这篇论文把科学公式的语法和语义分开建模再对齐，发现原生表示差异很大，但对比学习能救回来，做检索的可以看看。
该研究探讨科学公式的语法与语义两种模态的对应关系，发现其原生表示空间虽存在潜在相关性，但可观察对应极弱。作者用图编码器表示语法结构、文本编码器表示语义信息，并通过对比学习构建共享空间。实验表明，学习到的对齐显著提升跨模态检索性能。
Syntax Meets Semantics: Understanding Scientific Formulae
Scientific formulae are a fundamental component of scholarly communication, yet their dual nature -- as structured syntax and carriers of semantics -- remains underexplored in scholarly information retrieval. Although prior studies show that jointly modeling syntactic and semantic modalities improves retrieval performance, the relationship between their underlying representations has not been systematically investigated. In this work, we empirically study cross-modal correspondence between formula syntax and semantics. We find that their native representation spaces exhibit extremely weak observable correspondence despite strong latent correlation, indicating a substantial representation mismatch between the two modalities. We further evaluate whether this mismatch can be reduced using standard representation learning and alignment techniques. We represent syntactic structure using graph-based encoders and semantic information using text-based encoders, then apply contrastive learning to induce a shared representation space. Results show that the learned alignment substantially improves cross-modal retrieval, suggesting that explicit representation learning can recover correspondence absent from the original representation spaces.