It's not so much "making an AI from a compressor" as "making a compressor from 
an AI." Specifically, it has to be a kind of AI that predicts the next element 
in a sequence if given past elements of the sequence.

You run your prediction algorithm on the file you wish to compress, and store 
only those elements in the sequence that differ from the element your algorithm 
predicted at that position. Store the errors, in other words. You can then 
regenerate the original file (decompress) by running your algorithm and 
substituting the stored errors into the output.

If your algorithm requires training, then you should be able to train it on any 
representative example of the kind of data you want to compress.
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Artificial General Intelligence List: AGI
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