--- license: apache-2.0 task_categories: - text-generation - question-answering language: - en pretty_name: Arithmetic-Reasoning size_categories: - 10M A high-quality synthetic arithmetic and elementary mathematics reasoning dataset for training and evaluating small language models - not an "ultimate math" claim, but a clean, verified, tiered reasoning dataset where every answer is programmatically checked. This dataset was built to train **100M-ish models** that benefit disproportionately from clean, unambiguous examples. At ~50M examples (~45M train / 2.5M val / 2.5M test, ~5GB parquet) it is designed as a *reasoning* dataset: every sample has an instruction, a step-by-step reasoning trace, and a final answer, all verified to be mathematically correct. ### Why this dataset? Small models (25M-100M) trained on our earlier 5-minute budget went from 0.5% → 89.8% with scratchpad formats and to **98.3%** with `reverse-answers + scratchpad` - format and verification matter more than scale. This release distills those findings into a publishable, 100% verified dataset. # Problem Types - Top 10 + 8 more We cover 18+ operation families. Each `instruction` is sampled from 20+ phrasings with varied names/objects so at 1M tokens <1% duplicates. | # | Operation | Example Instruction | Reasoning | Answer | |---|-----------|---------------------|-----------|--------| | 1 | **Addition** | `Calculate 313921 + 108618.` | `313921 + 108618 = 422539` | `422539` | | 2 | **Subtraction** | `Please compute 964047 - 52578.9.` | `964047-50000=914047 | ... | 911468.1` | `911468.1` | | 3 | **Multiplication** | `Calculate 3088 x 1685.` | `3088*5*10^0=15440 | running=15440 | ... | 5203280` | `5203280` | | 4 | **Division** | `Divide 7763506128 by 8856.` | `77635/8856=8 | 8*8856=70848 | ... | 876638` | `876638` | | 5 | **Percentages** | `What is 86 percent of 5.6.` | `5.6*86=481.6 | 481.6/100=4.816` | `4.816` | | 6 | **Comparison** | `Which is smaller, 107473 or 709570?` | `107473 < 709570 | 107473 is smaller` | `107473 is smaller` | | 7 | **Fractions** | `Find 3/4 of 8324.` | `8324/4=2081 | 2081*3=6243` | `6243` | | 8 | **Word Problems** | `Layla has 95 bags with 608 lemons each and found 152 more lemons. How many lemons total?` | `95*608=57760 | 57760+152=57912` | `57912 lemons` | | 9 | **Algebra** | `Solve for x: x + 39 = 150` | `x = 150 - 39 = 111` | `111` | | 10 | **Geometry** | `What is the area of a rectangle 884 by 752?` | `884*752=664768` | `664768` | | | *+ 8 more:* `ratios, powers/roots, decimals, halving/doubling, sequences, multi-step, hard arithmetic, quantitative reasoning` - see `operation` field for full list. | | | | Full per-operation counts in `50M`: `word problems 13.6% | multi-step 10.7% | ratios 9.7% | hard arithmetic 5.7% | algebra 7.4% | fractions 4.6% | sequences 5.3% | geometry 5.1% | ...` (see `Per-operation` in generation log) ## Quickstart ```python from datasets import load_dataset ds = load_dataset("SagheerLab/Arithmetic-Reasoning") print(ds["train"][0]) # {'instruction': 'What is 86 percent of 5.6.', 'reasoning': '5.6*86=481.6 | 481.6/100=4.816', 'answer': '4.816', ...} # pretraining text format print(ds["train"][0]["text"]) # Calculate 86 percent of 5.6. # 5.6*86=481.6 | 481.6/100=4.816 # Answer: 4.816 ``` ```python from huggingface_hub import snapshot_download snapshot_download("SagheerLab/Arithmetic-Reasoning", repo_type="dataset", local_dir="./arithmetic-reasoning") ``` # Dataset Summary - **Size:** ~50M examples (~45M train / 2.5M val / 2.5M test, ~5GB parquet), 100% programmatically verified - **Generation:** deterministic `src/generate_data_v4.py` with `NAMES 120 + OBJECTS 150 + VERBS 100` for lexical variation, de-duplicated (<1% dupes) - **Tiers:** `easy 30% (1-2 digits, 1 step) | intermediate 35% (3-4 digits, 2-3 steps) | hard 25% (5-6 digits, 3-8 steps) | very hard 10% (competition/GSM8K-style)` - **License:** Apache 2.0 - see [Licensing](#licensing-information) # Dataset Structure ### Data Instances ```json { "instruction": "What is 86 percent of 5.6.", "reasoning": "5.6*86=481.6 | 481.6/100=4.816", "answer": "4.816", "text": "What is 86 percent of 5.6.