| --- |
| license: other |
| license_name: dgn-math-benchmark-research-use |
| license_link: https://huggingface.co/datasets/ORCHORDS/dgn-math-problems |
| pretty_name: DGN Math Benchmark |
| tags: |
| - mathematics |
| - math |
| - math-benchmark |
| - benchmark |
| - evaluation |
| - eval |
| - reasoning |
| - text-to-math |
| - math-reasoning |
| - latex |
| - algebra |
| - trigonometry |
| - geometry |
| - inequalities |
| - word-problems |
| - worked-solutions |
| - english |
| - english-translation |
| - textbook-derived |
| - mixed |
| task_categories: |
| - text-generation |
| - question-answering |
| language: |
| - en |
| size_categories: |
| - 10K<n<100K |
| library_name: datasets |
| library: |
| - datasets |
| - pandas |
| - pyarrow |
| configs: |
| - config_name: full |
| data_files: |
| - split: train |
| path: data/full/train-*.parquet |
| - split: test |
| path: data/full/test-*.parquet |
| - config_name: qa |
| data_files: |
| - split: train |
| path: data/qa/train-*.parquet |
| - split: test |
| path: data/qa/test-*.parquet |
| - config_name: verified |
| data_files: |
| - split: train |
| path: data/verified/train-*.parquet |
| - split: test |
| path: data/verified/test-*.parquet |
| - config_name: core |
| data_files: |
| - split: train |
| path: data/core/train-*.parquet |
| - split: test |
| path: data/core/test-*.parquet |
| - config_name: books |
| data_files: |
| - split: train |
| path: data/books/train-*.parquet |
| - split: test |
| path: data/books/test-*.parquet |
| - config_name: synthetic |
| data_files: |
| - split: train |
| path: data/synthetic/train-*.parquet |
| - split: test |
| path: data/synthetic/test-*.parquet |
| --- |
| |
| # DGN Math Benchmark |
|
|
| **12,554 question-answer pairs** - 2,132 of them with an engine-verified answer and |
| therefore usable as a scored benchmark. 3,617 problems come from scanned books, |
| 8,417 from additional problem books, 520 are generated and machine-checked. |
|
|
| > Every printed answer in this dataset was checked with a real symbolic engine (SymPy). |
| > Where the engine produced a concrete counterexample, the answer was either replaced by a |
| > recomputed value that the engine then re-verified (`corrected`), or the row was kept with |
| > the printed answer and flagged (`refuted`). Where the check was inconclusive the row is |
| > flagged `suspected` and is **not** counted as a book error. Nothing was silently corrected, |
| > and every row says in `answer_status` exactly how much its answer was checked. |
| |
| ## What this is |
| |
| An English-language mathematics benchmark for evaluating language models on |
| problem solving. Problems are given in LaTeX, every item carries a worked |
| solution, and the final answer is stored in the standard MATH convention |
| (`\boxed{...}`), so the dataset drops straight into the usual math harnesses. |
| |
| ## Configs |
| |
| | config | rows | what it is | |
| |---|---|---| |
| | `full` | 12,554 | every problem, every column, including the unverified ones | |
| | `qa` | 12,554 | the minimal MATH-style columns: problem, answer, metadata | |
| | `verified` | 2,132 | **the scored split** - only rows whose answer the engine confirmed | |
| | `core` | 3,617 | the scanned algebra book (11 chapters) | |
| | `books` | 8,417 | the additional problem books | |
| | `synthetic` | 520 | generated problems with computed, re-checked answers | |
| |
| Each config has a deterministic 85/15 train/test split (seed 42), stratified by |
| source and chapter. |
| |
| ## Columns (`full`) |
| |
| | column | type | meaning | |
| |---|---|---| |
| | `id` | string | stable identifier, e.g. `algebra_core.1.122` | |
| | `problem_id` | string | the problem number as printed in the book | |
| | `source` | string | which collection the problem comes from | |
| | `source_title` | string | human-readable name of that collection | |
| | `chapter` | int | chapter / topic number | |
| | `chapter_title` | string | chapter / topic name | |
| | `group` | string | difficulty group printed in the book (A / B / C) | |
| | `difficulty` | string | the difficulty glyph printed in the book (`□` easy, `■` hard) | |
| | `problem` | string | the statement, LaTeX, inline `$...$` and display `$$...$$` | |
| | `solution` | string | the worked solution, ending in the boxed answer | |
| | `final_answer` | string | the gold answer as bare LaTeX (no `$`, no `\boxed`) | |
| | `final_answer_boxed` | string | the same answer as `\boxed{...}` | |
| | `answer_status` | string | `verified` / `corrected` / `refuted` / `suspected` / `disputed` / `unverifiable` / `no-gold` / `synthetic-verified` / `synthetic-unverified` | |
| | `verification_note` | string | what the engine checked and what it found | |
| | `page` | int | the printed page the problem is on | |
|
|
| ### Answer status |
|
|
| | status | count | meaning | |
| |---|---|---| |
| | `verified` | 1,924 | the engine substituted the answer back into the problem and it held | |
