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October 20, 2025Open Access

The Counting Power of Transformers

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Transformers can express highly nonlinear counting properties, expanding their known expressiveness.
The research shows that transformers capture all semialgebraic counting properties, beyond linear counting capabilities.
A subclass of transformers is identified that completely characterizes semialgebraic counting properties, enhancing our understanding of their expressiveness.
Connections with Hilbert's tenth problem reveal new undecidability results for simple transformer models lacking positional encodings.

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This paper reveals transformers' ability to express nonlinear counting properties, suggesting new insights into computational power.

Sälzer et al. (2025) studied this question.

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