Mathieu Simon

Mathieu Cyrille Simon, Pascal Frossard, Christophe De Vleeschouwer

This paper explores self-supervised disentangled representation learning within sequential data, focusing on separating time-independent and time-varying factors in videos. We propose a new model that breaks the usual independence assumption between those factors by explicitly accounting for the causal relationship between the static/dynamic variables and that improves the model expressivity through additional Normalizing Flows. A formal definition of the factors is proposed. This formalism leads to the derivation of sufficient conditions for the ground truth factors to be identifiable, and to the introduction of a novel theoretically grounded disentanglement constraint that can be directly and efficiently incorporated into our new framework. The experiments show that the proposed approach outperforms previous complex state-of-the-art techniques in scenarios where the dynamics of a scene are influenced by its content.

Mathieu Cyrille Simon, Pascal Frossard, Christophe De Vleeschouwer

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.