The Cost Geometry of Belief: finite-resource inference under noisy observation (opens in new tab)

We equip the space of beliefs with a cost geometry (what it costs to pass from one belief to another): optimal transport in Wasserstein space, reweighted conformally by Fisher information (the price of the precision at stake), distinct from the Fisher-Rao metric. In the setting we consider, a finite machine maintains a digital twin of a system; observing the territory through finite, noisy sensors, we model its coherent output as a belief: a p...