Enriching Disentanglement: Definitions to Metrics

by   Yivan Zhang, et al.

Disentangled representation learning is a challenging task that involves separating multiple factors of variation in complex data. Although various metrics for learning and evaluating disentangled representations have been proposed, it remains unclear what these metrics truly quantify and how to compare them. In this work, we study the definitions of disentanglement given by first-order equational predicates and introduce a systematic approach for transforming an equational definition into a compatible quantitative metric based on enriched category theory. Specifically, we show how to replace (i) equality with metric or divergence, (ii) logical connectives with order operations, (iii) universal quantifier with aggregation, and (iv) existential quantifier with the best approximation. Using this approach, we derive metrics for measuring the desired properties of a disentangled representation extractor and demonstrate their effectiveness on synthetic data. Our proposed approach provides practical guidance for researchers in selecting appropriate evaluation metrics and designing effective learning algorithms for disentangled representation learning.


page 1

page 2

page 3

page 4


Evaluating Disentangled Representations

There is no generally agreed upon definition of disentangled representat...

On Causally Disentangled Representations

Representation learners that disentangle factors of variation have alrea...

Measuring Disentanglement: A Review of Metrics

Learning to disentangle and represent factors of variation in data is an...

A Category-theoretical Meta-analysis of Definitions of Disentanglement

Disentangling the factors of variation in data is a fundamental concept ...

DCI-ES: An Extended Disentanglement Framework with Connections to Identifiability

In representation learning, a common approach is to seek representations...

Disentangled Representation Learning

Disentangled Representation Learning (DRL) aims to learn a model capable...

Correcting Flaws in Common Disentanglement Metrics

Recent years have seen growing interest in learning disentangled represe...

Please sign up or login with your details

Forgot password? Click here to reset