# Latent Spectroscopy: Posterior Collapse as a Feature

arXiv: https://arxiv.org/abs/2605.22691 · HTML: https://mlsanity.com/paper/2605.22691/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 12 of 12)

- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Simple and Effective VAE Training with Calibrated Decoders](https://mlsanity.com/paper/2006.13202/) (2020)
- [The Usual Suspects? Reassessing Blame for VAE Posterior Collapse](https://mlsanity.com/paper/1912.10702/) (2019)
- [Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealing](https://mlsanity.com/paper/2310.15440/) (2023)
- [High-dimensional Asymptotics of VAEs: Threshold of Posterior Collapse and Dataset-Size Dependence of Rate-Distortion Curve](https://mlsanity.com/paper/2309.07663/) (2023)
- [Exploring how a Generative AI interprets music](https://mlsanity.com/paper/2308.00015/) (2023)
- [Posterior Collapse as a Phase Transition in Variational Autoencoders](https://mlsanity.com/paper/2510.01621/) (2025)
- [Learning symmetries in datasets](https://mlsanity.com/paper/2504.05174/) (2025)
- [Artificial Intelligence and Symmetries: Learning, Encoding, and Discovering Structure in Physical Data](https://mlsanity.com/paper/2602.02351/) (2026)

## Built on by (most cited first, 1 of 1)

- [β-VAEs as Effective Theories: Tolerance-Dependent Dimension](https://mlsanity.com/paper/2608.10599/) (2026)

## Abstract (arXiv)

We show that, in linear Gaussian VAEs, posterior collapse is a form of latent feature selection. Feature importance is set by each latent coordinate's contribution to reconstruction, itself given by the corresponding PCA eigenvalue. Varying the regularizer strength β reveals a ranked spectrum of collapse events, with thresholds set by the utility/PCA spectrum. A mode-by-mode analysis identifies the scale-invariant signal fraction as an order parameter obeying Landau scaling near collapse. WorldClim experiments confirm both the utility-threshold calibration and the predicted near-collapse scaling.