My question is about the article Linear-Time Self Attention with Codeword Histogram for Efficient Recommendation (depicted in the picture below).

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 this detail of the article.