Add comprehensive dataset card for MathSticks

README.md

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+---
+task_categories:
+- image-text-to-text
+language:
+- en
+tags:
+- visual-reasoning
+- symbolic-reasoning
+- math
+- matchstick-puzzles
+- benchmark
+---
+
+# MathSticks: A Benchmark for Visual Symbolic Compositional Reasoning with Matchstick Puzzles
+
+**Paper:** [MathSticks: A Benchmark for Visual Symbolic Compositional Reasoning with Matchstick Puzzles](https://huggingface.co/papers/2510.00483)
+**Code:** [https://github.com/Yuheng2000/MathSticks](https://github.com/Yuheng2000/MathSticks)
+
+## Overview
+MathSticks is a benchmark for Visual Symbolic Compositional Reasoning (VSCR) that unifies visual perception, symbolic manipulation, and arithmetic consistency. Each task presents an incorrect matchstick equation in a seven-segment style. The goal is to move exactly one or two sticks—under strict stick-conservation and digit-legibility constraints—to make the equation mathematically correct.
+
+- Two evaluation regimes:
+  - Text-guided: the equation string is provided to the model.
+  - Pure-visual: only the rendered puzzle image is provided.
+- Systematic coverage: digit scale (Levels 1–4), move complexity (1/2 sticks), solution multiplicity, and operator variation.
+- Scale: 1.4M generated instances; a curated test set of 400 items is released.
+
+<p align="center">
+  <img src="https://raw.githubusercontent.com/Yuheng2000/MathSticks/main/example.png" alt="MathSticks example predictions" width="300"/>
+  <br/>
+  <em>Example: input puzzle, reasoning trace, and move-format predictions.</em>
+  <br/>
+</p>
+
+Evaluations across 14 VLMs reveal substantial limitations: closed-source models succeed only on simple cases, open-source models fail in the pure-visual regime, while humans exceed 90% accuracy. These results establish MathSticks as a rigorous, diagnostic testbed for advancing compositional reasoning across vision and symbols.
+
+## Task Definition
+- Input: a rendered image of an incorrect equation composed of matchsticks (seven-segment digits). Optionally, a text equation string (text-guided regime).
+- Constraints: move one or two sticks only; no addition/removal; preserve digit legibility.
+- Objective: reach a valid arithmetic equation (addition or subtraction). Operator flips may be required by the minimal-move constraint in some cases.
+- Output format: a boxed sequence of Move operations, e.g. `\boxed{Move(A0, C3)}` or `\boxed{Move(A0, C3), Move(E1, F4)}`.
+
+## Data Format (Benchmark JSONL)
+Each line is one sample with the following fields:
+- `id` (string): unique sample identifier, e.g., `"00075585"`.
+- `level` (int): difficulty level (1–4) indicating digit scale.
+- `image` (string): image path relative to repo root, e.g., `level1/00075585_8-9=3.png`.
+- `problem` (string): the displayed (incorrect) equation string, e.g., `8-9=3`.
+- `solution_num` (list[int, int]): counts of solvable solutions by move budget `[one_move_count, two_move_count]`.
+- `mode_1_solution` (list): list of one-move solutions. Empty when `solution_num[0] == 0`.
+- `mode_2_solution` (list): list of two-move solutions. Each item has:
+  - `solution` (string): corrected equation (e.g., `"8 - 6 = 2"`).
+  - `moves` (list[string]): standardized move format strings, e.g., `["Move(B2, B5)", "Move(C3, C5)"]`.
+- `option_answer` (object): order-invariant representation of moves, for robust parsing:
+  - `mode_1` (list): each one-move answer as `{ "pick": [from_label], "place": [to_label] }`.
+  - `mode_2` (list): each two-move answer as `{ "pick": [from_label_1, from_label_2], "place": [to_label_1, to_label_2] }`.
+
+Example:
+```json
+{
+  "id": "00075585",
+  "level": 1,
+  "problem": "8-9=3",
+  "image": "level1/00075585_8-9=3.png",
+  "solution_num": [0, 4],
+  "mode_1_solution": [],
+  "mode_2_solution": [
+    {"solution": "8 - 6 = 2", "moves": ["Move(B2, B5)", "Move(C3, C5)"]},
+    {"solution": "9 - 9 = 0", "moves": ["Move(A5, C5)", "Move(C0, C6)"]},
+    {"solution": "6 + 3 = 9", "moves": ["Move(A2, G0)", "Move(B6, C6)"]},
+    {"solution": "9 - 0 = 9", "moves": ["Move(A5, B5)", "Move(B0, C6)"]}
+  ],
+  "option_answer": {
+    "mode_1": [],
+    "mode_2": [
+      {"pick": ["B2", "C3"], "place": ["B5", "C5"]},
+      {"pick": ["A5", "C0"], "place": ["C5", "C6"]},
+      {"pick": ["A2", "B6"], "place": ["G0", "C6"]},
+      {"pick": ["A5", "B0"], "place": ["B5", "C6"]}
+    ]
+  }
+}
+```
+
+Notes:
+- Pure-visual regime uses only `image` for model input; text-guided may also use `problem`.
+- The string move format is strict for parsing; `option_answer` provides an order-invariant equivalent when needed.
+
+## Sample Usage
+
+### 1) Run evaluation
+```bash
+python eval.py \
+  --input MathSticks_bench_400.jsonl \
+  --image-dir ./image \
+  --output predictions.jsonl
+```
+
+### 2) Score predictions
+```bash
+python cal_score.py \
+  --pred predictions.jsonl \
+  --label MathSticks_bench_400.jsonl \
+  --output score.json
+```
+
+### 3) Generate data (research use only)
+```bash
+python match_gen_flt.py
+```
+This enumerates positional encodings and writes the discovered solvable cases to `match_gen.jsonl`. It is computationally intensive and may take a long time.
+
+## Citation
+If you find MathSticks useful, please cite the paper:
+```bibtex
+@article{mathsticks2025,
+  title   = {MathSticks: A Benchmark for Visual Symbolic Compositional Reasoning with Matchstick Puzzles},
+  author  = {Anonymous},
+  journal = {arXiv preprint arXiv:TODO},
+  year    = {2025},
+  url     = {https://huggingface.co/papers/2510.00483}
+}
+```