# Model Metamers Reveal Invariances in Graph Neural Networks

arXiv: https://arxiv.org/abs/2510.17378 · HTML: https://mlsanity.com/paper/2510.17378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 20 Oct 2025.

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

- [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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNs](https://mlsanity.com/paper/2406.02997/) (2024)
- [On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems](https://mlsanity.com/paper/2405.01009/) (2024)
- [FlowX: Towards Explainable Graph Neural Networks via Message Flows](https://mlsanity.com/paper/2206.12987/) (2022)
- [TGB-Seq Benchmark: Challenging Temporal GNNs with Complex Sequential Dynamics](https://mlsanity.com/paper/2502.02975/) (2025)
- [Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shifts](https://mlsanity.com/paper/2408.09490/) (2024)

## Abstract (arXiv)

In recent years, deep neural networks have been extensively employed in perceptual systems to learn representations endowed with invariances, aiming to emulate the invariance mechanisms observed in the human brain. However, studies in the visual and auditory domains have confirmed that significant gaps remain between the invariance properties of artificial neural networks and those of humans. To investigate the invariance behavior within graph neural networks (GNNs), we introduce a model ``metamers'' generation technique. By optimizing input graphs such that their internal node activations match those of a reference graph, we obtain graphs that are equivalent in the model's representation space, yet differ significantly in both structure and node features. Our theoretical analysis focuses on two aspects: the local metamer dimension for a single node and the activation-induced volume change of the metamer manifold. Utilizing this approach, we uncover extreme levels of representational invariance across several classic GNN architectures. Although targeted modifications to model architecture and training strategies can partially mitigate this excessive invariance, they fail to fundamentally bridge the gap to human-like invariance. Finally, we quantify the deviation between metamer graphs and their original counterparts, revealing unique failure modes of current GNNs and providing a complementary benchmark for model evaluation.