My question is about the article [Linear-Time Self Attention with Codeword Histogram for Efficient Recommendation](https://people.duke.edu/~zg70/papers/LISA_camera_ready.pdf) (depicted in the picture below).

[![enter image description here][1]][1]

It is written in the article $X$ is a matrix (begining section 3.1) but It is seen the figure 2 a sequence of codeword indices represented as a vector and in figure 3 a sequence of codeword indices is represented as a matrix, so I don't understand the these details.

Please explain why the codeword indices are depicted as a vector in figure 2 and as a matrix in Figure 3.


  [1]: https://i.sstatic.net/VfrJO.jpg