\n5.6*86=481.6 | 481.6/100=4.816\nAnswer: 4.816", "operation": "percentage", "difficulty": "easy", "num_steps": 1, "max_digits": 2 } ``` ### Data Fields - `instruction` (string): the question, varied phrasing with names/objects - `reasoning` (string): step-by-step trace (`|` separates steps, `\n` for long division), last step is `answer` - `answer` (string): final answer only (with unit for word problems, e.g. `57912 lemons`) - `text` (string): `instruction + "\n" + reasoning + "\nAnswer: " + answer` for pretraining - `operation` (string): `addition | subtraction | multiplication | division | percentage | comparison | fractions | ... | word problems` - `difficulty` (string): `easy | intermediate | hard | very hard` - `num_steps` (int): reasoning steps (1 for easy, 2-3 for intermediate, 3-8 for hard) - `max_digits` (int): largest operand digits (1-6) ### Data Splits | Split | Size | Path | |-------|------|------| | train | ~45M | `parquet/train-*.parquet` (sharded, ~4.5GB) | | validation | ~2.5M | `parquet/validation-*.parquet` | | test | ~2.5M | `parquet/test-*.parquet` | All splits are IID from same generator, `seed 42`, `balanced-sizes`, `max_digits 6`, sharded for Viewer (`row_group_size=10000`, `write_page_index=True`). # Dataset Creation ### Curation Rationale Small LMs benefit from clean, unambiguous, verified reasoning traces. We built this to provide a tiered, diverse arithmetic reasoning dataset where `easy` teaches columns, `intermediate` teaches decomposition, `hard` teaches 3-8 step planning, and `very hard` teaches GSM8K-style 4-5 op word problems. ### Source Data Synthetic - generated by `src/generate_data_v4.py` (deterministic, efficient, <30s for 150K). No web crawl. Generation uses: - `PROMPT_TEMPLATES` 20+ per op (so at 100K <1% duplicate instructions) - `NAMES 120 + OBJECTS 150 + VERBS 100` for word problems (e.g., `Jaxson had 133 rainbows...` not just `Sarah had...`) - `balanced-sizes` uniform 1-6 digits, `DIVISOR_MAX_DIGITS 4`, `scratchpad-mul v2`, `scratchpad-div v3`, `scratchpad-sub` ### Data processing steps 1. Generate 150K raw examples with `seed 42` 2. Verification pipeline (100%): ```python true = calc(instruction) # independent python calc assert answer == true assert reasoning.split("|")[-1].strip().endswith(answer) or reasoning.split("\n")[-1].strip() == answer assert reasoning lines are arithmetically valid # else drop & regenerate (seen set ensures <1% dupes) ``` 3. Deduplicate `instruction` strings via `seen` set 4. Shuffle and split 90/5/5, write `Parquet` shards (`row_group_size=10000`, `write_page_index=True`), copy `best_3440x1440.png` banner ### Personal and Sensitive Information None - all synthetic. Names are sampled from common first names, no real PII. # Considerations for Using the Data ### Social Impact Helps make reasoning training accessible for small models without web-scale data. No harmful content. ### Discussion of Biases Word problems sample `NAMES` uniformly from a US-centric list - not representative of global names. Objects are everyday items. No systematic bias in math, but phrasing reflects English templates. ### Other Known Limitations - English only, 1-6 digit arithmetic (no logs, no negative numbers yet - planned for v2) - Fractions are `a/b` where `a` divisible by `b` (exact) - Division is exact or integer quotient (no decimal remainder except `very hard` GSM8K remainder) - Sequences are `+step`, `*2`, `Fibonacci`, `+3/*2 alternating` - not full competition variety # Additional Information ### Licensing Information **Apache 2.0** - permissive, allows commercial use, modification, distribution, and private use with attribution and a patent grant. You must include copyright/license notices. See `LICENSE` file. ### Citation No citation required, but if you use this dataset please cite: ``` @dataset{sagheerlab_arithmetic_reasoning_2026, title={Arithmetic-Reasoning: A High-Quality Synthetic Arithmetic Reasoning Dataset for Small LMs}, author={SagheerLab}, year={2026}, url={https://huggingface.co/datasets/SagheerLab/Arithmetic-Reasoning} } ``` ### Contributions Thanks to the synthetic data verification pipeline and tiered difficulty design. Banner image `best_3440x1440.png` included at repo root.