diff --git a/README.md b/README.md new file mode 100644 index 0000000000000000000000000000000000000000..2c002e556f63e1e184340db991e840a08fcca620 --- /dev/null +++ b/README.md @@ -0,0 +1,464 @@ +--- +pretty_name: MathNet — Olympiad Math Reasoning & Retrieval (Preview) +license: cc-by-4.0 +task_categories: + - question-answering + - text-generation + - image-to-text +language: + - en + - pt + - es + - fr + - it + - sr + - sl + - de + - zh + - ro + - ko + - nl + - ru + - mn + - mk + - pl + - hu +tags: + - mathematics + - olympiad + - reasoning + - competition-math + - multimodal + - retrieval + - iclr-2026 + - preview +size_categories: + - 10K + +MathNet + +Website +ICLR 2026 + +**Shaden Alshammari**1\*   **Kevin Wen**1\*   **Abrar Zainal**3\*   **Mark Hamilton**1 +**Navid Safaei**4   **Sultan Albarakati**2   **William T. Freeman**1†   **Antonio Torralba**1† + +1MIT   2KAUST   3HUMAIN   4Bulgarian Academy of Sciences   \*† equal contribution + + + +--- +[Quick Start](#quick-start) · [Overview](#overview) · [Tasks](#three-benchmark-tasks) · [Comparison](#how-mathnet-compares-to-existing-math-benchmarks) · [Dataset Stats](#dataset-at-a-glance) · [Data Sources](#data-sources) · [Pipeline](#data-pipeline) · [Schema](#schema) · [License](#license) · [Citation](#citation) + +--- +## Quick start + +```python +from datasets import load_dataset + +# Default: all problems +ds = load_dataset("ShadenA/MathNet", split="train") + +# Or a specific country / competition-body config +arg = load_dataset("ShadenA/MathNet", "Argentina", split="train") +apmo = load_dataset("ShadenA/MathNet", "Asia_Pacific_Mathematics_Olympiad_APMO", split="train") + +row = ds[0] +print(row["competition"], row["year"], row["country"]) +print(row["problem_markdown"]) +for img in row["images"]: + img.show() # PIL image — renders inline in the HF viewer +``` + +## Overview + +MathNet overview: large-scale multilingual data, high-quality solutions, diverse topics, and three evaluation tasks + +Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce **MathNet**, a high-quality, large-scale, multimodal, and multilingual dataset of Olympiad-level math problems together with a benchmark for evaluating mathematical reasoning in generative models **and** mathematical retrieval in embedding-based systems. + +MathNet spans **47 countries**, **17 languages**, and **two decades** of competitions, comprising **30,676 expert-authored problems with solutions** across diverse domains. Alongside the core dataset, we construct a retrieval benchmark of mathematically equivalent and structurally similar problem pairs curated by human experts. + +--- + +## Three benchmark tasks + +| | Task | What it measures | +|---|---|---| +| **I** | **Problem Solving** | Generative models on Olympiad problems, graded against expert solutions | +| **II** | **Math-Aware Retrieval** | Embedding models' ability to retrieve mathematically equivalent / structurally similar problems | +| **III** | **Retrieval-Augmented Problem Solving** | How retrieval quality affects reasoning when similar problems are given as context | + +Even state-of-the-art reasoners remain challenged: **78.4% (Gemini-3.1-Pro)** and **69.3% (GPT-5)** on `MathNet-Solve-Test`. Embedding models struggle with equivalence retrieval (Recall@1 under 5% for all tested models), and RAG gains are highly sensitive to retrieval quality — expert retrieval lifts DeepSeek-V3.2-Speciale to **97.3%** on `MathNet-RAG`. + + +## How MathNet compares to existing math benchmarks + +| Benchmark | Size | Languages | Multimodal | Source | Difficulty | +|---|---:|---|:-:|---|---| +| GSM8K | 8,500 | EN | — | Crowdsourced | Grade school | +| MATH | 12,500 | EN | — | Competitions/textbooks | High school | +| MATH-Vision | 3,040 | EN | ✓ | Math competitions | High school | +| OlympiadBench | 6,142 | EN, ZH | ✓ | Official websites | Olympiad | +| OlympicArena | 3,233 | EN, ZH | ✓ | Official websites | Olympiad | +| Omni-Math | 4,428 | EN | — | AoPS / contest pages | Olympiad | +| OlymMATH | 200 | EN, ZH | — | AoPS / official | Olympiad | +| MathArena | 162 | EN | ✓ | Newly released competitions | Olympiad | +| IMOBench | 460 | EN | — | IMO & national archives | Olympiad | +| **MathNet (ours)** | **30,676** | **17** (EN, ZH, ES, RU, FR, RO, + 11 more) | **✓** | **Official country booklets / international & national contests** | **Olympiad** | + +## Dataset at a glance + +MathNet dataset statistics: contest types, solution length vs. prior benchmarks, problems per year, topic distribution, and language distribution + +**What the figure shows.