pure-arith

Single-template integer arithmetic for evaluating base language models on add / subtract / multiply / divide across operand digit-lengths 1–5.

Built as tier 1 of the eval design described in byte_v2/design/eval/design_v2.md (internal).

Schema

Every row in every config has the same fields:

field	type	example	description
digits_a	int	3	digit count of the left operand
digits_b	int	2	digit count of the right operand
a	int	482	left operand
b	int	17	right operand
question	str	"482+17="	prompt string fed to the model
label	int	499	gold answer (integer)

Construction rules

• Integer-only. Subtraction is non-negative (a >= b). Division is exact (a == q * b, gold answer is q).
• Digit lengths. digits_a, digits_b ∈ {1, 2, 3, 4, 5}.
• Combinations. Target 200 samples per (op, digits_a, digits_b) tuple (100 tuples = 20,000 nominal samples), deduplicated by (a, b). Where the constraint set is too small (e.g. sub 1×1, div 1×1, div 2×2) the realized count is lower. Tuples impossible by construction (db > da for sub, db > da for div) are omitted.

Realized sizes

config	test rows
add	5,000
sub	2,845
mul	5,000
div	2,819
total	15,664

Usage

from datasets import load_dataset
ds = load_dataset("cyanfi/pure-arith", "mul", split="test")
print(ds[0])
# {'digits_a': 1, 'digits_b': 1, 'a': 7, 'b': 7, 'question': '7*7=', 'label': 49}

Intended use

Probe base-model competence on plain integer arithmetic across digit counts, scored by exact-match on output (not log-likelihood). Pair with Onlydrinkwater/int_* (larger random integers) for breadth, gsm8k for freeform NL arithmetic, and MMLU/CUTE/ARC-Challenge/BoolQ for pure NL.