---
title: "Syntax Meets Semantics: Understanding Scientific Formulae"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2608.02457v1"
permalink: "https://feed.astralor.com/items/itm_02abe418117c181fb1043adc"
published: "2026-08-03T16:31:06.000Z"
score: 76
channel: "ai"
tags: ["Contrastive Learning","Scientific Formulae","Representation Learning","Cross-modal Retrieval"]
---

# Syntax Meets Semantics: Understanding Scientific Formulae

## AI commentary

> What excites me about this paper is that it redefines formulae as dual-modality objects rather than mere symbol strings, which is especially valuable for those working on academic search, knowledge graphs, and AI-assisted review. The contrastive learning path it proposes is straightforward enough to test directly in existing systems.

## At a glance

Scientific formulae are essential in scholarly communication, yet their dual nature as structured syntax and carriers of semantics remains underexplored in retrieval systems. Previous work shows that jointly modeling syntax and semantics improves performance, but the relationship between their underlying representations is rarely examined. In this study, the authors represent formula syntax with graph-based encoders and semantics with text-based encoders. They find that the native representation spaces of these two modalities exhibit extremely weak observable correspondence, despite a strong latent correlation. This indicates a substantial representation mismatch. They then apply contrastive learning to induce a shared representation space. The learned alignment substantially improves cross-modal retrieval performance. The results suggest that explicit representation learning can recover correspondence that is absent in the original spaces. This work provides fresh insight into how scientific formulae can be better understood and retrieved, and it offers a practical path for improving scholarly information retrieval systems.

## Key points

- Scientific formulae have dual attributes of syntax and semantics, yet their relationship is rarely leveraged in retrieval systems.
- Experiments reveal that native formula syntax and semantics representation spaces show very weak observable correspondence but strong latent correlation.
- Applying contrastive learning with graph and text encoders effectively creates a shared representation space.
- Aligned cross-modal retrieval performance improves substantially, confirming the value of explicit representation learning.

## Full text

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.

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