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arXiv · 2601.16450

On the Expressive Power of Floating-Point Transformers

Sejun Park·Yeachan Park·Geonho Hwang
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Abstract

The study on the expressive power of transformers shows that transformers are permutation equivariant, and they can approximate all permutation-equivariant continuous functions on a compact domain. However, these results are derived under real parameters and exact operations, while real implementations on computers can only use a finite set of numbers and inexact machine operations with round-off errors. In this work, we investigate the representability of floating-point transformers that use floating-point parameters and floating-point operations. Unlike existing results under exact operations, we first show that floating-point transformers can represent a class of non-permutation-equivariant functions even without positional encoding. Furthermore, we prove that floating-point transformers can represent all permutation-equivariant functions when the sequence length is bounded, but they cannot when the sequence length is large. We also found the minimal equivariance structure in floating-point transformers, and show that all non-trivial additive positional encoding can harm the representability of floating-point transformers.

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Sejun Park, Yeachan Park, Geonho Hwang. 2026-01-23. On the Expressive Power of Floating-Point Transformers. https://arxiv.org/abs/2601.16450

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