Dataset dependence of the entropy-term effect on anomaly ranking

Characterize how the dataset determines the magnitude and direction of the anomaly-detection performance difference between the DBM mean-field energy and the proper variational free energy that subtracts mean-field entropy.

Background

The paper reports that using the mean-field energy E(v, μ) instead of the proper variational free energy E(v, μ) − H(μ) improves or preserves ranking performance on the two evaluated datasets, but the size of the effect differs substantially. The authors state that preliminary runs on additional tabular benchmarks showed both signs of the difference, leaving unresolved how the entropy penalty behaves across datasets and what determines its magnitude.

References

We therefore scope the claim: $E(\mu)$ is never significantly worse than $F_{\text{proper}$ on either dataset and the mechanism favouring it is generic, but the magnitude is a per-dataset empirical question---in preliminary runs on further tabular benchmarks we observed both signs of the difference.

— Revisiting Energy-based Tabular Anomaly Detection: Energy and Reconstruction are Complementary  (2608.14186 - Niimi, 14 Aug 2026) in Section ‘Mean-field energy vs. proper variational free energy’, subsection ‘How far does this generalise?’