APT4's tokenization contributes to arithmetic accuracy differences between Bielik-PL-11B-v3.0-Instruct and Bielik-11B-v3.0-Instruct through its handling of the no-break space, not through digit segmentation.

Relation: Contributes through a channel

factor

Digit and punctuation tokenization policyTokenizer property concerned.

subject tokenizer

APT4 tokenizerTokenizer whose handling contributes.

comparator tokenizer

Mistral-derived tokenizerTokenizer compared with.

outcome

arithmetic accuracy differences between Bielik-PL-11B-v3.0-Instruct and Bielik-11B-v3.0-InstructOutcome contributed to.

channel

the no-break space (U+00A0) as thousands separatorChannel of the contribution.

excluded channel

digit segmentationChannel without a contribution.

Method and evaluation protocol

Decision rule of the plan for the digit-tokenization mechanism: refutes if digit segmentation is identical on bare and comma-grouped numerals and no tokenizer-attributable format-differential deficit exists in GSM8K's format domain; partial if digit segmentation is identical but a separator-level tokenizer-attributable deficit exists; confirms only if segmentation differs on bare or comma-grouped numerals.

Dataset

2,500 synthetic arithmetic items generated with seed 20260703, each in four number formats and two instruction languages.Version: unspecified · Access: public

Reported results

Tokens per number equal in 5 of 6 renderings, differing only with no-break-space grouping; no-break-space differential 0.1736 [0.1535, 0.1956]; comma-against-space interaction -0.0035 [-0.023, 0.0136]; 14 of 1,319 GSM8K test final answers contain a comma and 0 a space or no-break space. Outcome of the rule: partial.

Uncertainty and replication

Rests on the intervals of the contributing findings.

Evidence references

audit.json · publichttps://github.com/stw2/tokenizer-science-tax/blob/2fc1a1b415a06b7648cdb37319ad573ccdc96a81/experiments/E02-digit-policy/results/audit.jsonprobe_results.json · publichttps://github.com/stw2/tokenizer-science-tax/blob/2fc1a1b415a06b7648cdb37319ad573ccdc96a81/experiments/E02-digit-policy/results/probe_results.jsons9_gsm8k_inventory.json · publichttps://github.com/stw2/tokenizer-science-tax/blob/c43f19850803969bc1fefe537caf14e54cfd9a9f/experiments/E02-digit-policy/data/audit/s9_gsm8k_inventory.jsonmetrics.json · publichttps://github.com/stw2/tokenizer-science-tax/blob/2fc1a1b415a06b7648cdb37319ad573ccdc96a81/experiments/E02-digit-policy/results/metrics.json

Limitations

The conditions of the refutes branch are also met as written; partial applies because a separator-level deficit exists, and the original report gave refutes. GSM8K final answers do not use the no-break space. The two models differ by 20B tokens of continued pretraining and by post-training as well as by the tokenizer; answer-only probes do not measure chain-of-thought arithmetic; MLX bf16 numerics differ from the paper's evaluation stack.