The HMM assumption in modeling the semantic structure of surgical videos may have limitations in capturing all the nuances and intricacies of surgical tool interactions. To improve the model and relax this assumption, one approach could be to integrate additional statistical models, such as Conditional Random Fields (CRFs), which can capture more complex dependencies between tools and phases in surgical videos. CRFs allow for the modeling of interdependencies between multiple variables, making them suitable for capturing the complex relationships present in surgical videos. By combining HMMs with CRFs, the model can better capture the dynamic and intricate nature of surgical tool interactions, leading to more accurate and robust predictions.