A translator learns a language not from a dictionary but from living conversations: they hear fragments of phrases, street noise, different accents. Out of that chaos they assemble rules that are written in no book. The same goes here: instead of squeezing black hole masses into a ready-made shape, the neural network listens to the signals themselves and works out on its own how those masses are distributed.
A conventional approach is like a tailor who sews a suit from three measurements and hopes it will fit any client. Parametric models set the peaks and kinks in advance, then merely adjust their height. But if the real distribution has an unexpected hump or dip, such a model simply will not see it. A normalizing flow works differently: it starts with a smooth hill and gradually kneads it like clay until the shape matches the data.
Testing on two simulated catalogs showed that the method can tell whether the black hole population changed over time or stayed the same. When evolution of the mass peak was built into the data, the diagnostic gave a positive shift, while for a stationary model it came out near zero. It is as if the translator recognized from intonation that speakers from different generations use different words.
On the real GWTC-5.0 data, the neural network saw two familiar peaks: near 10 and 35 solar masses. This agrees with the collaboration's official analysis, but here the shape was not imposed in advance. The diagnostic for the real data turned out close to zero, meaning there is no evidence that the mass distribution changed with redshift.
Such a tool will be useful not only for black holes. Any science where objects are observed with noise and not all of them are seen can use this approach: from counting exoplanets to the demographics of supernovae. A translator who learns from conversations rather than a dictionary may one day understand any accent in the Universe.
The injection campaign for GWTC-5.0 generated 1.57 billion signals, of which only 1.34 million passed the detection threshold, corresponding to roughly one survivor per thousand generated.