# RST: certifying and constructing prescribed information in variational autoencoders

arXiv: https://arxiv.org/abs/2605.18224 · HTML: https://mlsanity.com/paper/2605.18224/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 43 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 30 of 31)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [InfoVAE: Information Maximizing Variational Autoencoders](https://mlsanity.com/paper/1706.02262/) (2017)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [Towards Backward-Compatible Representation Learning](https://mlsanity.com/paper/2003.11942/) (2020)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [Avoiding Latent Variable Collapse With Generative Skip Models](https://mlsanity.com/paper/1807.04863/) (2018)
- [Fix your classifier: the marginal value of training the last weight layer](https://mlsanity.com/paper/1801.04540/) (2018)
- [Regular Polytope Networks](https://mlsanity.com/paper/2103.15632/) (2021)
- [Inducing Neural Collapse to a Fixed Hierarchy-Aware Frame for Reducing Mistake Severity](https://mlsanity.com/paper/2303.05689/) (2023)
- [Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealing](https://mlsanity.com/paper/2310.15440/) (2023)
- [Stationary Representations: Optimally Approximating Compatibility and Implications for Improved Model Replacements](https://mlsanity.com/paper/2405.02581/) (2024)
- [boldsymbolλ-Orthogonality Regularization for Compatible Representation Learning](https://mlsanity.com/paper/2509.16664/) (2025)
- [Controlling Posterior Collapse by an Inverse Lipschitz Constraint on the Decoder Network](https://mlsanity.com/paper/2304.12770/) (2023)
- [Beyond Vanilla Variational Autoencoders: Detecting Posterior Collapse in Conditional and Hierarchical Variational Autoencoders](https://mlsanity.com/paper/2306.05023/) (2023)
- [Posterior Collapse as a Phase Transition in Variational Autoencoders](https://mlsanity.com/paper/2510.01621/) (2025)

## Abstract (arXiv)

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.