A Stable Neural Statistical Dependence Estimator for Autoencoder Feature Analysis
Abstract
Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among inputs, latents, and reconstructions measurable, and we propose a stable neural dependence estimator based on an orthonormal density-ratio decomposition. Unlike MINE, our method avoids input concatenation and product-of-marginals re-pairing, reducing computational cost and improving stability. We introduce an efficient NMF-like scalar cost and demonstrate empirically that assuming Gaussian noise to form an auxiliary variable enables meaningful dependence measurements and supports quantitative feature analysis, with a sequential convergence of singular values.
Cite
@article{arxiv.2603.11428,
title = {A Stable Neural Statistical Dependence Estimator for Autoencoder Feature Analysis},
author = {Bo Hu and Jose C Principe},
journal= {arXiv preprint arXiv:2603.11428},
year = {2026}
}