# Evaluating Token-Level and Passage-Level Dense Retrieval Models for Math Information Retrieval

arXiv: https://arxiv.org/abs/2203.11163 · HTML: https://mlsanity.com/paper/2203.11163/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2022.

## Built on by (most cited first, 9 of 9)

- [PLAID: An Efficient Engine for Late Interaction Retrieval](https://mlsanity.com/paper/2205.09707/) (2022)
- [A Semantic Search Engine for Mathlib4](https://mlsanity.com/paper/2403.13310/) (2024)
- [A Symbolic Framework for Evaluating Mathematical Reasoning and Generalisation with Transformers](https://mlsanity.com/paper/2305.12563/) (2023)
- [DataFinder: Scientific Dataset Recommendation from Natural Language Descriptions](https://mlsanity.com/paper/2305.16636/) (2023)
- [Generalized Tree Edit Distance (GTED): A Faithful Evaluation Metric for Statement Autoformalization](https://mlsanity.com/paper/2507.07399/) (2025)
- [A Survey in Mathematical Language Processing](https://mlsanity.com/paper/2205.15231/) (2022)
- [MIRB: Mathematical Information Retrieval Benchmark](https://mlsanity.com/paper/2505.15585/) (2025)
- [Controlling Equational Reasoning in Large Language Models with Prompt Interventions](https://mlsanity.com/paper/2307.09998/) (2023)
- [Fuzzy Norm-Explicit Product Quantization for Recommender Systems](https://mlsanity.com/paper/2412.06069/) (2024)

## Abstract (arXiv)

With the recent success of dense retrieval methods based on bi-encoders, studies have applied this approach to various interesting downstream retrieval tasks with good efficiency and in-domain effectiveness. Recently, we have also seen the presence of dense retrieval models in Math Information Retrieval (MIR) tasks, but the most effective systems remain classic retrieval methods that consider hand-crafted structure features. In this work, we try to combine the best of both worlds: a well-defined structure search method for effective formula search and efficient bi-encoder dense retrieval models to capture contextual similarities. Specifically, we have evaluated two representative bi-encoder models for token-level and passage-level dense retrieval on recent MIR tasks. Our results show that bi-encoder models are highly complementary to existing structure search methods, and we are able to advance the state-of-the-art on MIR datasets.