README.md

---
license: mit
multilinguality: multilingual
task_categories:
- multiple-choice
pretty_name: Tokenization Robustness Math
tags:
- tokenization
- mathematics
dataset_info:
- config_name: tokenizer_robustness_completion_math_canonical
  features:
  - name: question
    dtype: string
  - name: choices
    list: string
  - name: answer
    dtype: int64
  - name: answer_label
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  - name: subcategories
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  - name: category
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  - name: lang
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  - name: second_lang
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  - name: notes
    dtype: string
  - name: id
    dtype: string
  - name: set_id
    dtype: string
  - name: variation_id
    dtype: string
  - name: vanilla_cos_sim_to_canonical
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    - name: Qwen/Qwen3-8B
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    - name: bigscience/bloom
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    - name: common-pile/comma-v0.1-1t
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    - name: google-bert/bert-base-multilingual-cased
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    - name: google/byt5-small
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    - name: google/gemma-2-2b
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    - name: gpt2
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    - name: meta-llama/Llama-3.2-1B
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    - name: microsoft/Phi-3-mini-4k-instruct
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    - name: mistralai/tekken
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    - name: tiktoken/gpt-4o
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    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: float64
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    - name: Qwen/Qwen3-8B
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    - name: gpt2
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    - name: microsoft/Phi-3-mini-4k-instruct
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    - name: mistralai/tekken
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    - name: tiktoken/gpt-4o
      dtype: float64
    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: float64
  - name: token_counts
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    - name: Qwen/Qwen3-8B
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    - name: bigscience/bloom
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    - name: common-pile/comma-v0.1-1t
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    - name: facebook/xglm-564M
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    - name: google-bert/bert-base-multilingual-cased
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    - name: google/byt5-small
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    - name: google/gemma-2-2b
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    - name: gpt2
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    - name: meta-llama/Llama-3.2-1B
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    - name: microsoft/Phi-3-mini-4k-instruct
      dtype: int64
    - name: mistralai/tekken
      dtype: int64
    - name: tiktoken/gpt-4o
      dtype: int64
    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: int64
  splits:
  - name: test
    num_bytes: 11202
    num_examples: 21
  download_size: 29976
  dataset_size: 11202
- config_name: tokenizer_robustness_completion_math_chinese
  features:
  - name: question
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  - name: choices
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  - name: answer
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  - name: id
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  - name: set_id
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  - name: variation_id
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  - name: vanilla_cos_sim_to_canonical
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    - name: tokenmonster/englishcode-32000-consistent-v1
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    - name: tiktoken/gpt-4o
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  - name: token_counts
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    - name: Qwen/Qwen3-8B
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    - name: google/byt5-small
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    - name: gpt2
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    - name: microsoft/Phi-3-mini-4k-instruct
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    - name: mistralai/tekken
      dtype: int64
    - name: tiktoken/gpt-4o
      dtype: int64
    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: int64
  splits:
  - name: test
    num_bytes: 11147
    num_examples: 21
  download_size: 34445
  dataset_size: 11147
- config_name: tokenizer_robustness_completion_math_decorative_unicode
  features:
  - name: question
    dtype: string
  - name: choices
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  - name: answer
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    - name: tiktoken/gpt-4o
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    - name: tokenmonster/englishcode-32000-consistent-v1
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  - name: token_counts
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    - name: microsoft/Phi-3-mini-4k-instruct
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    - name: mistralai/tekken
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    - name: tiktoken/gpt-4o
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    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: int64
  splits:
  - name: test
    num_bytes: 11986
    num_examples: 21
  download_size: 34660
  dataset_size: 11986
- config_name: tokenizer_robustness_completion_math_farsi
  features:
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  - name: choices
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    - name: tiktoken/gpt-4o
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    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: int64
  splits:
  - name: test
    num_bytes: 12034
    num_examples: 21
  download_size: 34859
  dataset_size: 12034
- config_name: tokenizer_robustness_completion_math_italian
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  splits:
  - name: test
    num_bytes: 11219
    num_examples: 21
  download_size: 34631
  dataset_size: 11219
- config_name: tokenizer_robustness_completion_math_latex
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    - name: tokenmonster/englishcode-32000-consistent-v1
      dtype: int64
  splits:
  - name: test
    num_bytes: 11494
    num_examples: 21
  download_size: 34230
  dataset_size: 11494
- config_name: tokenizer_robustness_completion_math_space_removal
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configs:
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  data_files:
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    path: tokenizer_robustness_completion_math_canonical/test-*
- config_name: tokenizer_robustness_completion_math_chinese
  data_files:
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    path: tokenizer_robustness_completion_math_chinese/test-*
- config_name: tokenizer_robustness_completion_math_decorative_unicode
  data_files:
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    path: tokenizer_robustness_completion_math_decorative_unicode/test-*
- config_name: tokenizer_robustness_completion_math_farsi
  data_files:
  - split: test
    path: tokenizer_robustness_completion_math_farsi/test-*
- config_name: tokenizer_robustness_completion_math_italian
  data_files:
  - split: test
    path: tokenizer_robustness_completion_math_italian/test-*
- config_name: tokenizer_robustness_completion_math_latex
  data_files:
  - split: test
    path: tokenizer_robustness_completion_math_latex/test-*
- config_name: tokenizer_robustness_completion_math_space_removal
  data_files:
  - split: test
    path: tokenizer_robustness_completion_math_space_removal/test-*
- config_name: tokenizer_robustness_completion_math_spelled_out
  data_files:
  - split: test
    path: tokenizer_robustness_completion_math_spelled_out/test-*
- config_name: tokenizer_robustness_completion_math_turkish
  data_files:
  - split: test
    path: tokenizer_robustness_completion_math_turkish/test-*
language:
- en
- fa
- zh
- it
- tr
size_categories:
- n<1K
---
# Dataset Card for Tokenization Robustness (Math)

