I have started investigating the HTM in a math perspective, I’m no math guru but my intuition in math is my strength (more on reading and less on formulating). And yes, I see set theory is very well fitting to express the operations in HTM. In relation to this, based on my investigation, I find the Automaton and Information Theory, have the potential also to express some parts of the HTM.
It’s too early to discuss this (without me giving any proof), but the HTM’s emergent algorithm has a lot of similarities with the Ant Colony Algorithm/Optimization which have been widely used already. However, like the ACO it is quite hard to prove if the algorithm is optimizing or not (mathematically) even if we know it is working. Also the reason why it’s somewhat useless to do a “DL vs. HTM” as if they are competing algos because they fall in roughly different domains.
I also think that (by intuition) the SP and TM are doing the same algorithm, except that they operate on different levels of abstraction.