# Machine Translation Weekly 84: Order Agnostic Cross-Entropy

I tend to be a little biased against autoregressive models. The way they operate: say exactly one subword, think for a while, and then say again exactly one subword, just does not sound natural to me. Moreover, with current models, a subword can be anything from a single character to a word as long as “Ausgußreiniger”. Non-autoregressive models generate everything in a single step. That does seem to be really natural either, but at least they offer an interesting alternative. Hopefully, one day, we can have something in-between these two extremes. Because the day did not come yet, today, I am going to comment on a paper that introduces an interesting loss function for non-autoregressive MT, which might a small step in this direction. The title of the paper is Order-Agnostic Cross Entropy for Non-Autoregressive Machine Translation, it has authors from Tencent AI Lab and will be published at this year’s ICML.

Autoregressive models are trained using the standard cross entropy. In non-autoregressive MT, it gets more interesting. Two possible alternatives to standard cross entropy in non-autoregressive models are Connectionist Temporal Classification and Aligned Cross Entropy. Both loss functions allow blank symbols to be inserted between the output tokens, so the output tokens get better aligned with the decoder states. I hypothesize that this makes reordering that internally needs to happen within the Transformer layers easier (although I have no proof for that). Both these alternatives enforce monotonic alignment between the decoder states and output symbols. After all, if they did not, would force the model to generate the target tokens in the correct order.

And here comes the trick that they use in this paper. They just use two loss functions. One is the standard cross-entropy which enforces the monotonic ordering most straightforwardly. The second one rewards the model for the correct word choice, regardless of the word order. The trick is to compute the maximum matching between the output states and embeddings of the target sentence and align the tokens and the states accordingly. It is nicely illustrated in Figure 1 (on page 2) of the paper:

Indeed, the paper shows improvements in translation quality (otherwise it probably would not get published these days). But what I liked the most about this paper is that it returns an old dichotomy in MT: modeling fluency and adequacy separately but in a very different fashion. Here, the cross-entropy model fluency (and also adequacy, but it has some issues with it), the order agnostic cross-entropy only cares about adequacy. However, unlike the old statistical models, they still have only one model trained end-to-end.

### Share the post

```
@misc{libovicky2021blog0620,
author = "Jindřich Libovický",
title = "Jindřich's Blog -- Machine Translation Weekly 84: Order Agnostic Cross-Entropy",
year = "2021",
month = jun,
url = "https://jlibovicky.github.io/2021/06/20/MT-Weekly-Order-Agnostic-Cross-Entropy",
note = "Online, Accessed: 06.09. 2022"
}
```