So i was studing the paper Adversarial Neural Machine Translation by Lijun Wu1, Yingce Xia2, Li Zhao3, Fei Tian3, Tao Qin3, Jianhuang Lai1,4 and Tie-Yan Liu. The link to the paper is : https://arxiv.org/pdf/1704.06933.pdf

In the paper , for feeding the sentence pairs into a GAN , they converted the word embeddings of the words in particular sentences and and concantenated into a 2D image like format to further perform convolution and pooling on it as is done in a typical GAN implementation.

In the words of the paper ,

The adversary is used to differentiate translation result $y'$ and the ground-truth translation $y$, given the source language sentence $x$. To achieve that, one needs to measure the translative matching degree of source-target sentence pair $(x, y)$. We turn to Convolution Neural Network (CNN) for this task (Yin et al., 2015; Hu et al., 2014), since with its layer- by-layer convolution and pooling strategies, CNN is able to accurately capture the hierarchical corre- spondence of $(x, y)$ at different abstraction levels. The general structure is shown in Figure 2. Specifically, given a sentence pair (x,y), we first construct a 2D image-like representation by simply concatenating the embedding vectors of words in x and y. That is, for i-th word $x_{i}$ in $x$ and j-th word $y_{j}$ in sentence $y$, we have the following feature map: $$z^{0}_{i, j} = [ x_{i}^{T} , y_{j}^{T} ]^{T}$$

I am not able to understand the significance of $x_{i}^{T}$ , basically the $T$ in the equation. Any help would be highly respected.


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