| --- |
| language: |
| - en |
| pretty_name: MicroReason Math |
| size_categories: |
| - 100K<n<1M |
| task_categories: |
| - text-generation |
| - question-answering |
| tags: |
| - math |
| - arithmetic |
| - algebra |
| - synthetic |
| - reasoning |
| - chain-of-thought |
| - compositional-generalization |
| configs: |
| - config_name: benchmark |
| data_files: |
| - split: val |
| path: data/benchmark/val.jsonl |
| - split: val_heldout_shape |
| path: data/benchmark/val_heldout_shape.jsonl |
| - split: test_id |
| path: data/benchmark/test_id.jsonl |
| - split: test_heldout_shape |
| path: data/benchmark/test_heldout_shape.jsonl |
| - split: test_extrapolation |
| path: data/benchmark/test_extrapolation.jsonl |
| - split: test_extrapolation_fresh |
| path: data/benchmark/test_extrapolation_fresh.jsonl |
| - config_name: sft |
| data_files: |
| - split: train |
| path: data/sft/train.jsonl |
| --- |
| |
| # MicroReason Math |
|
|
| Synthetic arithmetic and linear-algebra problems with exact answers and canonical step-by-step |
| solutions. They were generated to train and evaluate |
| [MicroReason-43M](https://huggingface.co/arpjw/microreason-43m), a small language model trained |
| from scratch. |
|
|
| **Generation and checking:** |
| - **Source:** every problem comes from a seeded grammar over random expression trees and linear |
| equations. |
| - **Answers:** each answer is verified by an independent exact solver. |
| - **Steps:** every solution step is checked to be correct. |
|
|
| The benchmark splits test generalization to **unseen problem structures** and to **larger |
| numbers** than those seen in training. |
|
|
| ```python |
| from datasets import load_dataset |
| |
| bench = load_dataset("arpjw/microreason-math", "benchmark") # 6 evaluation splits, 40,000 problems |
| sft = load_dataset("arpjw/microreason-math", "sft", split="train") # 100,000 training problems |
| ``` |
|
|
| ## Examples |
|
|
| ``` |
| Compute: 93 - (-90) * (-73) |
| 1. Multiply: -90 * (-73) = 6570 |
| 2. Subtract: 93 - 6570 = -6477 |
| answer: -6477 |
| |
| Find x: 23x + 7462 = 15(x - 2721) |
| 1. Expand: 23x + 7462 = 15x - 40815 |
| 2. Subtract 15x from both sides: 8x + 7462 = -40815 |
| 3. Subtract 7462 from both sides: 8x = -48277 |
| 4. Divide both sides by 8: x = -48277/8 |
| answer: -48277/8 |
| ``` |
|
|
| ## Splits |
|
|
| | Config / split | Problems | Shapes | What it measures | |
| | --- | ---: | ---: | --- | |
| | `benchmark` / `val` | 7,000 | 1,555 | In-distribution validation | |
| | `benchmark` / `val_heldout_shape` | 6,000 | 1,039 | Validation on problem structures never seen in training | |
| | `benchmark` / `test_id` | 7,000 | 1,574 | In-distribution test | |
| | `benchmark` / `test_heldout_shape` | 6,000 | 1,053 | Test on unseen structures (3–5 operators and equations) | |
| | `benchmark` / `test_extrapolation` | 7,000 | 1,214 | Test with 4–5 digit numbers (training uses 0–999) | |
| | `benchmark` / `test_extrapolation_fresh` | 7,000 | 1,209 | An independent second extrapolation suite (own seed, frozen separately) | |
| | `sft` / `train` | 100,000 | 9,407 | Supervised fine-tuning problems | |
|
|
| **Family mix:** |
| - **Expressions:** 1–5 operators over `+ − × ÷`. In-distribution splits are about 11% 1-op, |
| 20% 2-op, 16% 3-op, 10% 4-op and 8% 5-op. |
| - **Equations:** linear equations make up about 35% of in-distribution splits. |
| - **Held-out-shape splits:** only 3+ operator structures and equations. |
|
|
