FockTrust: Photonic Natural Gradients in Detector-Count Space

Photonic learners observe detector counts rather than optical states, so their natural gradient must follow the distribution actually measured. Loss, missed photons, dark counts, and readout alter which parameter directions remain distinguishable. We introduce FockTrust, which defines the Fisher metric directly in detector-count space. Shared base and parameter-shift histograms estimate the task gradient and full metric, while covariance-whitened readout moments map count geometry into tangent space. We also bound the effect of finite counts on the resulting step. In matched 2-by-2 experiments at dimension 32, retaining off-diagonal count couplings reduces final loss by 17.6-24.3% relative to diagonal directions under either trust rule. With trust rules tuned on separate development tasks, full count geometry lowers loss by 25.7% on 12 unseen graphs. The advantage over state-QFIM persists in a two-photon study. FockTrust makes the detector model part of optimization and identifies detector-count space as the operative geometry of measured photonic learning.