arith-v1 — Dataset card

Purpose

A small, fully controlled benchmark for comparing post-training methods (SFT, DPO, GRPO) on a task whose answers can be checked exactly by a program. It is a measurement instrument, not a training corpus for general-purpose models: every design choice favours unambiguous evaluation over breadth.

Loading

Each record kind has its own configuration, so every configuration has one schema: eval (the default: test, validation, dev), sft, preference and prompt.

from datasets import load_dataset

test = load_dataset("M-amir1998/arith-v1", "eval", split="test")
pairs = load_dataset("M-amir1998/arith-v1", "preference", split="preference_train")

Inside the framework, dataset.path: hf://M-amir1998/arith-v1 downloads the files and verifies every checksum against manifest.json.

Source and generation

100% synthetic, produced by posttrain data prepare (src/posttrainlab/data/), generator arith-v1.3, seed 20251018. Re-running the command reproduces every file bit-for-bit (posttrain data prepare --check, also run in CI). No model generated any of the text, and no external data was used.

Each problem is a small program of binary integer operations; rendering it yields the question and a reference solution, so the reference answer is correct by construction.

Categories (equal share in every split)

Category	Example	Steps
addition	What is 906 + 37?	1
subtraction	What is 349 - 209?	1
multiplication	What is 180 * 4? (12–199 × 3–9)	1
multi_step	What is 6 * 3 - 15? / What is (12 + 9) * 4?	2
word_problem	8 templates, e.g. buy/give away, boxes, wages, shelf	2

All answers are non-negative integers. Word problems use gender-neutral names (the name is repeated instead of using pronouns).

Schema and splits

Every record has id, category, prompt (instruction + question, exactly as shown to the model) and answer (int). Additional fields depend on the split kind:

Split	Kind	Records	Extra fields	Used by
sft_train	sft	1000	response	SFT
preference_train	preference	500	chosen, rejected, corruption	DPO
rl_train	prompt	500	–	GRPO (reward uses answer)
validation	eval	100	solution	development checks
test	eval	500	solution	all reported results
dev	eval	500	solution	hyperparameter selection (added in v1.1)
sft_extra	sft	2000	response	additional SFT problems (added in v1.2)
sft_train_3k	sft	3000	response	sft_train followed by sft_extra, for data-scaling studies
preference_test	preference	500	chosen, rejected, corruption	preference-accuracy metric
rl_extra	prompt	1000	–	additional RL prompts (added in v1.3)
rl_train_1500	prompt	1500	–	rl_train followed by rl_extra, for long GRPO runs

manifest.json records the SHA-256 of every file; loaders refuse a file whose checksum does not match.

Example sft_train record:

{"id": "sft_train-0000", "category": "subtraction",
 "prompt": "Solve the following problem. Show the calculation, then give the final result on its own last line in the form \"Answer: <integer>\".\n\nWhat is 349 - 209?",
 "answer": 140, "response": "349 - 209 = 140\nAnswer: 140"}

Contamination control

• Problems are identified by their math — (category, template, operands) — not their wording, so a test problem cannot reappear in training with a different name or item.
• Pools are drawn in a fixed order with evaluation pools first (test, validation, then rl_train, preference_train, sft_train, dev, sft_extra and rl_extra last); a key already drawn is rejected.
• manifest.json → contamination_checks lists prompt overlaps between every pair of pools: all zero. A unit test re-checks this on the committed files.
• preference_test is derived from test problems on purpose: it is evaluation-only and never used for training.

Preference pairs

chosen is the reference solution. rejected is a controlled corruption of it — one change, propagated through later steps like a real mistake:

corruption	Change	Share
arithmetic_slip	one step's result off by ±1, ±2 or ±10	25%
operand_error	one operand misread (adjacent-digit swap or ±1)	25%
inconsistent_answer	correct steps, wrong final answer line	25%
missing_answer	correct steps, no answer line	25%

Quality is verified during generation with the evaluation grader: every chosen must grade correct and well-formatted, every rejected must grade incorrect (and with the expected outcome type). A violation aborts the build.

Limitations and known biases

• Narrow domain: short integer arithmetic in one English prompt template. Success here says little about general reasoning.
• Template regularity: word problems come from 8 templates. Test problems share templates with training problems (only operands, names and items differ), so the test measures in-distribution generalisation, not robustness to new phrasings.
• Rejected responses are synthetic near-misses, not model samples; their distribution differs from the errors a model actually makes.
• Difficulty is uneven across categories by design (3-digit multiplication is harder than 2-digit addition), so per-category results matter more than the average.
• The problem space is finite. multiplication has only 1,316 distinct problems (12–199 × 3–9); after rl_extra, 96 are unused, so balanced splits cannot grow much further. Larger SFT sets would need a wider operand range, which would change the task. For harder problems see arith-hard-v1.

Versions

• 1.3.0 — adds rl_extra (1,000 prompts drawn after every earlier pool) and rl_train_1500 (rl_train then rl_extra), so long GRPO runs see each prompt fewer times. All earlier files are byte-identical.
• 1.2.0 — adds sft_extra (2,000 problems drawn after every earlier pool) and sft_train_3k (sft_train then sft_extra, so limits of 1k/2k/3k give nested subsets whose first 1,000 records are exactly sft_train). All earlier files are byte-identical.
• 1.1.0 — adds dev (500 problems) for hyperparameter selection. It is drawn after every v1.0 pool from its own RNG stream, so all v1.0 files are byte-identical (enforced by a test); results produced on v1.0 remain valid.
• 1.0.0 — initial release.

License

Apache-2.0, same as the repository.