arXiv:2511.01364cs.IRcs.LG2025-11

用深度学习提取数学表达式语义特征,实现更精准的检索。

A semantic-based deep learning approach for mathematical expression retrieval

  • 通过循环神经网络提取表达式嵌入特征
  • 在829个表达式上实现三类复杂度分类
  • 基于欧氏距离匹配,支持用户自定义召回数

数学表达式具有复杂的二维结构,符号可嵌套至多层(如上标、下标等)。现有方法多基于字符串匹配或向量空间模型,依赖语法相似性。本文提出一种基于深度学习的语义检索方法:利用深度循环神经网络(DRNN)提取表达式语义特征,并训练网络对表达式复杂度进行分类,按嵌套深度划分为简单、中等、复杂三类。训练完成后,提取网络最后一层全连接前的输出作为语义特征存入数据库。查询时,对输入表达式计算其特征,基于欧氏距离与数据库匹配,返回前k个最近邻结果,其中k由用户指定。实验基于包含829个数学表达式的数据库进行验证。

原文摘要 · Abstract (English)

Mathematical expressions (MEs) have complex two-dimensional structures in which symbols can be present at any nested depth like superscripts, subscripts, above, below etc. As MEs are represented using LaTeX format, several text retrieval methods based on string matching, vector space models etc., have also been applied for ME retrieval problem in the literature. As these methods are based on syntactic similarity, recently deep learning approaches based on embedding have been used for semantic similarity. In our present work, we have focused on the retrieval of mathematical expressions using deep learning approaches. In our approach, semantic features are extracted from the MEs using a deep recurrent neural network (DRNN) and these features have been used for matching and retrieval. We have trained the network for a classification task which determines the complexity of an ME. ME complexity has been quantified in terms of its nested depth. Based on the nested depth, we have considered three complexity classes of MEs: Simple, Medium and Complex. After training the network, outputs just before the the final fully connected layer are extracted for all the MEs. These outputs form the semantic features of MEs and are stored in a database. For a given ME query, its semantic features are computed using the trained DRNN and matched against the semantic feature database. Matching is performed based on the standard euclidean distance and top 'k' nearest matches are retrieved, where 'k' is a user-defined parameter. Our approach has been illustrated on a database of 829 MEs.

数学表达式语义检索深度学习

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。