Consider the lempel-ziv compression algorithm. Suppose I generate one billion pairs of uncompressed and compressed data. Consider this the training set. Could a deep learning algorithm be trained to give an uncompressed answer given a compressed sample as a test? Which deep learning model would be best for this? It might seem this problem is congruent to language translation where word pairs are equated. Beyond the simple case of comparing words in isolation, more advanced deep learning algorithms look at words in context but this has no analog in the example I gave above. Is there a way to measure the 'accuracy' of the deep learning algorithm' based on the size of the training set?
Beyond this trivial example (which I unfortunately do not have the resources to test) is a more useful problem. Can deep learning be applied to cryptanalysis in this way. Suppose I have a bunch of encrypted messages and their clear text equivalents but I do not have the algorithm for encryption/decryption. Can a deep learning algorithm be trained to decrypt anything encrypted by this algorithm from the freetext/encrypted pairs that I have? Is there a way to calculate 'error bars' for this algorithm as a function of the number of freetext/encrypted pairs?