My question is about the algorithm in the article Linear-Time Self Attention with Codeword Histogram for Efficient Recommendation, as described in the picture below.

It is written at beginning section 3.1 in the article $X$ is a matrix 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 these details.

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