Calibrating Semantic Uncertainty from Observable Language-Model Probabilities

What the math gives to ML

The paper formalizes a missing interface between token-level language-model probabilities and uncertainty over a finite set of scientific or operational states. Its key transferable asset is the semantic pushforward: a prespecified measurable map aggregates probability mass over verbal continuations into declared states, followed by held-out calibration against a reference posterior. This gives an auditable uncertainty head for language models whose quality can be measured by total-variation error, coverage, inverse stability, and paraphrase invariance rather than verbal confidence alone. The most practical neural-network adaptation is a frozen or lightly fine-tuned semantic response interface with a small calibrated state-distribution layer and an explicit paraphrase-stability test or regularizer.