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.

通过加入多尺度拓扑损失项，我们提出了TopDis（拓扑分解）方法，用于学习解耦表示。我们采用了一种不同的方法来分析数据流形的拓扑性质，并优化数据流形遍历的拓扑相似性，提出了一种可微分的解耦拓扑损失。我们的方法在无监督学习的情况下工作，并且通过实验证明，所提出的拓扑损失在与最先进结果相比的MIG、FactorVAE得分、SAP得分和DCI解耦得分方面具有改进的效果。此外，我们展示了如何在训练好的生成对抗网络中使用所提出的拓扑损失来找到解耦方向。

通过拓扑学习进行解缠学习