  We consider conceptual issues of deep learning (DL) for metric detectors
using test particle geodesics in curved spacetimes. Advantages of DL metric
detectors are emphasized from a view point of general coordinate
transformations. Two given metrics (two spacetimes) are defined to be conneted
by a DL isometry if their geodesic image data cannot be discriminated by any DL
metric detector at any time. The fundamental question of when the DL isometry
appears is extensively explored. If the two spacetimes connected by the DL
isometry are in superposition of quantum gravity theory, the post-measurement
state may be still in the same superposition even after DL metric detectors
observe the superposed state. We also demonstrate metric-detection DL's in 2+1
dimensional anti-de Sitter (AdS) spacetimes to estimate the cosmological
constants and Brown-Henneaux charges. In the AdS/CFT correspondence dictionary,
it may be expected that such metric detectors in the AdS bulk region correspond
to quantum measurement devices in the CFT at the AdS boundary.
