arith-hard-v1 — Dataset card

Purpose

A harder tier of arith-v1 for models that saturate it: every problem takes two or three steps with larger operands. Same prompt, answer format, schema, grader and preference-pair construction, so results on both tiers are directly comparable and every training method runs unchanged.

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

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

Source and generation

100% synthetic, produced by posttrain data prepare --dataset arith-hard-v1 (src/posttrainlab/data/arithmetic_hard.py), generator arith-hard-v1.0, seed 20261021. 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.

Categories (equal share in every split)

Category	Example	Steps
add_three	What is 7744 + 2709 + 210? (two 3–4-digit numbers and one 3-digit)	2
mul_2x2	What is 85 * 54? (12–99, no trailing zero), written as partial products	3
mul_3x2	What is 509 * 96? (101–999 × 12–99), written as partial products	3
multi_step_3	(a + b) * c - d, (a - b) * c + d, a * b + c * d, a * b - c * d	3
word_problem_3	6 three-step templates, e.g. boxes shared with friends, wages minus lessons	3

Example sft_train response (mul_3x2):

First, 509 * 90 = 45810.
Then, 509 * 6 = 3054.
Finally, 45810 + 3054 = 48864.
Answer: 48864

All answers are non-negative integers (1 to 96,709 in sft_train).

Splits

Split	Kind	Records	Used by
sft_train	sft	1000	SFT
preference_train	preference	500	DPO
rl_train	prompt	500	GRPO
validation	eval	100	development checks
test	eval	500	all reported results
dev	eval	500	hyperparameter selection
preference_test	preference	500	preference-accuracy metric (derived from test)

Contamination control, checksums and preference pairs (four controlled corruptions, 25% each, verified by the grader at build time) work exactly as in arith-v1.

Limitations

• Same narrow domain and single prompt template as arith-v1.
• Long multiplications are written as partial products, a format a model must learn in SFT; base models that compute differently are graded only on their final answer line.
• Difficulty was set by design, not calibrated on any model before release.

Versions

• 1.0.0 — initial release (v0.3 campaign).

License

Apache-2.0, same as the repository.