Entropy-Based Characterisation of the Polarised Regime in Latent Variable Models

• URL: http://arxiv.org/abs/2605.15965v1
• Date: Fri, 15 May 2026 13:55:55 GMT
• Title: Entropy-Based Characterisation of the Polarised Regime in Latent Variable Models
• Abstract summary: Variational Autoencoders (VAEs) often exhibit a polarised regime in which latent variables separate into active, passive, and mixed subsets.<n>We propose a simple information-theoretic classification of the polarised regime based on the entropy of the mean representation.
• Score: 5.199765487172328
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational Autoencoders (VAEs) often exhibit a polarised regime in which latent variables separate into active, passive, and mixed subsets. Existing criteria for identifying active dimensions depend on a Gaussian prior, limiting their applicability to variational models and specific priors. We propose a simple information-theoretic classification of the polarised regime based on the entropy of the mean representation. We show theoretically how this entropy couples to KL minimisation through entropy--variance bounds, and we relate the resulting criterion to Bonheme's active/passive conditions. We also clarify a key limitation: entropy of the mean alone cannot reliably distinguish active from mixed dimensions without additional signals from the variance representation. Empirically, we evaluate the entropy criterion on $β$-VAEs, identifiable VAEs, Least-Volume Autoencoders, and L2-regularised autoencoders, and find that it consistently recovers a polarised regime when such a regime is present across the model classes studied. Finally, we show that passive dimensions can yield small but consistent improvements on downstream tasks when latent codes are appropriately normalised, suggesting that collapse is often a matter of scale rather than absolute information removal.

Related papers

• Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation [71.74203645336385]
  Impute-EM alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data.<n>We characterize the update and show that the observed mask-indexed marginals match the targets at the limit.
  arXiv  Detail & Related papers  (2026-09-14T09:39:13Z)
• Trajectory-Aware Node Contributions and the Limits of Static Controllability [0.0]
  "emergent contribution" is a measure of a node's dynamical leverage.<n>"EC" reduces exactly to average controllability in the linear, time-invariant limit.<n>We place five estimated real systems from several domains within this phase space.
  arXiv  Detail & Related papers  (2026-06-02T02:56:36Z)
• Entropy-Controlled Flow Matching [0.08460698440162889]
  We propose a constrained variational principle over continuity-equation paths enforcing a global entropy-rate budget d/dt H(mu_t) >= -lambda.<n>We obtain certificate-style mode-coverage and density-floor guarantees with Lipschitz, and construct near-optimal counterexamples for unconstrained flow matching.
  arXiv  Detail & Related papers  (2026-02-25T06:07:01Z)
• The Entropic Signature of Class Speciation in Diffusion Models [12.212582407125089]
  We show that tracking the class-conditional entropy of a latent semantic variable given a noisy state provides a reliable signature of transition regimes.<n>We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation.
  arXiv  Detail & Related papers  (2026-02-10T10:56:46Z)
• Disentanglement via Latent Quantization [60.37109712033694]
  In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. We demonstrate the broad applicability of this approach by adding it to both basic data-re (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models.
  arXiv  Detail & Related papers  (2023-05-28T06:30:29Z)
• Bayesian Renormalization [68.8204255655161]
  We present a fully information theoretic approach to renormalization inspired by Bayesian statistical inference. The main insight of Bayesian Renormalization is that the Fisher metric defines a correlation length that plays the role of an emergent RG scale. We provide insight into how the Bayesian Renormalization scheme relates to existing methods for data compression and data generation.
  arXiv  Detail & Related papers  (2023-05-17T18:00:28Z)
• Alignment Entropy Regularization [13.904347165738491]
  We use entropy to measure a model's uncertainty. We evaluate the effect of entropy regularization in encouraging the model to distribute the probability mass only on a smaller subset of allowed alignments.
  arXiv  Detail & Related papers  (2022-12-22T18:51:02Z)
• Disentangling Generative Factors of Physical Fields Using Variational Autoencoders [0.0]
  This work explores the use of variational autoencoders (VAEs) for non-linear dimension reduction. A disentangled decomposition is interpretable and can be transferred to a variety of tasks including generative modeling.
  arXiv  Detail & Related papers  (2021-09-15T16:02:43Z)
• Benign Overfitting of Constant-Stepsize SGD for Linear Regression [122.70478935214128]
  inductive biases are central in preventing overfitting empirically. This work considers this issue in arguably the most basic setting: constant-stepsize SGD for linear regression. We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares.
  arXiv  Detail & Related papers  (2021-03-23T17:15:53Z)
• GroupifyVAE: from Group-based Definition to VAE-based Unsupervised Representation Disentanglement [91.9003001845855]
  VAE-based unsupervised disentanglement can not be achieved without introducing other inductive bias. We address VAE-based unsupervised disentanglement by leveraging the constraints derived from the Group Theory based definition as the non-probabilistic inductive bias. We train 1800 models covering the most prominent VAE-based models on five datasets to verify the effectiveness of our method.
  arXiv  Detail & Related papers  (2021-02-20T09:49:51Z)
• Neural Decomposition: Functional ANOVA with Variational Autoencoders [9.51828574518325]
  Variational Autoencoders (VAEs) have become a popular approach for dimensionality reduction. Due to the black-box nature of VAEs, their utility for healthcare and genomics applications has been limited. We focus on characterising the sources of variation in Conditional VAEs.
  arXiv  Detail & Related papers  (2020-06-25T10:29:13Z)
• Generalized Entropy Regularization or: There's Nothing Special about Label Smoothing [83.78668073898001]
  We introduce a family of entropy regularizers, which includes label smoothing as a special case. We find that variance in model performance can be explained largely by the resulting entropy of the model. We advise the use of other entropy regularization methods in its place.
  arXiv  Detail & Related papers  (2020-05-02T12:46:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.