While the lower bounds on Kantorovich distance computed by the method provide valuable insights into the difference between output distributions, there may be opportunities to tighten these bounds further. One approach to potentially tightening the lower bounds is to refine the analysis by considering additional factors or metrics that could provide more precise information about the similarity or dissimilarity of the output distributions. This could involve incorporating more complex metrics or refining the analysis process to capture more nuanced aspects of the output distributions. By enhancing the analysis methodology and considering more detailed information, it may be possible to achieve tighter lower bounds on the Kantorovich distance.