Part of the machinery is a cylinder that orchestrates various very low level operations this means that the Jacquard cards can specify a higher level operation. Exactly how sophisticated it is, or is supposed to be, I'm not sure.

And now that you've challenged me I can't remember where I saw this piece of information. Time for a quick web search.

Found something, I don't think this is where i saw it first but it will do:

"Later drawings (1858) depict a regularised grid layout.[18][19] Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, roughly equivalent to microcode in modern CPUs, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify.[7]"

https://en.wikipedia.org/wiki/Analytical_engine