Some inhibitory cells are important for active dendrites, but those aren’t in HTM. The ones HTM model target perisomatically, so they don’t operate on distal dendritic segments, just the total excitation level from proximal dendrites.
There are many types of interneurons, many of which aren’t included in HTM in any form. The theories aren’t ready for that yet. Right now, they’re mostly driven by constraints, like what the brain must do and whether it could implement a hypothetical process. I expect that’ll change quickly at some point in the future.
Other groups will figure out how the cortex works by modelling everything, if that’s the right approach. I don’t think the tools for experimentation are quite at that point yet. They aren’t good enough to use strict statistical standards if a scientist wants to publish anything ever, even though the tools are very advanced. In neuroscience, results are usually reported if there’s less than a 1 in 20 chance of being a statistical anomaly, whereas in particle physics it’s 3.5 million to count as a discovery. That’s pretty extreme, but a 1 in 20 chance of falsehood is actually much higher because if you check a bunch of things there are more false positives. The technology for experimentation is developing pretty quickly, I think, so maybe neuroscience will have the tools to get info for exact modelling in the near future.
Some aspects of the brain are complex systems, but not all of them. For example, an individual neuron isn’t a complex system (I mean, it’s super complicated when you get down to receptors and whatnot, but it’s not a network). What neurons do can say a lot about what the whole thing does. For example, local summation on distal dendrites says there are OR processes going on, and like 90% of synapses between excitatory cortical cells are involved (or some large percent). Other things say things too, like connections and receptive fields.
I think the modeling approach to AI only works if you get all the details right, but neuroscience isn’t there yet. There are exciting new experimental techniques based on genetics, which might develop to the point where that approach works, or might not.