arXiv：cs.LG· Isaac Manring, Kejun Huang·· 4 小时前AI 评分42
拐点与平滑性：Laplace 类源下实解析 nICA 的可辨识性
Kinks vs. Smoothness: Identifiability of Real Analytic nICA for Laplace-like Sources
AI 导读
研究证明，当源概率密度函数的一阶导数只有有限个不连续点时，实解析生成函数下的非线性独立成分分析（nICA）可精确恢复潜在因子（至平凡歧义），Laplace 分布是满足该假设的典型例子。
正文
Abstract:Many machine learning systems try to explain complex data - like images or financial time series - in terms of hidden, independent factors that generated them. Recovering the true underlying factors, rather than some scrambled version of them, is the central challenge of nonlinear Independent Component Analysis (nICA). We prove identifiability (exact recovery) up to trivial ambiguities for real analytic generating functions when source probability density functions have a finite number of discontinuities in the first derivative. The Laplace distribution is the most prominent example satisfying this assumption. Our proof relies on the contrast between kinks in the source distribution and the smoothness of real analytic functions. Real analytic functions comprise a broad class of generating mechanisms, and can be approximated with Normalizing Flows or Variational Autoencoders with standard activation functions (e.g., tanh, softplus, GELU), so our result applies with minimal changes to existing training pipelines. We perform experiments on real and synthetic data with both Normalizing Flows and Variational Auto-Encoders demonstrating their identifiability properties. In experiments on CelebA data we recover several interpretable latent factors controlling unique attributes across the dataset.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.21926 [cs.LG] |
| (or arXiv:2609.21926v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.21926 arXiv-issued DOI via DataCite |
Submission history
From: Isaac Manring [view email]
[v1]
Fri, 18 Sep 2026 15:48:56 UTC (2,032 KB)
[v2]
Wed, 7 Oct 2026 15:10:23 UTC (2,143 KB)
来源：arXiv：cs.LG · arxiv.org