# ICAL: Implicit Character-Aided Learning for Enhanced Handwritten Mathematical Expression Recognition

arXiv: https://arxiv.org/abs/2405.09032 · HTML: https://mlsanity.com/paper/2405.09032/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Modeling Coverage for Neural Machine Translation](https://mlsanity.com/paper/1601.04811/) (2016)
- [Syntax-Aware Network for Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2203.01601/) (2022)
- [Multi-Scale Attention with Dense Encoder for Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/1801.03530/) (2018)
- [When Counting Meets HMER: Counting-Aware Network for Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2207.11463/) (2022)
- [Handwritten Mathematical Expression Recognition with Bidirectionally Trained Transformer](https://mlsanity.com/paper/2105.02412/) (2021)
- [CoMER: Modeling Coverage for Transformer-based Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2207.04410/) (2022)
- [Handwritten Mathematical Expression Recognition via Attention Aggregation based Bi-directional Mutual Learning](https://mlsanity.com/paper/2112.03603/) (2021)

## Built on by (most cited first, 4 of 4)

- [TAMER: Tree-Aware Transformer for Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2408.08578/) (2024)
- [Uni-MuMER: Unified Multi-Task Fine-Tuning of Vision-Language Model for Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2505.23566/) (2025)
- [GryphOne: Symbol-Aware Masked Diffusion for Structural Refinement in Offline Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2602.03370/) (2026)
- [Link prediction Graph Neural Networks for structure recognition of Handwritten Mathematical Expressions](https://mlsanity.com/paper/2511.02288/) (2025)

## Abstract (arXiv)

Significant progress has been made in the field of handwritten mathematical expression recognition, while existing encoder-decoder methods are usually difficult to model global information in LaTeX. Therefore, this paper introduces a novel approach, Implicit Character-Aided Learning (ICAL), to mine the global expression information and enhance handwritten mathematical expression recognition. Specifically, we propose the Implicit Character Construction Module (ICCM) to predict implicit character sequences and use a Fusion Module to merge the outputs of the ICCM and the decoder, thereby producing corrected predictions. By modeling and utilizing implicit character information, ICAL achieves a more accurate and context-aware interpretation of handwritten mathematical expressions. Experimental results demonstrate that ICAL notably surpasses the state-of-the-art(SOTA) models, improving the expression recognition rate (ExpRate) by 2.25%/1.81%/1.39% on the CROHME 2014/2016/2019 datasets respectively, and achieves a remarkable 69.06% on the challenging HME100k test set. We make our code available on the GitHub: https://github.com/qingzhenduyu/ICAL