提出稳定神经依赖估计器，用于分析自编码器特征的统计关联。
A Stable Neural Statistical Dependence Estimator for Autoencoder Feature Analysis
- 基于正交密度比分解设计新估计方法
- 避免输入拼接与边际重配，计算更稳定高效
- 假设高斯噪声辅助变量，实现可量化特征分析
互信息等统计依赖度量适用于自编码器分析，但对确定性、无噪声网络可能病态。本文采用变分（高斯）公式，使输入、隐变量与重构间的依赖关系可测，并提出一种基于正交密度比分解的稳定神经依赖估计器。相比MINE，本方法避免输入拼接与边际重配，降低计算开销并提升稳定性。引入类似NMF的标量损失函数，实验证明假设高斯噪声构造辅助变量，可实现有意义的依赖度量，并支持定量特征分析，呈现奇异值的逐步收敛。
原文摘要 · Abstract (English)
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.
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