I was wondering the same and learned the model doesn't know about itself during training [0]
[0] https://developers.googleblog.com/closing-the-knowledge-gap-...
[0] https://developers.googleblog.com/closing-the-knowledge-gap-...
That training on existing models is what brings out various other things about other models; then there's models that are just like snowballs, where you build one iteration, then you give it it's identity, then you train on that with the same synthetic generaiton.
So a model could generation include at some point it's own name.
Synthetic data is generated by other models, and yes this is often where identity propagates.
I think with the snowballing you mean things like iterative self distillation? That’s definitely not done unsupervised, because of the risk of model collapse, and typically heavily curated and/or mixed with real data.