Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be impossible in the unsupervised i.i.d. setting under a general nonlinear map from factors to observations. In this work, however, we demonstrate that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism. We only assume that the latent factors have independent discontinuities in their density, without requiring the factors to be statistically independent. We introduce this novel form of identifiability, termed quantized factor identifiability, and provide a comprehensive proof of the recovery of the quantized factors.

翻译：解耦旨在仅从观测分布中恢复有意义的潜在真实因子，并通过可识别性理论进行形式化表述。在无监督独立同分布场景下，若观测数据由一般非线性映射从因子生成，则独立潜在因子的可识别性已被证明不可能实现。然而，本文证明在一般非线性微分同胚映射下，量化潜在因子是可恢复的。我们仅假设潜在因子的密度具有独立不连续点，无需因子间具有统计独立性。我们提出这种新型可识别性——量化因子可识别性，并给出量化因子可恢复性的完整证明。