<!-- Provide a quick summary of the dataset. -->

<img src="toksuite-logo.png" alt="TokSuite Logo" width="250px" style="margin-left:'auto' margin-right:'auto' display:'block'"/>

# TokSuite Benchmark (Math Collection)

## Dataset Description

This dataset is part of **TokSuite**, a comprehensive benchmark designed to measure how different tokenization strategies affect language model behavior under controlled conditions.

This specific subset focuses on **mathematical text completion**, containing multiple-choice math questions with a variety of **surface-form perturbations** that stress tokenizer handling of numbers, symbols, formatting, scripts, and mathematical notation.

- **Curated by:** R3 Research Team  
- **Domain:** Mathematics  
- **License:** MIT License  

### Dataset Summary

TokSuite isolates the impact of tokenization by holding **model architecture, training data, training budget, and initialization constant**, varying only the tokenizer.

The Math benchmark evaluates performance on:
- A **canonical mathematical formulation**
- Multiple **perturbed variants** that preserve mathematical meaning while altering surface representation

These perturbations reflect realistic variation in how mathematical expressions are written, formatted, localized, and queried in practice.

**Key Features:**
- 21 canonical math questions with unambiguous answers
- Perturbations targeting notation, symbols, scripts, and formatting
- Parallel structure with TokSuite language benchmarks
- Designed for **evaluation**, not training

### Supported Tasks

- **Multiple-Choice Math Question Answering**
- **Tokenizer Robustness Evaluation**
- **Symbolic and Numerical Text Processing**

---

## Dataset Structure

### Data Fields

| Field | Type | Description |
|------|------|-------------|
| `question` | `string` | Mathematical question text |
| `choices` | `list[string]` | Multiple-choice answer options |
| `answer` | `int64` | Index of the correct answer |
| `answer_label` | `string` | Letter label of the correct answer |
| `split` | `string` | Dataset split identifier (all entries are `test`) |
| `subcategories` | `string` | Perturbation category |
| `lang` | `string` | Domain identifier (`math`) |
| `notes` | `string` | Additional context about the perturbation |
| `id` | `string` | Unique question identifier |
| `set_id` | `float64` | Question set grouping identifier |
| `variation_id` | `float64` | Variation number within a question set |
| `vanilla_cos_sim_to_canonical` | `dict[string, float]` | Cosine similarity to canonical form using raw token sequences |
| `trimmed_cos_sim_to_canonical` | `dict[string, float]` | Cosine similarity after token normalization |
| `token_counts` | `dict[string, int]` | Number of tokens produced per tokenizer |

