Along with the paper, we have uploaded the cancer by cancer Boltzmann Semantic Score on each dataset for all the $k$s in $\{1, 3, 5, 20, 50\}$ 
in the supplementary materials. Please note that the error bars in the plots are \textbf{the variability of each LVM over different patients}. 
Thus, error bars are huge for small $k$s which shows the intesne variability of LVMs. However, as $k$ increases, the average Boltzmann  Semantic
 Score increases and the variability reduces, which is mainly because it is easier for LVMs to find matches in bigger state spaces. 
However, we believe $k=5$ is a good choice which is not too tight nor too loose that loses it's sensitivity. 

Please note that the supplementary materials is organized in a way that the directory names are the cancer types, and the name of each '.png' file
 shows the name of the file with full details. 
For example, '/BRCA/top-1\_Coral-Gemma-7b-Jamba-Llama3-8b-Bio-Llama3-8b.png' shows that it belongs to BRCA cancer, and it is the average BSS calculated based on $k=1$.