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

Disentanglement Learning via Topology

The ability to represent and compare machine learning models is crucial in
order to quantify subtle model changes, evaluate generative models, and gather
insights on neural network architectures. Existing techniques for comparing
data distributions focus on global data properties such as mean and covariance;
in that sense, they are extrinsic and uni-scale. We develop a first-of-its-kind
intrinsic and multi-scale method for characterizing and comparing data
manifolds, using a lower-bound of the spectral variant of the
Gromov-Wasserstein inter-manifold distance, which compares all data moments. In
a thorough experimental study, we demonstrate that our method effectively
discerns the structure of data manifolds even on unaligned data of different
dimensionalities; moreover, we showcase its efficacy in evaluating the quality
of generative models.

用 Gromov-Wasserstein 距离的下界，通过对所有数据矩计算，基于内在和多尺度的方法对比数据流形。实验证明，该方法能够有效地识别不同维度未对齐数据的结构，并展示了在评估生成模型质量方面的功效。