# PA-CDM: Position-Aware Character Detection Matching for Evaluating Handwritten Mathematical Expression Recognition

arXiv: https://arxiv.org/abs/2609.12917 · HTML: https://mlsanity.com/paper/2609.12917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [OmniDocBench: Benchmarking Diverse PDF Document Parsing with Comprehensive Annotations](https://mlsanity.com/paper/2412.07626/) (2024)
- [UniMERNet: A Universal Network for Real-World Mathematical Expression Recognition](https://mlsanity.com/paper/2404.15254/) (2024)
- [Image Over Text: Transforming Formula Recognition Evaluation with Character Detection Matching](https://mlsanity.com/paper/2409.03643/) (2024)
- [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)
- [MathWriting: A Dataset For Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2404.10690/) (2024)
- [PosFormer: Recognizing Complex Handwritten Mathematical Expression with Position Forest Transformer](https://mlsanity.com/paper/2407.07764/) (2024)
- [VEHME: A Vision-Language Model For Evaluating Handwritten Mathematics Expressions](https://mlsanity.com/paper/2510.22798/) (2025)
- [Uni-MuMER: Unified Multi-Task Fine-Tuning of Vision-Language Model for Handwritten Mathematical Expression Recognition](https://mlsanity.com/paper/2505.23566/) (2025)

## Abstract (arXiv)

Handwritten mathematical expression recognition (HMER) is conventionally scored by exact-match rates and string-similarity metrics that are blind to where an error occurs: two predictions with identical token-error counts receive identical scores whether they misplace a subscript or swap the operands of a fraction. Render-based character detection matching (CDM) aligns glyphs robustly but remains position-blind---on controlled fraction-operand swaps it scores 0.8595 where position-aware scoring yields 0.6253. Tree-edit metrics exhibit a complementary blind spot: rewrites outside the parser's normalization coverage are penalized as structural errors (0.8552 where render-based metrics score 1.0). We propose PA-CDM, a position-aware metric that couples character detection matching with position-forest encoding and divergence-level weighting; StructPerturb v2.0, a frozen benchmark of 1,340 controlled perturbation pairs across 15 type--intensity cells; and a cross-metric consistency protocol combining a sensitivity matrix, a human study, and LLM-judge calibration. In a six-annotator study, PA-CDM attains the highest correlation with human judgments among seven automatic metrics (Spearman rho=0.9535, n=990). A frontier LLM judge correlates slightly higher (rho=0.9613) but is costly, nondeterministic, and API-dependent; PA-CDM approaches it at zero marginal cost with deterministic, diagnosable behavior.