Comment by kastnerkyle

RNN for discrete structured prediction tasks often use a technique called beam search during decoding (see for example papers on neural MT), which is about as close as you can get to a true Viterbi when you don't have independence assumptions. The CTC mentioned above is also a special type of "reductionist" dynamic programming which uses some awesome and clever stuff to remain backproppable. It only works for monotonic alignments (input larger than desired output).