So a major aspect of cortex will be inverse and forward learning. This idea was inspired by some birdsong work, but I can't find the papers.
The big question is how does the brain do something like one-shot learning? Birds can hear something and then produce almost the identical output, but how?
The answer is that through feedback birds can learn how their motor commands map onto auditory commands and vice-versa. The idea is that young birds are babbling - randomly searching through their motor outputs. The babbles are a direct result of certain motor neurons firing. The action-potentials of these neurons are sent via efferent copy to the sensory areas. The sensory neurons at the same time receive the auditory feedback of the actual sound produced by the babble, these spikes are also sent to the motor neurons.
So with the feeback, both directions of learning can take place. The sensory neuron that responded to a particular sound can learn which motor neurons make that sound. The motor neurons that produce a particular sound can learn which sensory neurons hear that sound. So, when a bird hears a sound, the bird has already learned how sounds map onto the motor-neurons. It would then be pretty easy to activate the same motor-neurons to produce a similar sound.
The thing is, you don't even need the actual sound to do this. A spike from thalamus to cortex will activate a bunch of cortical neurons who send their spikes back. So thalamus can learn which neurons it activates. Similary a spike from cortex will activate thalamus and send spikes back. So cortex can learn its mapping back to thalamus. During the wakefulnesss, thalamus is being set by the environment - so cortex can learn features of the environment. During sleep, cortex can learn its features by activating thalamus and seeing which neurons turn on. This is essentially generative modeling, as cortex is learning what its features are in thalamus. Then you can extend this up the hierarchy.
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