Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability
Provides a principled theoretical foundation and practical method for unsupervised disentanglement, addressing a fundamental bottleneck in representation learning.
This paper proves that enforcing functional orthogonality on the Jacobian of the generative mapping yields identifiability for unsupervised disentanglement in general nonlinear models, without requiring statistical independence. Experiments with normalizing flows confirm reliable recovery of ground-truth factors, challenging prior impossibility claims.
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.