拓扑度作为不纠缠的离散诊断,并应用于 $Δ$VAE

Mahefa Ratsisetraina Ravelonanosy, Vlado Menkovski, Jacobus W. Portegies
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引用次数: 0

摘要

我们研究了以单位球$\mathcal{S}^2$为潜在空间的扩散变异自动编码器($\Delta$VAE)捕捉数据集中的拓扑和几何结构以及分解潜在因素的能力。为此,我们引入了一种新的解缠诊断方法:即编码器的拓扑度,它是从数据流形到潜空间的映射。通过使用同调理论的工具,我们推导并实现了一种计算该度的算法。我们使用该算法计算训练过程中产生的模型的编码器度。我们的实验结果表明,$\Delta$VAE 可以获得相对较小的 LSBD 分数,而且无论初始化后的度数是多少,训练后编码器的度数都会变成 $-1$ 或 $+1$,这意味着所得到的编码器至少与同构同向。
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Topological degree as a discrete diagnostic for disentanglement, with applications to the $Δ$VAE
We investigate the ability of Diffusion Variational Autoencoder ($\Delta$VAE) with unit sphere $\mathcal{S}^2$ as latent space to capture topological and geometrical structure and disentangle latent factors in datasets. For this, we introduce a new diagnostic of disentanglement: namely the topological degree of the encoder, which is a map from the data manifold to the latent space. By using tools from homology theory, we derive and implement an algorithm that computes this degree. We use the algorithm to compute the degree of the encoder of models that result from the training procedure. Our experimental results show that the $\Delta$VAE achieves relatively small LSBD scores, and that regardless of the degree after initialization, the degree of the encoder after training becomes $-1$ or $+1$, which implies that the resulting encoder is at least homotopic to a homeomorphism.
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