# Generalization Limits of Graph Neural Networks in Identity Effects Learning

arXiv: https://arxiv.org/abs/2307.00134 · HTML: https://mlsanity.com/paper/2307.00134/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 25 of 25)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Expressive Power of Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/2006.15646/) (2020)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Molecular graph generation with Graph Neural Networks](https://mlsanity.com/paper/2012.07397/) (2020)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunities](https://mlsanity.com/paper/2302.01018/) (2023)
- [Generalization Analysis of Message Passing Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2202.00645/) (2022)
- [WL meet VC](https://mlsanity.com/paper/2301.11039/) (2023)
- [On the approximation capability of GNNs in node classification/regression tasks](https://mlsanity.com/paper/2106.08992/) (2021)
- [Invariance, encodings, and generalization: learning identity effects with neural networks](https://mlsanity.com/paper/2101.08386/) (2021)
- [Which Learning Algorithms Can Generalize Identity-Based Rules to Novel Inputs?](https://mlsanity.com/paper/1605.04002/) (2016)

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

- [VC dimension of Graph Neural Networks with Pfaffian activation functions](https://mlsanity.com/paper/2401.12362/) (2024)
- [Do stable neural networks exist for classification problems? -- A new view on stability in AI](https://mlsanity.com/paper/2401.07874/) (2024)
- [Weisfeiler and Leman Go Measurement Modeling: Probing the Validity of the WL Test](https://mlsanity.com/paper/2307.05775/) (2023)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have emerged as a powerful tool for data-driven learning on various graph domains. They are usually based on a message-passing mechanism and have gained increasing popularity for their intuitive formulation, which is closely linked to the Weisfeiler-Lehman (WL) test for graph isomorphism to which they have been proven equivalent in terms of expressive power. In this work, we establish new generalization properties and fundamental limits of GNNs in the context of learning so-called identity effects, i.e., the task of determining whether an object is composed of two identical components or not. Our study is motivated by the need to understand the capabilities of GNNs when performing simple cognitive tasks, with potential applications in computational linguistics and chemistry. We analyze two case studies: (i) two-letters words, for which we show that GNNs trained via stochastic gradient descent are unable to generalize to unseen letters when utilizing orthogonal encodings like one-hot representations; (ii) dicyclic graphs, i.e., graphs composed of two cycles, for which we present positive existence results leveraging the connection between GNNs and the WL test. Our theoretical analysis is supported by an extensive numerical study.