 13)

- [Graph Neural Networks with Adaptive Readouts](https://mlsanity.com/paper/2211.04952/) (2022)
- [Meta-Aggregator: Learning to Aggregate for 1-bit Graph Neural Networks](https://mlsanity.com/paper/2109.12872/) (2021)
- [Learnable Commutative Monoids for Graph Neural Networks](https://mlsanity.com/paper/2212.08541/) (2022)
- [Learning Social Welfare Functions](https://mlsanity.com/paper/2405.17700/) (2024)
- [Equilibrium Aggregation: Encoding Sets via Optimization](https://mlsanity.com/paper/2202.12795/) (2022)
- [Generalised f-Mean Aggregation for Graph Neural Networks](https://mlsanity.com/paper/2306.13826/) (2023)
- [Subspace Representations for Soft Set Operations and Sentence Similarities](https://mlsanity.com/paper/2210.13034/) (2022)
- [InkStream: Real-time GNN Inference on Streaming Graphs via Incremental Update](https://mlsanity.com/paper/2309.11071/) (2023)
- [A New Lightweight Hybrid Graph Convolutional Neural Network -- CNN Scheme for Scene Classification using Object Detection Inference](https://mlsanity.com/paper/2407.14658/) (2024)
- [On the Lipschitz Continuity of Set Aggregation Functions and Neural Networks for Sets](https://mlsanity.com/paper/2505.24403/) (2025)
- [Improving Set Function Approximation with Quasi-Arithmetic Neural Networks](https://mlsanity.com/paper/2602.04941/) (2026)
- [Beyond Weighted Summation: Learnable Nonlinear Aggregation Functions for Robust Artificial Neurons](https://mlsanity.com/paper/2603.19344/) (2026)
- [MaxSketch: Robust Distinct Counting in Streams via Random Projections](https://mlsanity.com/paper/2605.15571/) (2026)

## Abstract (arXiv)

Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum. However, recent results showed that universal function representation by sum- (or max-) decomposition requires either highly discontinuous (and thus poorly learnable) mappings, or a latent dimension equal to the maximum number of elements in the set. To mitigate this problem, we introduce a learnable aggregation function (LAF) for sets of arbitrary cardinality. LAF can approximate several extensively used aggregators (such as average, sum, maximum) as well as more complex functions (e.g., variance and skewness). We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures such as DeepSets and library-based architectures like Principal Neighborhood Aggregation, and can be effectively combined with attention-based architectures.