Language Models Learn Universal Representations of Numbers and Here’s Why You Should Care

Michal \v{S}tef\'anik, Timothee Mickus, Marek Kadl\v{c}{\'\i}k, Bertram H{\o}jer, Michal Spiegel, Ra\'ul V\'azquez, Aman Sinha, Josef Kucha\v{r}, Philipp Mondorf, Pontus Stenetorp


Abstract
Prior work has shown that large language models (LLMs) often converge to accurate input embedding for numbers, based on sinusoidal representations.In this work, we demonstrate that these representations are in fact strikingly systematic, to the point of being almost perfectly universal: different LLM families develop equivalent sinusoidal structures, and number representations are broadly interchangeable in a large swathe of experimental setups.We show that properly factoring in this characteristic is crucial when it comes to assessing how accurately LLMs encode numeric and other ordinal information, and that mechanistically enhancing this sinusoidality can also lead to reductions of LLMs’ arithmetic errors.
Anthology ID:
2026.acl-long.1415
Volume:
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
Month:
July
Year:
2026
Address:
San Diego, California, United States
Editors:
Maria Liakata, Viviane P. Moreira, Jiajun Zhang, David Jurgens
Venue:
ACL
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Publisher:
Association for Computational Linguistics
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Pages:
30663–30681
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URL:
https://preview.aclanthology.org/ingest-acl/2026.acl-long.1415/
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Cite (ACL):
Michal \v{S}tef\'anik, Timothee Mickus, Marek Kadl\v{c}{\'\i}k, Bertram H{\o}jer, Michal Spiegel, Ra\'ul V\'azquez, Aman Sinha, Josef Kucha\v{r}, Philipp Mondorf, and Pontus Stenetorp. 2026. Language Models Learn Universal Representations of Numbers and Here’s Why You Should Care. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 30663–30681, San Diego, California, United States. Association for Computational Linguistics.
Cite (Informal):
Language Models Learn Universal Representations of Numbers and Here’s Why You Should Care (\v{S}tef'anik et al., ACL 2026)
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https://preview.aclanthology.org/ingest-acl/2026.acl-long.1415.pdf
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