Defining and Measuring Disentanglement for non-Independent Factors of Variation

ICLR 2025 Conference Submission12510 Authors

Keywords: disentanglement, representation learning, dependent factors, sufficiency, minimality

Abstract: Representation learning is an approach that allows to discover and extract the factors of variation from the data. Intuitively, a representation is said to be disentangled if it separates the different factors of variation in a way that is understandable to humans. Definitions of disentanglement and metrics to measure it usually assume that the factors of variation are independent of each other. However, this is generally false in the real world, which limits the use of these definitions and metrics to very specific and unrealistic scenarios. In this paper we give a definition of disentanglement based on information theory that is also valid when the factors are not independent. Furthermore, we demonstrate that this definition is equivalent to having a representation composed of minimal and sufficient variables. Finally, we propose a method to measure the degree of disentanglement from the given definition that works when the factors are not independent. We show through different experiments that the method proposed in this paper correctly measures disentanglement with independent and non-independent factors, while other methods fail in the latter scenario.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 12510