---

## Dataset Creation

### Curation Rationale

This dataset was created to:
1. Systematically evaluate tokenizer robustness on **mathematical notation and structure**
2. Measure sensitivity to changes in formatting, symbols, scripts, and numeric representation
3. Isolate tokenization effects from mathematical reasoning difficulty
4. Provide standardized benchmarks for math-focused language models

Canonical questions are intentionally **simple and high-accuracy**, allowing researchers to attribute performance degradation to tokenization rather than reasoning complexity.

### Source Data

- Canonical math questions were manually authored
- Each question was perturbed while preserving mathematical equivalence
- Canonical accuracy was validated across TokSuite models

---

## Perturbation Categories (Math)

1. **Canonical**  
The baseline mathematical text written in a standard, well-formatted form with no perturbations. This serves as the reference condition for evaluating all other perturbations.

2. **Chinese**  
Rewrites mathematical text using Chinese characters for numbers, operators, or surrounding descriptions, testing tokenizer robustness to non-Latin scripts in math contexts.

3. **Decorative Unicode**  
Replaces standard mathematical symbols with visually similar decorative or stylized Unicode characters (e.g., fancy numerals or operators), stressing Unicode normalization and symbol handling.

4. **Farsi**  
Introduces Persian (Farsi) numerals or script elements into mathematical expressions, testing tokenizer robustness to right-to-left scripts and cross-script numeric representations.

5. **Italian**  
Rewrites textual components of math problems in Italian while preserving the same mathematical structure and solution.

6. **LaTeX**  
Encodes mathematical expressions using LaTeX-style syntax (e.g., `\frac`, `^`, `_`), stressing tokenizer handling of markup-heavy mathematical notation.

7. **Space Removal**  
Removes or alters spacing within mathematical expressions and surrounding text, stressing tokenizer assumptions about whitespace in math contexts.

8. **Spelled-Out Forms**  
Replaces numerals or symbols with fully spelled-out textual equivalents (e.g., numbers written as words), increasing sequence length and altering token boundaries.

9. **Turkish**  
Rewrites textual components of math problems in Turkish while preserving the underlying mathematical meaning.

---

## Considerations for Using the Data

- **Language variety:** The dataset uses standard mathematical notation and English-language math phrasing, and may not represent informal or pedagogical math language.
- **Script focus:** Mathematical expressions are primarily written using ASCII and standard Unicode; LaTeX, decorative Unicode, and non-Latin scripts are included as perturbations.
- **Domain coverage:** Questions focus on general mathematics and may not represent highly specialized or advanced mathematical domains.
- **Question simplicity:** Designed for high baseline accuracy, which may not reflect real-world mathematical task complexity.

---

## Additional Information

### Dataset Curators

The dataset was curated by the TokSuite research team at R3.

### Licensing Information

MIT License

### Citation Information

If you use this dataset in your research, please cite the TokSuite paper:

```bibtex
@inproceedings{toksuite2026,
  title={TokSuite: Measuring the Impact of Tokenizer Choice on Language Model Behavior},
  author={Altıntaş, Gül Sena and Ehghaghi, Malikeh and Lester, Brian and Liu, Fengyuan and Zhao, Wanru and Ciccone, Marco and Raffel, Colin},
  year={2026}
}
```

**Paper**: [TokSuite: Measuring the Impact of Tokenizer Choice on Language Model Behavior](TBD)

### Contributions

This dataset is part of TokSuite, which includes:
- 14 language models with identical architectures but different tokenizers
- Multilingual benchmark datasets (English, Turkish, Italian, Farsi, Chinese)
- Comprehensive analysis of tokenization's impact on model behavior


### Contact

For questions or issues related to this dataset, please refer to the TokSuite project or contact the authors of the paper.

---

<div align="center">
  
**Part of the [TokSuite Project](TBD)**

*Understanding Tokenization's Role in Language Model Behavior*

</div>