Generate random matrices of a user-specified size, and in a single location set a pixel to true in half of them, and false in the other half. Quickly train a convolutional neural network to classify the matrices ('class' 1 vs 'class 2'). Then use a deep dream image to find the location of the single informative bit.
This is a very simple but powerful example. "Traditional" machine learning algorithms fail (a long, slow failure). The CNN converges quickly! The binary matrices can be rectangular, or they can be vectors. The data could represent almost anything...a single nucleotide variant in aligned genomes, a fraudulent transaction in a ledger, ....