The gamma sky, captured by the Fermi telescope, is a grand symphony of thousands of sources. Here, the rhythmic pulsations of pulsars, the powerful chords of active galactic nuclei, but most of all — unidentified objects, whose part remains a mystery. Traditional methods of searching for new physics require a precise score: you need to know what the signal from dark matter annihilation or axion-photon oscillations sounds like. But nature may not play the tune we expect. So scientists turned to weakly supervised learning — a technique that catches dissonance even without knowing the notes.

The idea is as elegant as ear training. Imagine two audio recordings: the first is a flawless orchestra (pure background), the second is the same orchestra, but an uninvited soloist might have been in the hall, their voice weaving into the sound (mixed sample). The weakly supervised classifier learns to distinguish these recordings, revealing features uncharacteristic of the background. Just as an experienced listener unerringly senses a false note, the algorithm sharpens its sensitivity to the slightest deviations. The study used real and synthesized with normalizing flows spectra (methods of spectroscopy and photometry), and the classifier was an ensemble of decision trees with gradient boosting.

The authors tested the method in three scenarios. In the first, separating pulsars from active galactic nuclei: with an anomaly class fraction of 10%, weak supervision achieved a true discovery rate of about 0.7, nearly matching the supervised counterpart. In the second, searching for dark matter subhalos of 80 GeV annihilating into b-quarks. Here the modest result (discovery fraction ~0.4 at a low false-alarm rate) highlighted the key point: the method does not require precise knowledge of the signal spectrum, and thus can see things that don't fit any model. The third scenario is even more subtle: the search for spectral distortions from axion-photon oscillations (idea of Roberto Peccei) in a galaxy. Even with a signal fraction of 3%, the algorithm caught anomalies, although the false-positive rate increased — an inevitable price for freedom from templates. To hear the quiet voice of a soloist, you have to amplify all sounds, risking taking hissing for a new part.

Such a strategy does not replace targeted searches, but gives astrophysicists an automatic unusualness detector. It ranks hundreds and thousands of sources, singling out the most suspicious candidates. In the future, the method will be applied to the entire Fermi dataset and data from new observatories. Deep neural networks, Bayesian analysis — all this will turn the blind hunt for anomalies into a discovery pipeline. It's noteworthy that similar approaches are already used at the Large Hadron Collider to search for new particles — anomalies do not recognize boundaries between the sky and the accelerator.

When Vera Rubin noticed peculiarities in the rotation of galaxies, she wasn't looking for dark matter: she saw an anomaly. When Jocelyn Bell Burnell discovered radio pulses, she didn't model a neutron star: she noticed disharmony. Weakly supervised algorithms continue this tradition: listening to the sky without knowing what you're looking for, and being surprised.