Transformers, while not exactly functions, don't have a feedback mechanism similar to e.g. the cortical algorithm or any other neuronal structure I'm aware of. In general, the ML field is less concerned with replicating neural mechanisms than following the objective gradient.
Numenta has attempted to implement a system to this effect (see the wiki page https://en.wikipedia.org/wiki/Hierarchical_temporal_memory) for quite some time with not particularly much success.
Personally I think the kinds of minds we create in silico will end up being very different, because the advantages and disadvantages of the medium are just very different; for example, having a much stronger central processor and much weaker distributed memory, along with specialized precise circuits in addition to probabilistic ones.
(I did AI and Psychology at degree level, I understand there are definitely also big differences too, like hormones and biological neurones being very async)