# Generalized Graph Variational Autoencoders: Bounded Divergences Control Posterior Collapse

arXiv: https://arxiv.org/abs/2609.29546 · HTML: https://mlsanity.com/paper/2609.29546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence](https://mlsanity.com/paper/2312.01133/) (2023)
- [q-VAE for Disentangled Representation Learning and Latent Dynamical Systems](https://mlsanity.com/paper/2003.01852/) (2020)
- [Epitomic Variational Graph Autoencoder](https://mlsanity.com/paper/2004.01468/) (2020)
- [GraphNetz: Statistical Benchmarking of Graph Neural Networks with Paired Tests and Rank Aggregation](https://mlsanity.com/paper/2605.09099/) (2026)
- [Perspectives on Tsallis Statistics for Artificial Intelligence](https://mlsanity.com/paper/2608.01223/) (2026)
- [When Should Graph Attention Be Sparse? Learning a Per-Edge Tsallis Index](https://mlsanity.com/paper/2608.02938/) (2026)

## Abstract (arXiv)

The variational graph autoencoder (VGAE) regularizes its posterior toward the prior with the Kullback-Leibler divergence, a choice inherited from the variational autoencoder rather than argued for. We introduce the generalized graph variational autoencoder (GGVA), which replaces that term with any member of the R'enyi-Tsallis family of order q while leaving every other part of the model untouched. Both members admit closed forms for diagonal Gaussians and both recover the KL exactly as q → 1, so the VGAE is the q=1 arm of our own model rather than a separate baseline, and any measured difference is attributable to a single scalar. Our analysis identifies boundedness, not the order, as the operative property: for q<1 the Tsallis divergence is bounded above by 1/(1-q), independently of the latent width, whereas the KL and the R'enyi divergence of the same order are unbounded. On ten graphs spanning three synthetic families, a social network, three citation networks, a connectome, a power grid and a road network, q moves the retained posterior information by up to 49× relative to the VGAE, while the R'enyi arm at the same order stays within 1.02-1.30× of it on all six larger real graphs (isolating the bound as the cause). The retained information is usable: probing the frozen embedding for node class, a label absent from the objective, gives GGVA up to +0.14 macro-F1 over the VGAE on CiteSeer, with the R'enyi control again tracking the VGAE. We also report what the design was built to expose: none of this reaches held-out link-prediction accuracy on any of the six larger real graphs, and boundedness delays posterior collapse rather than preventing it.