Traditional Variational Autoencoders (VAEs) are constrained by the limitations of the Evidence Lower Bound (ELBO) formulation, particularly when utilizing simplistic, non-analytic, or unknown prior distributions. These limitations inhibit the VAE's ability to generate high-quality samples and provide clear, interpretable latent representations. This work introduces the Entropy Decomposed Variational Autoencoder (ED-VAE), a novel re-formulation of the ELBO that explicitly includes entropy and cross-entropy components. This reformulation significantly enhances model flexibility, allowing for the integration of complex and non-standard priors. By providing more detailed control over the encoding and regularization of latent spaces, ED-VAE not only improves interpretability but also effectively captures the complex interactions between latent variables and observed data, thus leading to better generative performance.

翻译：传统变分自编码器（VAEs）受限于证据下界（ELBO）公式的局限性，尤其是在使用简单、非解析或未知先验分布时。这些限制阻碍了VAE生成高质量样本并提供清晰、可解释潜在表示的能力。本文提出熵分解变分自编码器（ED-VAE），这是一种对ELBO的全新重构，明确包含熵与交叉熵分量。该重构显著增强了模型的灵活性，允许集成复杂与非标准先验分布。通过对潜在空间的编码与正则化提供更精细的控制，ED-VAE不仅提升了可解释性，还能有效捕捉潜在变量与观测数据间的复杂交互作用，从而获得更优的生成性能。