| | `corrected` | 17 | the printed answer was refuted and replaced by a re-verified recomputation | |
| | `refuted` | 60 | the engine found a concrete counterexample: the printed answer does not hold | |
| | `suspected` | 114 | the recomputed answer differs from the printed one, but no counterexample was found - **not** counted as a book error | |
| | `disputed` | 102 | a third read of the scanned page disagreed with the bulk transcription | |
| | `unverifiable` | 3,969 | outside the reach of automatic checking | |
| | `no-gold` | 5,848 | the source page carries no printed answer for this problem | |
| | `synthetic-verified` | 191 | generated template; the printed statement was parsed, solved and compared with the printed answer | |
| | `synthetic-unverified` | 329 | generated template; the answer is a derived quantity no engine could re-check - not scored | |
|
|
| `verified` means the engine substituted the answer back into the problem and it held. |
| `corrected` means the printed answer was refuted and replaced by a recomputed answer |
| that the engine then re-verified. `refuted` means the engine produced a **concrete |
| counterexample** - the printed root fails the equation, the printed tuple satisfies no |
| equation of the system, or the printed interval misses a point that satisfies the |
| inequality. `suspected` means the recomputed answer differs from the printed one but |
| no counterexample was found; a difference in a radical's scope can look the same, so |
| these are **not** counted as book errors. `disputed` means a third independent read of |
| the scanned page disagreed with the bulk transcription. `unverifiable` means the |
| printed answer exists but is outside the reach of automatic checking - word problems, |
| open-ended proofs, and answers that are not a number or a set. `no-gold` means the |
| source page carries no printed answer for that problem. |
|
|
| Only `verified`, `corrected` and `synthetic-verified` rows are scored. |
|
|
| ## Answer format |
|
|
| The convention is the one used by the MATH dataset and by the standard evaluation |
| harnesses: |
|
|
| * inline mathematics is written `$...$`, display mathematics `$$...$$` |
| * the gold answer is stored twice: `final_answer` holds the bare LaTeX |
| (`\frac{3}{4}`), `final_answer_boxed` holds `\boxed{\frac{3}{4}}` |
| * the `solution` column ends with the boxed answer, so a harness that extracts the |
| last `\boxed{...}` from the solution gets the same string |
| * decimals use a point, never a comma |
| * there is no mixing of `\(...\)` and `$...$` delimiters |
|
|
| ```python |
| from datasets import load_dataset |
| |
| ds = load_dataset("ORCHORDS/dgn-math-problems", "verified", split="test") |
| print(ds[0]["problem"]) |
| print(ds[0]["final_answer_boxed"]) |
| ``` |
|
|
| ## Scoring |
|
|
| The scoring model, the comparison tiers and a reporting template are documented in |
| `BENCHMARKING.md` at the root of this repository, and implemented in |
| `evaluate_benchmark.py`. In short, a prediction is compared with the gold answer at |
| four strengths - exact string, numeric, symbolic and set equivalence - and the |
| strictest tier that decides the item is the one that is reported, so a model cannot |
| be rewarded for a merely numerically close answer. |
|
|
| ```bash |
| python evaluate_benchmark.py \ |
| --dataset hf_dataset/data/verified/test-00000-of-00001.parquet \ |
| --predictions predictions.jsonl \ |
| --out report.json |
| ``` |
|
|
| ## How the data was produced |
|
|
| 1. **Transcription.** The scanned books were transcribed page by page with a vision |
| model into structured JSON, twice, with the two passes arbitrated by SymPy. The |
| additional books were transcribed from their page images with the same pipeline. |
| 2. **Verification.** Every answer was checked with SymPy: back-substitution into |
| equations and systems, exact endpoint evaluation for inequalities, symbolic |
| evaluation for limits and integrals, numeric identity testing for proofs. |
| 3. **Adjudication.** Every flagged answer was re-read a third time, directly from |
| the page image, and only corrections that the engine could confirm were written |
| back. |
| 4. **Generation.** The synthetic slice is produced by templates that compute the |
| answer with SymPy and then re-check it; an item that fails the re-check is |
| dropped. |
|
|
| ## Provenance and rights |
|
|
| The problems are drawn from Russian-language university entrance-exam mathematics |
| problem books and problem collections that are publicly available on the |
| postypashki.ru site. All rights in the underlying texts remain with their authors |
| and publishers; this repository redistributes transformed, machine-checked English |
| transcriptions for research and evaluation purposes and makes no claim of |
| original authorship of the problem statements. `license` is therefore `other`. |
|
|
| The `answer_status` and `verification_note` columns exist so that any user of this |
| benchmark can see exactly how much trust each item's answer has earned. |
|
|
