Measuring Local Posterior Activity in Variational Language Model Units

Abstract

Language-model evaluation commonly focuses on final predictive distributions through likelihood, calibration, accuracy, entropy, and variability across predictions. Internal probabilistic activity offers a complementary measurement level by describing how distributions are represented within the computation that produces those predictions. EVE, the Elemental Variational Expanse, is a variational language-model unit that maps a selected hidden activation to an input-conditioned Gaussian posterior. During the forward computation, the unit exposes divergence from a reference prior, posterior scale, posterior mean energy, and active-unit fraction. These quantities form an internal measurement panel evaluated alongside deterministic, dropout-based, and ensemble-based predictive references. Controlled evaluations show competitive predictive behavior together with directly observable posterior activity. Validation-selected posterior readouts provide distinct calibration and tail-risk operating points, while controlled changes in context quality and target frequency produce systematic variation in both output metrics and internal posterior statistics. The resulting framework combines predictive evaluation with explicit probabilistic measurements inside language-model computation.

Keywords

• variational language-model units
• local posterior activity
• internal probabilistic measurements
• uncertainty quantification
• posterior scale
• Kullback–Leibler activity
• calibration
• tail risk
• non-stationarity

Citation

Ruffenach, Yves. “Measuring Local Posterior Activity in Variational Language Model Units.” Preprint, version 1, July 28, 2026. DOI: 10.5281/zenodo.21641827.