| **How shapes are held out:** a *shape* is the operator structure of an expression tree, such as |
| `(- n (* n n))`, or an equation template. |
| - **Assignment:** each shape is hashed into exactly one of train-visible (80%), held-out-val |
| (10%) or held-out-test (10%). |
| - **Coverage guarantee:** every operator and pairing in a held-out shape also appears in a |
| training shape. Held-out problems are new *combinations*, not new primitives. |
|
|
| **Contamination checks:** |
| - No problem appears in more than one split. |
| - Every evaluation problem was checked against the 435 k-document general-text corpus |
| (Cosmopedia) used in pretraining. |
|
|
| ## Fields |
|
|
| | Field | Description | |
| | --- | --- | |
| | `id` | Stable record id | |
| | `prompt` | The problem as posed to the model, e.g. `Compute: …` or `Find x: …` | |
| | `solution_steps` | Canonical worked solution: post-order reductions or fixed equation moves | |
| | `final_answer` | Exact answer: an integer, or a reduced fraction like `-48277/8` | |
| | `answer_type` | `integer` or `rational` | |
| | `kind` | `expression` or `linear_equation` | |
| | `math_text` | The bare expression or equation | |
| | `variable` | `x` for equations, else null | |
| | `family` | `expression_1op` … `expression_5op`, `linear_equation` | |
| | `shape` | Structural template (used for held-out splits and cluster bootstrap) | |
| | `difficulty` | Integer difficulty level | |
| | `number_range` | `in_distribution` (0–999) or `extrapolation` (4–5 digits) | |
| | `params` | JSON string of the sampled numbers | |
| | `seed` | Generator seed (string; a 64-bit unsigned integer) | |
| | `semantic_fingerprint` | Hash of the canonical problem, used for de-duplication | |
| | `generator_version` | `3.0` | |
|
|
| ## Exact original files |
|
|
| `data/` holds loader-friendly copies, with `seed` and `params` stored as strings. `raw/` holds the |
| byte-exact files produced by the generator. Their sha256 hashes match the frozen manifests in the |
| MicroReason repository: |
|
|
| | File | sha256 | |
| | --- | --- | |
| | `raw/benchmark_val.jsonl` | `4d9b10b32896…` | |
| | `raw/benchmark_val_heldout_shape.jsonl` | `fabbcecef5dd…` | |
| | `raw/benchmark_test_id.jsonl` | `2085da0f3c2e…` | |
| | `raw/benchmark_test_heldout_shape.jsonl` | `a370443a077d…` | |
| | `raw/benchmark_test_extrapolation.jsonl` | `28db77f8794d…` | |
| | `raw/benchmark_test_extrapolation_fresh.jsonl` | `35d481707bd9…` | |
| | `raw/sft_train.jsonl` | `0020a0e550aa…` | |
|
|
| ## How MicroReason-43M scores |
|
|
| Greedy decoding, show-work prompt, exact final answer: |
|
|
| | Model | `test_id` | `test_heldout_shape` | `test_extrapolation` | `test_extrapolation_fresh` | |
| | --- | ---: | ---: | ---: | ---: | |
| | `sft-long` | 87.1% | 81.4% | 10.2% | 9.5% | |
| | `grpo` | 87.8% | 82.0% | 10.1% | 9.3% | |
| | `extra-sft` | 88.8% | 83.1% | 7.8% | 7.4% | |
|
|
| ## Not included |
|
|
| The larger training pools used for pretraining, mid-training, long SFT and RL are not included: |
| 6 M + 5 M + 4 M records. They come from the same generator and are rebuilt deterministically from |
| their seeds. |
|
|
| ## Notes |
|
|
| - **Prompt conventions:** in MicroReason the show-work prompt appends ` Show your work.` to |
| `prompt`. Solutions are rendered as numbered lines inside `[steps] … [/steps]`, followed by |
| `[answer]…[/answer]`. |
| - **Purpose:** these are synthetic problems for studying small-model reasoning and generalization. |
| They are not representative of natural-language math word problems. |
|
|
