arXiv subjects

Zegu Zhang

Publications and source records attributed to Zegu Zhang.

3 recordsLinked to original sources

arXiv2026

RST: certifying and constructing prescribed information in variational autoencoders

Posterior-collapse diagnostics can show that a VAE uses its latent representation, but they do not determine whether a specified information view crosses a representation/readout interface fixed before training. Reconstruction-Student-Teacher (RST) makes this stronger requirement explicit: Reconstruction supplies the VAE objective, the Student is a fixed witness, and the Teacher is a frozen information specification. We derive a teacher-relative certificate showing that a positive margin guarantees transmission of the declared information through the prescribed interface, while every input-independent representation lies at or below the boundary. A centered regular-simplex witness turns this certificate into an explicit construction: a minimum-dimensional closed-form teacher code, its complete affine solution fiber, witness-visible and witness-null routing, a margin-energy path, function-space departure from the centered input-independent point, preservation cylinders, and orthogonal multi-view composition. Experiments on five datasets test boundary crossing, stronger KL pressure, teacher counterfactuals, null routing, escape, preservation, cross-seed reuse, and cross-architecture reuse. On CIFAR-100, auxiliary learned readers remain natively decodable but fail under no-refit transfer, whereas the same fixed RST witness directly reads independently trained ConvVAE and ResVAE encoders. Affine adapters recover transferred auxiliary readers, localizing much of the failure to interface-coordinate mismatch rather than absence of information. These results support prescribed alignment as distinct from ordinary decodability.

cs.LG↗

arXiv2026

A Testable Certificate for Constant Collapse in Teacher-Guided VAEs

Posterior collapse in variational autoencoders is often diagnosed by its symptoms: a small KL term, a strong decoder, or weak use of the latent code. These signals are useful, but they do not define a collapse boundary. We study a concrete failure mode, input-independent constant collapse, and show that this case admits an exact threshold. For any fixed nonconstant teacher distribution $T(\cdot\mid x)$, the best constant student is the dataset-average teacher distribution, and its alignment cost is the teacher mutual information $I_T(X;T)$. Therefore, if a strictly latent-only raw witness achieves alignment loss below this value, with a safety margin, the witness cannot be constant in the input. This identity turns a qualitative failure mode into a measurable one. In CIFAR-100 experiments with per-seed teacher search, full training stays on the certified side of the boundary, removing alignment drives the raw witness into the constant-student regime, and restarting from a collapsed checkpoint with alignment enabled restores the certificate. Tiny-ImageNet-200 fixed-target runs show the same prevention--collapse--rescue pattern across three independently searched teachers. Standard VAE-style baselines, including methods that preserve reconstruction quality or post-hoc predictability, remain negative under the raw certificate. The guarantee is intentionally narrow: it certifies that the matched nonconstant teacher-relative variation passes through the latent pathway, rather than claiming that all forms of posterior collapse have been ruled out.

cs.LG↗

arXiv2026

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

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 $\delta_{\text{collapse}}$. We prove that when the reconstruction loss is constrained to this region, the collapsed solution is mathematically excluded from the feasible parameter space. \textbf{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.

cs.LG↗