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...
| Authors | Zegu Zhang, Jianhua Peng, Jian Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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