Two points:
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With hierarchy, I would expect a higher level to feedback a context framing the sequence. In practice, this might look like the HTM time input encoder with the current input time fields staying the same and a new “context field” feedback from a higher level.
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Do we have some HTM way of establishing a circular/repetitive task with online learning? This should be an important research line as this is a common task in the brain. The “central pattern generator” comes to mind. Granted - this is a lower brain function but I would not think it out of line to add a mechanism to do this with canonical HTM.