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

arXiv:2603.10935v4 Announce Type: replace-cross Abstract: 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 elta_{ext{collapse}}. We prove that when the reconstruction loss is constrained to this region, the collapsed solution is mathematically excluded from the feasible parameter space. extbf{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., sigma^2 < lambda_{max}) and works with arbitrary neural architectures. The code is available at https://github.com/tsegoochang/spherical-vae-with-Cluster.

Source: arXiv cs.AI | 2026-05-19