Calibrated Probability Forecast Sequences and Measure-Valued Martingales

What the math gives to ML

The paper characterizes sequential auto-calibrated probability forecasts as measure-valued martingales: conditioning on the current forecast history, the expected later predictive measure equals the current one. This gives a principled consistency constraint for neural models that emit distributions at multiple information or refinement steps. The most direct transfer is a moment-based regularizer that permits forecasts to sharpen while preventing systematic, history-dependent probability drift.