Disentanglement Learning via Topology

We propose TopDis (Topological Disentanglement), a method for learning disentangled representations via adding multi-scale topological loss term. Disentanglement is a crucial property of data representations substantial for the explainability and robustness of deep learning models and a step towards high-level cognition. The state-of-the-art method based on VAE minimizes the total correlation of the joint distribution of latent variables. We take a different perspective on disentanglement by analyzing topological properties of data manifolds. In particular, we optimize the topological similarity for data manifolds traversals. To the best of our knowledge, our paper is the first one to propose a differentiable topological loss for disentanglement. Our experiments have shown that the proposed topological loss improves disentanglement scores such as MIG, FactorVAE score, SAP score and DCI disentanglement score with respect to state-of-the-art results. Our method works in an unsupervised manner, permitting to apply it for problems without labeled factors of variation. Additionally, we show how to use the proposed topological loss to find disentangled directions in a trained GAN.