Can HTM predict previous inputs?

My opinion that this issue needs the hierarchy is because, if I have correctly understood your question, the sequence memory does not seem to be sufficient to solve this by itself, I think it is a process that involves semantic memory and, as far as I know, the semantic knowledge is stored in distinct associative cortices and its evocation depends on the pre-frontal cortex. I started studying the HTM theory a short time ago and I’m not familiar with the nupic, so I can not help you much more, it would be better someone with more experience to comment on it.
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