about the LNN structure as follows.

- At the coarsest resolution, the main function of the trained LNN is decomposed into Clusters $1$, $2$, $3$ and $4$. Cluster $1$ captures the input information about black pixels in the shape of a $6$ and white pixels in the shape of a $7$, and it has a positive and negative correlation with the output dimensions corresponding to “6” and “7”, respectively. Cluster $2$ correlates negatively with the region in the shape of a $9$, and positively with the other areas. It has a positive correlation with the recognition of “2” and “6,” and it has a negative one with “0,” “4” and “9.” Cluster $3$ correlates positively with the black pixels in the left part of an image, and it has a positive correlation with “0,” “4” and “6,” and a negative correlation with “3” and “7.” Cluster $4$ captures the 0-shaped region, and it has a larger correlation with the output of “0” compared with the other digits.

- Cluster $2$ is decomposed into three smaller clusters, $7$, $8$ and $9$. Cluster $7$ captures similar input information to Cluster $2$, and it also correlates strongly with the lower area of an 