# Spherical VAE with Cluster-Aware Feasible Regions: Guaranteed Prevention of Posterior Collapse

arXiv: https://arxiv.org/abs/2603.10935 · HTML: https://mlsanity.com/paper/2603.10935/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 12 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [Improving Explorability in Variational Inference with Annealed Variational Objectives](https://mlsanity.com/paper/1809.01818/) (2018)
- [Posterior Collapse as a Phase Transition in Variational Autoencoders](https://mlsanity.com/paper/2510.01621/) (2025)

## Abstract (arXiv)

Variational autoencoders (VAEs) frequently suffer from posterior collapse, where the latent variables become uninformative as the approximate posterior degenerates to the prior. While recent work has characterized collapse as a phase transition determined by data covariance properties, existing approaches primarily aim to avoid rather than eliminate collapse. We introduce a novel framework that theoretically guarantees non-collapsed solutions by leveraging spherical shell geometry and cluster-aware constraints. Our method transforms data to a spherical shell, computes optimal cluster assignments via K-means, and defines a feasible region between the within-cluster variance W and collapse loss δcollapse. We prove that when the reconstruction loss is constrained to this region, the collapsed solution is mathematically excluded from the feasible parameter space. Critically, we introduce norm constraint mechanisms that ensure decoder outputs remain compatible with the spherical shell geometry without restricting representational capacity. Unlike prior approaches, our method provides a strict theoretical guarantee with minimal computational overhead without imposing constraints on decoder outputs. Experiments on synthetic and real-world datasets demonstrate 100% collapse prevention under conditions where conventional VAEs completely fail, with reconstruction quality matching or exceeding state-of-the-art methods. Our approach requires no explicit stability conditions (e.g., σ2 < λmax) and works with arbitrary neural architectures. The code is available at https://github.com/tsegoochang/spherical-vae-with-Cluster.