# Machine Translation Weekly 43: Dynamic Programming Encoding

One of the narratives people (including me) love to associate with neural machine translation is that we got rid of all linguistic assumptions about the text and let the neural network learn their own way independent of what people think about language. It sounds cool, it almost gives a science-fiction feeling. What I think that we really do is that we move our assumptions about language from hard constrains of discrete representation into soft constraints of inductive biases that we impose on our neural architecture.

This is also the case of the paper I am going to discuss today. It throws away the assumption that input should be tokenized into words that unigram statistics are a good heuristic for segmentation. This is replaced by fully learned segmentation that should be tailored specifically to the task of machine translation. The title of the paper is Dynamic Programming Encoding for Subword Segmentation in Neural Machine Translation, it has authors from the Monash University and from Google Research and will appear on this year’s ACL conference.

The main idea of the paper is to build a hybrid character-subword decoder: character on the input, subwords on the output. It is a standard autoregressive decoder that conditions the current output on what it generated before. The inputs to the decoder are characters, but the outputs of the decoder are subwords. At inference time, it would look like in the following figure:

The more interesting question is, how such a model can be trained. The paper introduces a simple dynamic programming algorithm that can sum probabilities of all possible subword segmentation of the input even though there is exponentially many of them and it would never be possible to enumerate them explicitly. The reason why they can use the dynamic programming algorithm is that the state of the decoder does not depend on what subwords were previously chosen, but only on what characters the subwords consist of.

Unlike the figure above, the algorithm does not care what the next step will be, it rather asks what must have happened, so that the decoder ended up in the $i$-th state. It iterates over all possible subwords that might have been the last step that caused the decoder to end up in the $i$-th state. For all of them, we already computed the probability was assigned to the state.

Although the model is a fully functional machine translation model, the authors decided for some reason not to use it so and only used it to learn the segmentation of the target side of parallel data. Similarly to all dynamic programming algorithms of this kind, we can replace the probability summation with argmax (i.e., instead of summing all possibilities, just take always the best one) and thus get the most probable sequence of subwords given the model. This what the authors do and what they use to segment the training data.

So in the end, this interesting model ends up as a very expensive way of preprocessing the training data. It improves the translation quality, it makes a small but significant improvement compared both to standard BPE and BPE dropout. Also, compared to BPE, it leads to segmentation that makes much more sense. This is a selection from Table 4 from the paper (the first column is classical byte-pair encoding, the second column is the new method):

Still, I am quite disappointed that they did not show how the model works when used for translation. Is it that bad? Or the authors did not bother to implement the decoding?

The drawback of this method is that you still need the classical segmentation of the source. At inference time, we do not need to care about the target-side segmentation, we will use whatever the decoder generates, but the source sentence, of course, needs to get segmented before it is fed into the encoder. I was thinking if a similar approach could be used also for the source sentence… and unfortunately probably not. But maybe someone else will figure it out. Anyway, I still believe that this paper is an important step on the way of getting rid of any pre-defined text segmentation and making one step further in not making much assumptions about language.