From Core to Detail: Unsupervised Disentanglement with Entropy-Ordered Flows

TL;DR

This paper introduces EOFlows, a novel normalizing-flow framework that orders latent variables by entropy, enabling flexible, interpretable, and compressed representations with strong denoising capabilities.

Contribution

The paper proposes entropy-ordered flows (EOFlows), a new method for unsupervised representation learning that orders latent dimensions by explained entropy, allowing adaptive and interpretable compression.

Findings

Uncovers semantically interpretable features in CelebA.

Enables high compression and effective denoising.

Scales well to high-dimensional data like images.

Abstract

Learning unsupervised representations that are both semantically meaningful and stable across runs remains a central challenge in modern representation learning. We introduce entropy-ordered flows (EOFlows), a normalizing-flow framework that orders latent dimensions by their explained entropy, analogously to PCA's explained variance. This ordering enables adaptive injective flows: after training, one may retain only the top C latent variables to form a compact core representation while the remaining variables capture fine-grained detail and noise, with C chosen flexibly at inference time rather than fixed during training. EOFlows build on insights from Independent Mechanism Analysis, Principal Component Flows and Manifold Entropic Metrics. We combine likelihood-based training with local Jacobian regularization and noise augmentation into a method that scales well to high-dimensional data such as images. Experiments on the CelebA dataset show that our method uncovers a rich set of semantically interpretable features, allowing for high compression and strong denoising.