# GraViti: Graph-Level Variational Autoencoders with Relaxed Permutation Invariance

arXiv: https://arxiv.org/abs/2605.16668 · HTML: https://mlsanity.com/paper/2605.16668/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 66 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 30 of 36)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Structure-Aware Transformer for Graph Representation Learning](https://mlsanity.com/paper/2202.03036/) (2022)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Attending to Graph Transformers](https://mlsanity.com/paper/2302.04181/) (2023)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Categorical Flow Matching on Statistical Manifolds](https://mlsanity.com/paper/2405.16441/) (2024)
- [Multilevel Graph Matching Networks for Deep Graph Similarity Learning](https://mlsanity.com/paper/2007.04395/) (2020)
- [Graph Neural Networks with Adaptive Readouts](https://mlsanity.com/paper/2211.04952/) (2022)
- [Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning](https://mlsanity.com/paper/2104.09856/) (2021)
- [On Structural Expressive Power of Graph Transformers](https://mlsanity.com/paper/2305.13987/) (2023)
- [Poisson Variational Autoencoder](https://mlsanity.com/paper/2405.14473/) (2024)
- [Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoders](https://mlsanity.com/paper/2210.16844/) (2022)
- [Aligning Transformers with Weisfeiler-Leman](https://mlsanity.com/paper/2406.03148/) (2024)

## Built on by (most cited first, 2 of 2)

- [GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations](https://mlsanity.com/paper/2609.35527/) (2026)
- [Latent Flow Matching for Molecular Graph Generation](https://mlsanity.com/paper/2610.06468/) (2026)

## Abstract (arXiv)

We introduce GraViti, a transformer-based graph-level variational autoencoder that encodes entire graphs into single, fixed-dimensional latent vectors rather than per-node embeddings, yielding a graph-level latent space that supports smooth interpolation, property-guided search, and other downstream tasks beyond the reach of node-level approaches. GraViti achieves state-of-the-art reconstruction accuracy on large molecular graph datasets while offering competitive single-step generative performance. Our central finding concerns where permutation invariance is needed in such a model, and where it is not. The encoder remains permutation-invariant throughout, ensuring the model generalizes to graphs regardless of input order. The reconstruction loss, however, does not need to be: when training data is provided in a consistent node order, comparing predictions to targets directly in that order, without a graph-matching step, is sufficient. Relaxing invariance in the loss alone lets GraViti avoid the cubic-cost matching step required by prior graph-level autoencoders, reducing complexity to quadratic while improving reconstruction fidelity. We show the resulting latent space is chemically meaningful, supporting controlled molecular editing and property optimization, recovering established chemical trends, and enabling direct regression of graph-level properties from latent embeddings.