Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability

2026-06-19

AI Summary

This work proposes a novel approach to unsupervised disentangled representation learning that circumvents the need for statistical independence or causal assumptions traditionally required for identifiability. By imposing a local orthogonality constraint on the Jacobian of the generative mapping, the authors introduce “functional orthogonality” as a disentanglement principle and theoretically establish the identifiability of nonlinear generative models under this condition. The method is implemented using normalizing flows trained with an orthogonality regularizer. Experiments demonstrate successful recovery of the true underlying latent factor structure, thereby validating the theoretical claims and offering new insights into the mechanisms enabling disentanglement in variational autoencoders. These findings challenge the prevailing view that unsupervised disentanglement is fundamentally unattainable.

Abstract

This paper explores unsupervised disentangled representation learning from a functional perspective. We define latent concepts as factors that influence observations through locally orthogonal directions, formalized as an orthogonality constraint on the Jacobian of the generative mapping. We prove that this condition yields identifiability of general nonlinear generative models, without requiring statistical independence or causal assumptions, provided the latent domain admits all combinations of factor values. Experiments with orthogonality-regularized normalizing flows empirically confirm the theory, demonstrate reliable recovery of ground-truth factors, and shed light on the success of VAEs. These findings challenge the prevailing impossibility claims for unsupervised disentanglement and provide a principled alternative foundation.

Problem

• unsupervised disentanglement
• identifiability
• functional orthogonality
• representation learning
• nonlinear generative models

Innovation

• unsupervised disentanglement
• functional orthogonality
• identifiability
• Jacobian orthogonality
• normalizing flows