Reliability and Collapse of Neural Mutual-Information Estimators for Eavesdropper-Leakage Assessment in Wireless Physical-Layer Security

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Mutual information neural estimation (MINE) and related variational estimators are increasingly used as empirical eavesdropper-leakage indicators in wireless physical-layer security (PLS) systems that lack a closed-form secrecy rate. We ask whether, given a matched estimation target, such estimators recover the true eavesdropper mutual information (MI). Across three wiretap systems of increasing complexity—a Gaussian wiretap, an orthogonal frequency-division multiple access (OFDMA) Rayleigh-fading wiretap, and a discrete-codebook sparse code multiple access (SCMA) wiretap test bed—we compare each held-out estimate against its own numerically computed reference, spanning four lower-bound estimators (DV/MINE, NWJ, SMILE, InfoNCE) and one upper-bound estimator (CLUB). Three findings emerge. i) A three-tier reliability hierarchy (estimator-vs-reference slopes $0.98 / 0.76 / 0.05$ ): the estimate tracks the truth for the Gaussian wiretap, underestimates it for the discrete codebook, and collapses for the OFDMA fading channel. ii) The fading collapse persists even with the matched target (YE,HE) —recovering only 5–17% of the true conditional MI despite larger budgets and longer training, consistent with a function-class/finite-sample limitation under the tested protocols rather than a simple training-length failure. All four lower-bound estimators collapse; CLUB is not a reliable substitute—it overestimates the truth on the calibrated systems yet itself falls below the true MI under fading—so neither bound direction gives a reliable absolute leakage value. iii) Paired-design rankings are preserved only for single-parameter, large-separation comparisons; under multiple coupled variables ranking falls to chance on the hardest high-leakage pairs and is at best weakly rank-correlated overall (Kendall τ = 0.27 ). We conclude that a near-zero neural MI estimate can coincide with substantial true leakage, so—for the tested estimators, critic families, sample budgets, and channel models—these estimators are unsafe as absolute eavesdropper-leakage indicators in the tested fading-mixture regime and should be used for comparative ranking only under matched, single-parameter, clearly separated designs, not for coupled multi-variable selection.