# Graph Neural Networks with Adaptive Readouts

arXiv: https://arxiv.org/abs/2211.04952 · HTML: https://mlsanity.com/paper/2211.04952/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Learning Aggregation Functions](https://mlsanity.com/paper/2012.08482/) (2020)

## Built on by (most cited first, 29 of 29)

- [GraphEdit: Large Language Models for Graph Structure Learning](https://mlsanity.com/paper/2402.15183/) (2024)
- [Search to Fine-tune Pre-trained Graph Neural Networks for Graph-level Tasks](https://mlsanity.com/paper/2308.06960/) (2023)
- [An end-to-end attention-based approach for learning on graphs](https://mlsanity.com/paper/2402.10793/) (2024)
- [Graph Classification via Reference Distribution Learning: Theory and Practice](https://mlsanity.com/paper/2408.11370/) (2024)
- [Advancing Drug Discovery with Enhanced Chemical Understanding via Asymmetric Contrastive Multimodal Learning](https://mlsanity.com/paper/2311.06456/) (2023)
- [What Do GNNs Actually Learn? Towards Understanding their Representations](https://mlsanity.com/paper/2304.10851/) (2023)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [Sequential Signal Mixing Aggregation for Message Passing Graph Neural Networks](https://mlsanity.com/paper/2409.19414/) (2024)
- [Heterogeneous graphs model spatial relationships between biological entities for breast cancer diagnosis](https://mlsanity.com/paper/2307.08132/) (2023)
- [Scalable Expressiveness through Preprocessed Graph Perturbations](https://mlsanity.com/paper/2406.11714/) (2024)
- [Edge-DIRECT: A Deep Reinforcement Learning-based Method for Solving Heterogeneous Electric Vehicle Routing Problem with Time Window Constraints](https://mlsanity.com/paper/2407.01615/) (2024)
- [GraViti: Graph-Level Variational Autoencoders with Relaxed Permutation Invariance](https://mlsanity.com/paper/2605.16668/) (2026)
- [Learning Representations without Compositional Assumptions](https://mlsanity.com/paper/2305.19726/) (2023)
- [Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodes](https://mlsanity.com/paper/2311.12644/) (2023)
- [HyperGALE: ASD Classification via Hypergraph Gated Attention with Learnable Hyperedges](https://mlsanity.com/paper/2403.14484/) (2024)
- [A Novel Technique for Query Plan Representation Based on Graph Neural Nets](https://mlsanity.com/paper/2405.04814/) (2024)
- [Predictive Covert Communication Against Multi-UAV Surveillance Using Graph Koopman Autoencoder](https://mlsanity.com/paper/2409.17048/) (2024)
- [FuncGNN: Learning Functional Semantics of Logic Circuits with Graph Neural Networks](https://mlsanity.com/paper/2506.06787/) (2025)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [Graph-level representations using ensemble-based readout functions](https://mlsanity.com/paper/2303.02023/) (2023)
- [HYVE: Hybrid Vertex Encoder for Neural Distance Fields](https://mlsanity.com/paper/2310.06644/) (2023)
- [Reqo: A Comprehensive Learning-Based Cost Model for Robust and Explainable Query Optimization](https://mlsanity.com/paper/2501.17414/) (2025)
- [On the use of Graphs for Satellite Image Time Series](https://mlsanity.com/paper/2505.16685/) (2025)
- [S2-UniSeg: Fast Universal Agglomerative Pooling for Scalable Segment Anything without Supervision](https://mlsanity.com/paper/2508.06995/) (2025)
- [Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion](https://mlsanity.com/paper/2509.18452/) (2025)
- [Towards Efficient Hypergraph and Multi-LLM Agent Recommender Systems](https://mlsanity.com/paper/2512.06590/) (2025)
- [Diffusion-Guided Pretraining for Brain Graph Foundation Models](https://mlsanity.com/paper/2602.09437/) (2026)
- [Property-Driven Evaluation of GNN Expressiveness at Scale: Datasets, Framework, and Study](https://mlsanity.com/paper/2603.00044/) (2026)
- [Estimating Subgraph Importance with Structural Prior Domain Knowledge](https://mlsanity.com/paper/2605.12009/) (2026)

## Abstract (arXiv)

An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions designed such that the resulting hypothesis space is permutation invariant. Prior work on deep sets indicates that such readouts might require complex node embeddings that can be difficult to learn via standard neighborhood aggregation schemes. Motivated by this, we investigate the potential of adaptive readouts given by neural networks that do not necessarily give rise to permutation invariant hypothesis spaces. We argue that in some problems such as binding affinity prediction where molecules are typically presented in a canonical form it might be possible to relax the constraints on permutation invariance of the hypothesis space and learn a more effective model of the affinity by employing an adaptive readout function. Our empirical results demonstrate the effectiveness of neural readouts on more than 40 datasets spanning different domains and graph characteristics. Moreover, we observe a consistent improvement over standard readouts (i.e., sum, max, and mean) relative to the number of neighborhood aggregation iterations and different convolutional operators.