When is a reconstruction a measurement, and when is it a hypothesis?
Two scientific inverse problems contributed to InverseBench (ICLR 2025), on real survey cadences.
Mapping a star's surface from its brightness alone, the data pin down 19 numbers out of 4,608 map pixels — so most of any published map is the prior, not the observation. Because the unmeasurable subspace is computable, “the model is inventing structure” stops being a caveat and becomes a measurement: a matched prior recovers genuinely hidden structure, while surfaces it has never seen come back anti-correlated with the truth.