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    <abstract>Large language models manipulate numerical expressions fluently, yet it is unclear whether a number inferred from a collection enters the same internal interface as an explicit numeral or number word. We test digits, English number words, and counts of repeated tokens in five Qwen3 base models from 0.6B to 14B. After each quantity expression but before a comparison, parity, or equality question, we interchange one residual-stream state between forms. Textual-count states preserve held-out cardinal order, even at fixed sequence length. In behaviourally competent 8B and 14B cases, digit and number-word states are bidirectionally interchangeable. At the tested collection boundary, however, a count state does not transfer even to a different count of the same form, and no count–sign direction meets the same one-shot criteria. A same-depth sweep and symbol-derived linear subspace do not recover a bidirectional local interface. Longer interventions and a separate mixture-of-experts model reveal strong but directional bridges. Counting information and correct behaviour can therefore coexist without a locally portable state at the tested boundary.</abstract>
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%0 Conference Proceedings
%T Numbers Through Signs: How LLMs Connect Counts, Number Words, and Numerals
%A Yoo, J. Albert
%Y Valentino, Marco
%Y Ferreira, Deborah
%Y Thayaparan, Mokanarangan
%Y Ranaldi, Leonardo
%Y Cheng, Jo-Ku
%Y Freitas, Andre
%S The Proceedings of the 4th Workshop on Mathematical Natural Language Processing (MathNLP 2026)
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-468-2
%F yoo-2026-numbers
%X Large language models manipulate numerical expressions fluently, yet it is unclear whether a number inferred from a collection enters the same internal interface as an explicit numeral or number word. We test digits, English number words, and counts of repeated tokens in five Qwen3 base models from 0.6B to 14B. After each quantity expression but before a comparison, parity, or equality question, we interchange one residual-stream state between forms. Textual-count states preserve held-out cardinal order, even at fixed sequence length. In behaviourally competent 8B and 14B cases, digit and number-word states are bidirectionally interchangeable. At the tested collection boundary, however, a count state does not transfer even to a different count of the same form, and no count–sign direction meets the same one-shot criteria. A same-depth sweep and symbol-derived linear subspace do not recover a bidirectional local interface. Longer interventions and a separate mixture-of-experts model reveal strong but directional bridges. Counting information and correct behaviour can therefore coexist without a locally portable state at the tested boundary.
%U https://aclanthology.org/2026.mathnlp-main.21/
%P 285-290

Markdown (Informal)

[Numbers Through Signs: How LLMs Connect Counts, Number Words, and Numerals](https://aclanthology.org/2026.mathnlp-main.21/) (Yoo, MathNLP 2026)

• Numbers Through Signs: How LLMs Connect Counts, Number Words, and Numerals (Yoo, MathNLP 2026)

ACL

• J. Albert Yoo. 2026. Numbers Through Signs: How LLMs Connect Counts, Number Words, and Numerals. In The Proceedings of the 4th Workshop on Mathematical Natural Language Processing (MathNLP 2026), pages 285–290, Budapest, Hungary. Association for Computational Linguistics.