You could automatically encode a KNN model as a set of logical if-then rules: "if x1 > 10 and x2 < 3 then 4 nearest labels are [1, 1, 1, 0]" so the information

You could automatically encode a KNN model as a set of logical if-then rules: "if x1 > 10 and x2 < 3 then 4 nearest labels are [1, 1, 1, 0]" so the information is there. For KNN you could also train weights for every variable (how much should they count in the distance calculation?). For deep learning you have way more parameters and architecture choices than for nearest neighbors (mostly the distance metric and the number of neighbors to consider). After that, both learn a mapping from input data to a target.