| --- |
| license: gpl-2.0 |
| task_categories: |
| - image-text-to-text |
| - audio-text-to-text |
| - text-generation |
| language: |
| - en |
| tags: |
| - mathematics |
| - arithmetic |
| - multimodal |
| --- |
| |
| # MultimodalMathBenchmarks |
|
|
| This repository contains the datasets for the paper [Multiplication in Multimodal LLMs: Computation with Text, Image, and Audio Inputs](https://huggingface.co/papers/2604.18203) (ACL Findings 2026). |
|
|
| It covers the public benchmark datasets and their modality assets (text, images, and audio) used to evaluate the arithmetic capabilities of multimodal LLMs. |
|
|
| ## Canonical Upload Manifest |
|
|
| | HF path | Local source | Count | Purpose | |
| | --- | --- | ---: | --- | |
| | `SharedMultimodalGrid.csv` | `SavedData/SharedMultimodalGrid.csv` | 10,000 rows | Canonical metadata table for the paired multimodal multiplication benchmark | |
| | `TextFiles/` | `SavedData/TextFiles/` | 10,000 `.txt` files | Text renderings for `mm_*` benchmark items | |
| | `Images/` | `SavedData/Images/` | 10,000 `.png` files | Image renderings for `mm_*` benchmark items | |
| | `AudioFiles/` | `SavedData/AudioFiles/` | 10,000 `.mp3` files | Audio renderings for `mm_*` benchmark items | |
| | `HDSv2.csv` | `SavedData/HDSv2.csv` | 1,000 rows | Canonical heuristic-disagreement probe set | |
| | `HDSv2Images/` | `SavedData/HDSv2Images/` | 144 `.png` files | Image renderings for the `HDSv2` test split only | |
| | `Trapsv2.csv` | `SavedData/Trapsv2.csv` | 30 rows | Canonical adversarial trap set | |
| | `Trapsv2Images/` | `SavedData/Trapsv2Images/` | 30 `.png` files | Image renderings for every trap item | |
|
|
| ## Dataset Summary |
|
|
| The release contains three benchmark families: |
|
|
| 1. `SharedMultimodalGrid.csv` |
| - 10,000 shared multiplication problems paired across text, image, and audio. |
| - Split counts: `train=7026`, `val=1416`, `test=1558`. |
| - Each row uses an `mm_XXXXX` ID that maps directly to: |
| - `TextFiles/mm_XXXXX.txt` |
| - `Images/mm_XXXXX.png` |
| - `AudioFiles/mm_XXXXX.mp3` |
|
|
| 2. `HDSv2.csv` |
| - 1,000 heuristic-disagreement problems for fingerprinting and probe-style evaluation. |
| - Split counts: `train=701`, `val=155`, `test=144`. |
| - `HDSv2Images/` contains exactly the 144 `test`-split item IDs from `HDSv2.csv`. |
|
|
| 3. `Trapsv2.csv` |
| - 30 adversarial trap problems designed to target heuristic-specific failures. |
| - No split column; all rows are held-out trap items. |
| - `Trapsv2Images/` contains one PNG for every row in `Trapsv2.csv`. |
|
|
| ## Dataset Structure |
|
|
| ### Shared Multimodal Grid |
|
|
| Canonical table: `SharedMultimodalGrid.csv` |
|
|
| Columns: |
| `id, a, b, a_times_b, template_a, template_b, digits_a, digits_b, nonzero_a, nonzero_b, digit_total, nonzero_total, complexity_c, stratum_id, split` |
|
|
| Notes: |
| - `id` is the stable benchmark ID, e.g. `mm_00001`. |
| - `a`, `b`, and `a_times_b` are the multiplication operands and exact product. |
| - `digit_total`, `nonzero_total`, and `complexity_c` support difficulty analyses. |
| - `split` is the deterministic train/val/test assignment used by the pipeline. |
|
|
| ### HDSv2 |
|
|
| Canonical table: `HDSv2.csv` |
|
|
| Columns: |
| `id, a, b, product, design_family, canonical_target_heuristic, canonical_target_margin, ot_cost, dd_cost, rc_cost, heuristic_definition_version, target_heuristic, ot_score, dd_score, rc_score, category, notes, digit_total, nonzero_total, complexity_c, split` |
|
|
| ### Trapsv2 |
|
|
| Canonical table: `Trapsv2.csv` |
|
|
| Columns: |
| `id, a, b, product, trap_type, design_family, canonical_target_heuristic, heuristic_definition_version, target_heuristic, expected_error_type, notes, digit_total, nonzero_total, complexity_c` |
|
|
| ## Modality and Evaluation Notes |
|
|
| - The paired multimodal benchmark includes text, image, and audio assets. |
| - `HDSv2Images/` is intentionally a test-only image release for probe evaluation. |
| - `Trapsv2Images/` covers the full trap set. |
| - Studies on this dataset show that accuracy falls sharply as arithmetic load $C$ (the product of total and non-zero digit count) grows. |
|
|
| ## Citation |
|
|
| ``` |
| @inproceedings{balter2026multiplication, |
| title={{Multiplication in Multimodal LLMs: Computation with Text, Image, and Audio Inputs}}, |
| author={Balter, Samuel Gideon and Jerzak, Ethan and Jerzak, Connor Thomas}, |
| booktitle={Findings of the Association for Computational Linguistics: ACL 2026}, |
| year={2026} |
| } |
| ``` |
