Recent theoretical work established the unsupervised identifiability of quantized factors under any diffeomorphism. The theory assumes that quantization thresholds correspond to axis-aligned discontinuities in the probability density of the latent factors. By constraining a learned map to have a density with axis-aligned discontinuities, we can recover the quantization of the factors. However, translating this high-level principle into an effective practical criterion remains challenging, especially under nonlinear maps. Here, we develop a criterion for unsupervised disentanglement by encouraging axis-aligned discontinuities. Discontinuities manifest as sharp changes in the estimated density of factors and form what we call cliffs. Following the definition of independent discontinuities from the theory, we encourage the location of the cliffs along a factor to be independent of the values of the other factors. We show that our method, Cliff, outperforms the baselines on all disentanglement benchmarks, demonstrating its effectiveness in unsupervised disentanglement.

翻译：近期的理论研究表明，在任何微分同胚变换下，量化因子均具备无监督可识别性。该理论假设量化阈值对应于潜在因子概率密度中轴对齐的不连续性。通过约束学习到的映射使其密度具有轴对齐的不连续性，我们可以恢复因子的量化过程。然而，将这一高层原理转化为有效的实践准则仍然具有挑战性，尤其是在非线性映射下。本文通过促进轴对齐不连续性，提出了一种无监督解缠结的判定准则。不连续性表现为因子估计密度的急剧变化，形成我们称之为“悬崖”的结构。依据理论中独立不连续性的定义，我们鼓励沿某一因子的“悬崖”位置独立于其他因子的取值。我们证明，本方法Cliff在所有解缠结基准测试中均优于基线方法，展现了其在无监督解缠结任务中的有效性。