提出机制独立性原则，实现无需统计假设的可识别解耦表征
Mechanistic Independence: A Principle for Identifiable Disentangled Representations
- 用机制独立性定义潜在因子作用方式，摆脱分布依赖
- 多种独立性准则均能保证非线性不可逆混合下的子空间可识别
- 通过图论揭示潜在子空间结构，适合理论研究与模型设计
解耦表征旨在恢复观测数据背后的潜在变化因素，但其可识别性仍未完全明确。本文引入统一框架，通过机制独立性实现解耦，该性质基于潜在因子如何作用于观测变量，而非其潜在分布。这一视角对潜在密度变化保持不变，即使此类变化引发因子间的统计依赖。在此框架下，我们提出一系列相关独立性准则——从支持基、稀疏性到高阶条件——并证明每种都能在非线性、非可逆混合条件下实现潜在子空间的可识别性。进一步建立这些准则的层级关系，并以图论方式刻画潜在子空间为连通分量。这些结果澄清了无需依赖统计假设即可识别解耦表征的条件。
原文摘要 · Abstract (English)
Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through mechanistic independence, which characterizes latent factors by how they act on observed variables rather than by their latent distribution. This perspective is invariant to changes of the latent density, even when such changes induce statistical dependencies among factors. Within this framework, we propose several related independence criteria -- ranging from support-based and sparsity-based to higher-order conditions -- and show that each yields identifiability of latent subspaces, even under nonlinear, non-invertible mixing. We further establish a hierarchy among these criteria and provide a graph-theoretic characterization of latent subspaces as connected components. Together, these results clarify the conditions under which disentangled representations can be identified without relying on statistical assumptions.
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