Kinks vs. Smoothness: Identifiability of Real Analytic nICA for Laplace-like Sources
The paper claims exact nonlinear ICA recovery when analytic generators meet source distributions with derivative “kinks,” including Laplace-like densities.
Manring and Huang prove identifiability up to trivial ambiguities for real analytic generating functions under that source assumption. The argument turns on a mismatch: finite nonsmooth points in the source density cannot be hidden by smooth analytic maps. They say the result fits common normalizing-flow and VAE setups using activations such as tanh, softplus, and GELU. Experiments on synthetic, real, and CelebA data are reported, including recovery of interpretable latent factors.
ArXiv · AI/CL/LG's note
Manring and Huang prove identifiability up to trivial ambiguities for real analytic generating functions under that source assumption. The argument turns on a mismatch: finite nonsmooth points in the source density cannot be hidden by smooth analytic maps. They say the result fits common normalizing-flow and VAE setups using activations such as tanh, softplus, and GELU. Experiments on synthetic, real, and CelebA data are reported, including recovery of interpretable latent factors.
ArXiv · AI/CL/LG's note
score 4