** *(a)* A mix of national, regional, TST, and international competitions. *(b)* MathNet solutions are **substantially longer** than those in prior math benchmarks — long-form proofs, not one-line answers. *(c)* Problems per year — the corpus has grown steadily since the early 2000s. *(d)* Coverage across geometry, algebra, combinatorics, number theory, and their sub-topics. *(e)* **74% English, 26% non-English** across **17 languages**; Portuguese, Spanish, French, Italian, Serbian, Slovenian, German, Chinese, Romanian, Korean, Dutch, Russian, Mongolian, Macedonian, Polish, and Hungarian all appear. + +### Topic taxonomy (excerpt) + +MathNet ships with a curated olympiad-style taxonomy. Top-level domains include: + +- **Geometry** — plane (triangles, quadrilaterals, circles, concurrency/collinearity, transformations, Miquel/Simson/Brocard, geometric inequalities, combinatorial geometry, analytic methods), solid, differential, non-Euclidean +- **Algebra** — prealgebra, polynomials, inequalities, functional equations, sequences/series, linear algebra, abstract algebra +- **Number Theory** — divisibility, primes, modular arithmetic, Diophantine equations, quadratic residues, \(p\)-adic methods +- **Combinatorics** — counting, graph theory, extremal / pigeonhole, invariants/monovariants, games, coloring, generating functions +- **Calculus / Analysis** — limits, inequalities, real analysis, combinatorial analysis +- **Probability & Statistics** — discrete and continuous + +Every problem carries a hierarchical topic path (e.g. `Geometry > Plane Geometry > Quadrilaterals > Cyclic quadrilaterals`) usable for stratified evaluation or curriculum construction. + +## Data sources + +Each year, participating IMO countries contribute original problems for use in their national contests and team selection examinations. MathNet is built from **official problem booklets** collected from **47 countries spanning 1985–2025** — **1,595 PDF volumes** totalling more than **25,000 pages**. Unlike prior math benchmarks that rely on community platforms such as AoPS, every problem and solution in MathNet is authored and disseminated by national teams themselves, ensuring expert-level quality, stylistic consistency, and immunity from the noisy or informal annotations that plague crowd-sourced collections. + +A meaningful portion of the collection — particularly older national booklets — was physically obtained and scanned by hand by our IMO expert co-authors, who have attended the International Mathematical Olympiad since 2006 and accumulated a personal archive of official competition materials over nearly two decades. + +## Data pipeline + +MathNet data extraction and curation pipeline + +Extracting aligned problem–solution pairs from a heterogeneous corpus of mathematical documents is non-trivial: some booklets separate problems and solutions into different sections, others interleave them; numbering schemes and naming conventions vary across countries and even within a single document. Regex-based heuristics break down at this scale, so we designed a multi-stage LLM pipeline. + +**Stage 1 — Document ingestion & segmentation.** All booklets are converted to Markdown via `dots-ocr`, a multilingual document parsing framework designed for both digital typeset PDFs and scanned copies across many languages. `Gemini-2.5-Flash` then identifies problem and solution segments by outputting only their line numbers, and records authors, hints, remarks, source file, and page numbers for provenance. + +**Stage 2 — Problem–solution extraction.** Given the line segments from Stage 1, `GPT-4.1` extracts the corresponding problem and solution in LaTeX-friendly Markdown, together with a surrounding text buffer to handle cases where content spans across context boundaries. + +**Stage 3 — Extraction verification.** Each extracted pair passes three independent checks before being retained: +1. **Rule-based similarity check** — text similarity between the extraction and original OCR output ensures the LLM made only formatting changes and introduced no hallucinated content. +2. **GPT-4.1-as-judge** — GPT-4.1 compares page screenshots against the extracted pair to catch OCR errors, incorrect figure associations, and incomplete solutions. +3. **Human expert review** — low-confidence cases are manually reviewed by annotators. A pair is retained only if all three mechanisms agree. + +Provenance (source booklet, page numbers, authors where given) is preserved on every problem. + +## What this preview contains + +A **diverse 100-problem slice** sampled round-robin across countries, prioritizing problems with figures