A Stable Neural Statistical Dependence Estimator for Autoencoder Feature Analysis

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.