# A Scientific Document Retrieval and Reordering Method by Incorporating HFS and LSD
## 4 Experimental Process and Result Analysis
### System Experiment
#### 4.2.3 Comparative Experiment  
To ensure a fair comparison, optimal hyperparameters were selected through grid search or in accordance with the original research papers. SearchOnMath [32] is a specialized tool for mathematical formula retrieval, meticulously designed to accurately match mathematical expressions and retrieve pertinent scientific documents based on these expressions. Tangent-CFT [33], conversely, is a mathematical expression embedding model that utilizes a depth-first search algorithm to transform paths between symbols within the expression tree into a list of symbol tuples. Subsequently, it leverages _FastText_ to retrieve  
Figure 4: Values of nDCG@10 across various datasets.  
mathematical expressions through averaging. For the sake of comparative experiments, ColBERT [34]--a representation-based text matching method--was utilized. Figure 5 presents the literature retrieval results achieved using different methods.  
Figure 5 illustrates the average nDCG (K = 10) values across 10 query expressions when employing various methods. Notably, SearchOnMath [32] and Tangent-CFT [33] solely rely on the information within the mathematical expressions, without taking into account other attributes of scientific documents. This approach can occasionally result in matches with intermediate results from the mathematical reasoning process, potentially leading to the retrieval of scientific literature unrelated to the intended topic. Conversely, ColBERT [34]--characterized by numerous parameters and a large model--concentrates on modeling text content. However, this approach can introduce noise into the retrieval process, ultimately having a detrimental impact on the results.  
The primary objective of the method proposed in this study is to enhance the precision and efficiency of scientific literature retrieval models. As evident in the provided Figure 6, query execution time using different methods is a critical consideration, and it is apparent that the structure of mathematical expressions significantly influences this duration. Specifically, more intricate expressions require more time for execution. Through the process of decomposing mathematical expressions, establishing indexes, and utilizing the distilled model to compute semantic similarity, the method substantially reduces the time required for the model to retrieve the most suitable scientific documents. Consequently, the approach presented in this paper holds a distinct advantage in terms of execution time.  
In summary, the method based on hesitant fuzzy sets and local semantic distillation proves to be a highly efficient and accurate approach for retrieving relevant scientific documents in response to queries. This effectiveness stems from HFS's capability to consider not only the textual content of mathematical expressions but also their structural features, which play a pivotal role in matching both the expressions themselves and their underlying semantics. Furthermore, the model obtained through KD effectively implements the matching of context semantics, resulting in reduced retrieval times. By combining the mathematical expression feature matching module with the use of context semantics to  
Figure 5: Comparison results of NDCG (k = 10) values across different methods.  
re-rank retrieval results, a significant improvement in the accuracy of scientific document retrieval is achieved.