InvGNN: Learning Invertible Node Representations on Graphs

Giannis Nikolentzos, Dimitrios Kelesis, Nikolaos Nakis
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:93262-93282, 2026.

Abstract

Over the past decade, Graph Neural Networks (GNNs) have become a standard tool for solving machine learning problems on graphs. While many aspects of GNNs have been studied in depth, including their efficiency and expressive power, the invertibility of these models has remained largely unexplored. Standard aggregation functions, such as the mean, max and sum operators, are not invertible, which limits their applicability in tasks requiring invertible transformations. In this work, we introduce an invertible GNN layer. By stacking multiple such layers, we construct fully invertible GNN models, which we refer to as InvGNNs. These models inherit the benefits of invertible neural networks, including low memory usage for deep architectures, exact likelihood computation, and generative modeling capabilities. We demonstrate that InvGNNs can match the expressive power of the 1-dimensional Weisfeiler-Leman algorithm, showing that invertibility does not compromise model expressiveness. On standard graph classification benchmarks, our model performs comparably to other well-established GNNs. Beyond classification, we demonstrate the potential of invertible layers through density estimation tasks, including outlier detection and node feature generation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-nikolentzos26a, title = {{I}nv{GNN}: Learning Invertible Node Representations on Graphs}, author = {Nikolentzos, Giannis and Kelesis, Dimitrios and Nakis, Nikolaos}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {93262--93282}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/nikolentzos26a/nikolentzos26a.pdf}, url = {https://proceedings.mlr.press/v306/nikolentzos26a.html}, abstract = {Over the past decade, Graph Neural Networks (GNNs) have become a standard tool for solving machine learning problems on graphs. While many aspects of GNNs have been studied in depth, including their efficiency and expressive power, the invertibility of these models has remained largely unexplored. Standard aggregation functions, such as the mean, max and sum operators, are not invertible, which limits their applicability in tasks requiring invertible transformations. In this work, we introduce an invertible GNN layer. By stacking multiple such layers, we construct fully invertible GNN models, which we refer to as InvGNNs. These models inherit the benefits of invertible neural networks, including low memory usage for deep architectures, exact likelihood computation, and generative modeling capabilities. We demonstrate that InvGNNs can match the expressive power of the 1-dimensional Weisfeiler-Leman algorithm, showing that invertibility does not compromise model expressiveness. On standard graph classification benchmarks, our model performs comparably to other well-established GNNs. Beyond classification, we demonstrate the potential of invertible layers through density estimation tasks, including outlier detection and node feature generation.} }
Endnote
%0 Conference Paper %T InvGNN: Learning Invertible Node Representations on Graphs %A Giannis Nikolentzos %A Dimitrios Kelesis %A Nikolaos Nakis %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-nikolentzos26a %I PMLR %P 93262--93282 %U https://proceedings.mlr.press/v306/nikolentzos26a.html %V 306 %X Over the past decade, Graph Neural Networks (GNNs) have become a standard tool for solving machine learning problems on graphs. While many aspects of GNNs have been studied in depth, including their efficiency and expressive power, the invertibility of these models has remained largely unexplored. Standard aggregation functions, such as the mean, max and sum operators, are not invertible, which limits their applicability in tasks requiring invertible transformations. In this work, we introduce an invertible GNN layer. By stacking multiple such layers, we construct fully invertible GNN models, which we refer to as InvGNNs. These models inherit the benefits of invertible neural networks, including low memory usage for deep architectures, exact likelihood computation, and generative modeling capabilities. We demonstrate that InvGNNs can match the expressive power of the 1-dimensional Weisfeiler-Leman algorithm, showing that invertibility does not compromise model expressiveness. On standard graph classification benchmarks, our model performs comparably to other well-established GNNs. Beyond classification, we demonstrate the potential of invertible layers through density estimation tasks, including outlier detection and node feature generation.
APA
Nikolentzos, G., Kelesis, D. & Nakis, N.. (2026). InvGNN: Learning Invertible Node Representations on Graphs. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:93262-93282 Available from https://proceedings.mlr.press/v306/nikolentzos26a.html.

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