---
license: apache-2.0
datasets:
- ddrg/math_text
- ddrg/math_formulas
- ddrg/math_formula_retrieval
- ddrg/named_math_formulas
language:
- en
base_model:
- google-bert/bert-base-cased
---
# MAMUT-Bert (Math Mutator BERT)

<!-- Provide a quick summary of what the model is/does. -->

MAMUT-BERT is a pretrained language model based on [bert-base-cased](https://huggingface.co/bert-base-cased), further pretrained on mathematical texts and formulas.
It was introduced in [MAMUT: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training](https://arxiv.org/abs/2502.20855).

The model aims to provide improved mathematical understanding by extending BERT with domain-specific knowledge from mathematical LaTeX formulas and terminology. 

## Model Details

### Overview

MAMUT-BERT was pretrained on four math-specific tasks across four datasets.

- **[Mathematical Formulas (MF)](https://huggingface.co/datasets/ddrg/math_formulas):** A Masked Language Modeling (MLM) task on math formulas written in LaTeX.
- **[Mathematical Texts (MT)](https://huggingface.co/datasets/ddrg/math_text):** An MLM task on natural language text containing inline LaTeX math (*mathematical texts*). The masking probability was biased toward mathematical tokens (inside math environment $...$) and domain-specific terms (e.g., *sum*, *one*, ...)
- **[Named Math Formulas (NMF)](https://huggingface.co/datasets/ddrg/named_math_formulas):** A Next-Sentence-Prediction (NSP)-style task: given a formula and the name of a mathematical identity (e.g., Pythagorean Theorem), classify whether they match.
- **[Math Formula Retrieval (MFR)](https://huggingface.co/datasets/ddrg/math_formula_retrieval):** Another NSP-style task to decide if two formulas describe the same mathematical identity or concept.

![Training Overview](mamutbert-training.png)

To support mathematical syntax, *300 additional mathematical [LaTeX-specific tokens](added_tokens.json)* were added to the tokenizer, e.g., `\sum`, `\frac`, and `pmatrix`.


### Model Sources

<!-- Provide the basic links for the model. -->


- **Base Model:** [bert-base-cased](https://huggingface.co/google-bert/bert-base-cased)
- **Pretraining Code:** [aieng-lab/transformer-math-pretraining](https://github.com/aieng-lab/transformer-math-pretraining)
- **MAMUT Repository:** [aieng-lab/math-mutator](https://github.com/aieng-lab/math-mutator)
- **Paper:** [MAMUT: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training](https://arxiv.org/abs/2502.20855)

## Uses

<!-- Address questions around how the model is intended to be used, including the foreseeable users of the model and those affected by the model. -->

MAMUT-BERT is intended for downstream tasks that require improved mathematical understanding, such as:

- Formula classification
- Retrieval of *semantically* similar formulas
- Math-related question answering

**Note: This model was saved without the MLM or NSP heads and requires fine-tuning before use in downstream tasks.**

Similarly trained models are [MAMUT-MathBERT based on `tbs17/MathBERT`](https://huggingface.co/aieng-lab/MathBERT-mamut) and [MAMUT-MPBERT based on `AnReu/math_structure_bert`](https://huggingface.co/ddrg/math_structure_bert) (best of the three models according to our evaluation).


## Training Details

Training configurations are described in [Appendix C of the MAMUT paper](https://arxiv.org/abs/2502.20855).


## Evaluation

<!-- This section describes the evaluation protocols and provides the results. -->

The model is evaluated in [Section 7 and Appendix C.4 of the MAMUT paper](https://arxiv.org/abs/2502.20855) (MAMUT-BERT).


## Environmental Impact

<!-- Total emissions (in grams of CO2eq) and additional considerations, such as electricity usage, go here. Edit the suggested text below accordingly -->

- **Hardware Type:** 8xA100
- **Hours used:** 48
- **Compute Region:** Germany


## Citation

<!-- If there is a paper or blog post introducing the model, the APA and Bibtex information for that should go in this section. -->

**BibTeX:**

```bibtex
@article{
  drechsel2025mamut,
  title={{MAMUT}: A Novel Framework for Modifying Mathematical Formulas for the Generation of Specialized Datasets for Language Model Training},
  author={Jonathan Drechsel and Anja Reusch and Steffen Herbold},
  journal={Transactions on Machine Learning Research},
  issn={2835-8856},
  year={2025},
  url={https://openreview.net/forum?id=khODmRpQEx}
}
```