Align & Translate with Transformers
In this part, we are going to take a deep look into this paper: Jointly Learning to Align and Translate with Transformer Models which was published by Apple Inc. in 2019. The official code for this paper can be found in the official Fairseq GitHub repository: fairseq/joint_alignment_translation.
Since translation and alignment tasks are very closely related, the publishers of this paper presented an approach to train a Transformer model to produce both accurate translations and alignments. The alignments are extracted from the attention probabilities learned during training. This approach produced competitive results compared to other statistical alignment tools such as GIZA++ without sacrificing translation accuracy.
Attention Matrix
In this part, we are going to recap how the encoderdecoder multihead attention sublayer works and how the attention matrix is represented. Let $d_{\text{emb}},\ d_{k},\ d_{v},\ H$ denote the embedding dimension, dimensions of the key and value projections and number of heads, respectively.
The multihead attention between a source sentence of $M$ tokens and a target sentence of $N$ tokens is calculated via the following equation:
\[\text{MultiHead}\left( Q,\ K,\ V \right) = Concat\left( A_{1},\ ...\ A_{H} \right)W^{O}\] \[A_{i} = Attention\left( QW_{i}^{Q},\ KW_{i}^{K},\ VW_{i}^{V} \right) = \text{softmax}\left( \frac{QW_{i}^{Q}\left( KW_{i}^{K} \right)^{T}}{\sqrt{d_{k}}} \right)VW_{i}^{V}\]Where:

$A_{i} \in \mathbb{R}^{M \times N}$ is the Attention matrix of the $i^{th}$ head out of $H$ heads.

$W_{i}^{Q} \in \mathbb{R}^{d_{\text{emb}} \times d_{k}},\ W_{i}^{K} \in \mathbb{R}^{d_{\text{emb}} \times d_{k}},\ W_{i}^{V} \in \mathbb{R}^{d_{\text{emb}} \times d_{v}},\ W^{O} \in \mathbb{R}^{Nd_{v} \times d_{\text{emb}}}$ are projections matrices of the $i^{th}$ head. All of them are learned parameters.
Each alignment matrix $A_{i}$ gives a probability distribution over source/target pair. This distribution is then converted to a discrete alignment by aligning each target word to the corresponding source word with the highest attention probability.
Layer Average Baseline
As we can see from the previous sections, there are multiple heads and multiple layers in the transformer architecture. Which alignment should be considered the correct alignment of the input pair?
In the paper, they found out that the best results come from averaging all attention heads of the secondtolast layer out of the six decoder layers they used. They refer to this as “the layer average baseline”.
Multitask Learning
Multitask learning is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. In this paper, the publishers exploited the correlation between Translation and Alignment tasks to create a multiobjective loss function $\mathcal{L}$:
\[\mathcal{L} = \mathcal{L}_{t} + \lambda\mathcal{L}_{a}\left( A \right)\]Where:

$\lambda$ is a hyperparameters to weigh the importance of these two loss functions.

$\mathcal{L}_{t}$ is the translation loss function given a source sentence $s = \left[ s_{1}\text{…}s_{M} \right]$ and a target sentence $t = \left[ t_{1}\text{…}t_{N} \right]$:
 $\mathcal{L}_{a}$ is the alignment loss:
The alignment loss is calculated in a supervised manner using the layeraverage baseline as the true alignment. First, they converted the true alignments into a probability distribution. Let $G_{N \times M}$ denote a 01 matrix such that $G_{i,j} = 1$ if the $j^{th}$ source token is aligned to the $i^{th}$ target token. Then, they normalized the rows of $G$ to get matrix $G^{p}$.
Calculating the translation loss $\mathcal{L}_{t}$ needs a masked target while calculating the alignment loss $\mathcal{L}_{a}$ needs the target without masking. That’s why the loss function is implemented by executing two forward passes of the decoder model: One with the masking of the future target tokens for computing the translation loss $\mathcal{L}_{t}$ and the other one with no masking for computing the alignment loss $\mathcal{L}_{a}$.
Results
To achieve stateoftheart results, they change to the big transformer configuration with an embedding size of 1024 and 16 attention heads, 6 layers in the encoder and decoder. The total number of parameters is 213M. They trained the transformer with a batch size of 7168 tokens on 64 Volta GPUs for 30k updates and apply a learning rate of $1e^{3}$, $\beta_{1} = 0.9$, $\beta_{2} = 0.98$. The dropout probability is set to $0.3$.
As we can see from this table, the multitask learning with full context (knowing of all target words) and with alignment generated from GIZA++ toolkit achieved the least AER while maintaining the translation BLEU score on two different languagepairs.