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.

翻译：我们提出TopDis（拓扑解耦），一种通过添加多尺度拓扑损失项来学习解耦表示的方法。解耦是数据表示的关键属性，对深度学习模型的可解释性和鲁棒性至关重要，也是迈向高级认知的一步。基于VAE的现有最优方法通过最小化潜变量联合分布的总相关性来实现解耦。我们通过分析数据流形的拓扑特性，采用不同的视角来解决解耦问题。具体而言，我们优化数据流形遍历的拓扑相似性。据我们所知，本文首次提出用于解耦的可微拓扑损失函数。实验表明，所提出的拓扑损失在MIG、FactorVAE分数、SAP分数和DCI解耦分数等指标上均优于现有最优结果。该方法以无监督方式运行，因此可应用于缺乏标注变化因子的实际问题。此外，我们还展示了如何利用所提出的拓扑损失在预训练的GAN中寻找解耦方向。