Irregular distribution in latent space causes posterior collapse,
misalignment between posterior and prior, and ill-sampling problem in
Variational Autoencoders (VAEs). In this paper, we introduce a novel adaptable
three-stage Uniform Transformation (UT) module -- Gaussian Kernel Density
Estimation (G-KDE) clustering, non-parametric Gaussian Mixture (GM) Modeling,
and Probability Integral Transform (PIT) -- to address irregular latent
distributions. By reconfiguring irregular distributions into a uniform
distribution in the latent space, our approach significantly enhances the
disentanglement and interpretability of latent representations, overcoming the
limitation of traditional VAE models in capturing complex data structures.
Empirical evaluations demonstrated the efficacy of our proposed UT module in
improving disentanglement metrics across benchmark datasets -- dSprites and
MNIST. Our findings suggest a promising direction for advancing representation
learning techniques, with implication for future research in extending this
framework to more sophisticated datasets and downstream tasks.

通过引入一种新颖的可适应三阶段均匀变换（UT）模块，解决变分自编码器中的潜在空间不规则分布问题，该模块包括高斯核密度估计（G-KDE）聚类、非参数高斯混合建模（GM）和概率积分变换（PIT），通过将不规则分布重新配置成潜在空间中的均匀分布，显著增强了潜在表示的分离性和可解释性，克服了传统 VAE 模型在捕捉复杂数据结构方面的局限性。实证评估表明，我们提出的 UT 模块在改善标准数据集（dSprites 和 MNIST）上的分离度度量方面非常有效。研究结果为推进表示学习技术指明了有希望的方向，并为将该框架扩展到更复杂数据集和下游任务的未来研究提供了启示。