通过函数正交性实现无监督解耦，无需独立性假设
Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability
- 用雅可比矩阵正交约束定义潜在概念，从函数角度建模
- 理论证明该条件可保证非线性生成模型的可识别性
- 实验验证方法能准确恢复真实因子，适用于主流自编码器
本文从函数视角探索无监督解耦表示学习。我们将潜在概念定义为通过局部正交方向影响观测的因子，形式化为生成映射雅可比矩阵上的正交性约束。证明该条件在潜空间允许所有因子组合的前提下，可实现一般非线性生成模型的可识别性，无需统计独立性或因果假设。采用正交性正则化的归一化流实验验证了理论，实证展示了对真实因子的可靠恢复，并揭示了变分自编码器（VAE）成功的原因。这些发现挑战了当前关于无监督解耦不可行的普遍观点，提供了原则性的新基础。
原文摘要 · Abstract (English)
This paper explores unsupervised disentangled representation learning from a functional perspective. We define latent concepts as factors that influence observations through locally orthogonal directions, formalized as an orthogonality constraint on the Jacobian of the generative mapping. We prove that this condition yields identifiability of general nonlinear generative models, without requiring statistical independence or causal assumptions, provided the latent domain admits all combinations of factor values. Experiments with orthogonality-regularized normalizing flows empirically confirm the theory, demonstrate reliable recovery of ground-truth factors, and shed light on the success of VAEs. These findings challenge the prevailing impossibility claims for unsupervised disentanglement and provide a principled alternative foundation.
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