# An Algebra of Transformers

arXiv:2610.36795v1 Announce Type: cross Abstract: On the theoretic analyses on transforms, they mainly focus on the computability analysis, such the Turing-completeness of unbounded precision transformers, the advantage of parallelizability of unbounded precision transformers and the limitations of bounded precision transformers. This paper give transformers an algebra for reasoning, which relies heavily on the functional decomposition results of transformers. This algebra uses functional decompositions as atomic actions, includes sequential composition and parallel composition, recursion for feedback and abstraction for hidden layers. As we know, it is the first attempt to model transformers logically and can be used to verify the correctness of transformer based applications.

## Why It Matters

Most theoretical work on transformers focuses on computability—Turing completeness, parallelizability, and the limits of bounded precision—rather than on reasoning with them. This paper gives transformers a logical algebra built from functional decomposition, with sequential and parallel composition, recursion, and abstraction, and it is the first attempt to model transformers formally for verification. The approach matters because it connects [transformers](../transformers.md) to [symbolic AI](../symbolic-ai.md) and formal [knowledge and reasoning](../knowledge-reasoning.md), opening the door to verifying transformer-based applications instead of treating them as opaque black boxes.

## Sources

- rss: https://arxiv.org/abs/2610.36795

*Back to [Recent News](../../news.md) · [Sub-article index](../index.md).*