so the multimodal path is visible end-to-end. Images are **embedded** in the parquet as HF `Image()` features — they render inline in the dataset viewer and decode to PIL on load. + +## Schema + +| Column | Type | Notes | +|---|---|---| +| `unique_id` | string | Stable SHA-256 content hash | +| `country` | string | Country / regional body of origin | +| `competition` | string | e.g. `IMO 2023`, `Cono Sur Mathematical Olympiad` | +| `year` | int32 | Year of competition | +| `section` | string\|null | Day / round / level | +| `problem_number` | string | As printed in the booklet | +| `problem_markdown` | string | Problem statement (Markdown + LaTeX) | +| `solutions_markdown` | list<string> | Official / provided solutions | +| `answers_markdown` | list<string> | Final answers when stated separately | +| `topics` | list<list<string>> | Hierarchical tags | +| `topics_flat` | list<string> | Joined `A > B > C` strings | +| `language` | string | Source booklet language | +| `source_booklet` | string | Booklet id (e.g. `ARG_2003`) | +| `booklet_source` | string | Upstream collection label | +| `has_images` | bool | Whether the problem cites figures | +| `num_images` | int32 | Count of referenced figures | +| `images` | list<Image> | Inlined bytes, decoded to PIL | +| `natural_language_description` | string\|null | LLM-assisted NL rephrasing | +| `main_ideas` | list<string> | LLM-assisted key solution ideas | +| `final_answer` | string\|null | LLM-extracted final answer | +| `problem_type` | string\|null | `proof`, `answer`, `proof and answer`, … | +| `metadata_confidence` | float32 | Self-rated confidence of LLM metadata | +| `original_problem_markdown` | string\|null | Pre-normalization text | + +> The enriched fields (`natural_language_description`, `main_ideas`, `final_answer`, `problem_type`, `metadata_confidence`) are **LLM-assisted** and not fully human-audited in the preview. Treat them as convenience annotations, not ground truth. + +## Configs / splits + +One config per **country or regional body** plus a default `all` config unioning everything. Each config has a single `train` split — this is a preview, not the train/test partitioning of `MathNet-Solve` (which is `train: 23,776`, `test: 6,400`, `test-hard: 500` in the full release). + +## Intended uses & limitations + +**Good for.** Olympiad-level reasoning evaluation, multilingual math evaluation, figure-grounded multimodal math, topic-stratified analysis, retrieval benchmarks over mathematical structure, and **RL training** — the large pool of expert-written solutions provides dense rewards for verifiable-answer problems, while the math-aware similarity pairs open a new axis: rewarding a model for retrieving a structurally equivalent problem is a natural, automatically verifiable signal that does not require a closed-form answer. + +**Caveats.** +- **Not contamination-clean.** Olympiad problems are indexed widely; assume leakage when evaluating pretrained models. +- **Preview schema may change** before the full release. +- **LLM-assisted metadata is imperfect.** + +## License + +With the kind support of IMO President Gregor Dolinar, we reached out to the leaders of all participating countries and obtained their permission to share this dataset publicly. Where a country or contest organization asserts its own copyright, that copyright is retained and takes precedence — see `competition`, `country`, and `source_booklet` on each row. For all remaining problems where no explicit copyright was asserted, the dataset is released under **[Creative Commons Attribution 4.0 International (CC BY 4.0)](https://creativecommons.org/licenses/by/4.0/)**. + +In short: use freely, cite the paper, and respect any explicit rights claimed by the original national team. + +If you are a rightsholder with a concern, please open an issue or email [shaden@mit.edu](mailto:shaden@mit.edu). + +## Citation + +```bibtex +@inproceedings{alshammari2026mathnet, + title = {MathNet: A Global Multimodal Benchmark for Mathematical + Reasoning and Retrieval}, + author = {Alshammari, Shaden and Wen, Kevin and Zainal, Abrar and + Hamilton, Mark and Safaei, Navid and Albarakati, Sultan and + Freeman, William T. and Torralba, Antonio}, + booktitle = {International Conference on Learning Representations}, + year = {2026}, + url = {https://mathnet.mit.edu} +} +``` + +## Links + +- 🌐 **Website & paper:** +- 🔭 **Browse all 30K problems:** +- ✉️ **Contact:** [shaden@mit.edu](mailto:shaden@mit.edu) + +

© 2026 Massachusetts Institute of Technology · MathNet · ICLR 2026

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