Fixed Universal Transformers
We introduce \emph{universal transformers}: fixed transformers that can simulate any transformer in a given class via a suitable input embedding. Analogous to a universal Turing machine, the input embedding encodes a description of the target model while all internal parameters remain fixed. We provide explicit sparse constructions achieving universality when the embedding dimension is sufficiently large, and further show that universality is generic: randomly initialized transformers are universal almost surely, which aligns with recent empirical results of Zhong and Andreas (2024). We empirically validate our theory on the algorithmic tasks of parenthesis balancing and multi-hop reasoni...
| Authors | Jingwen Liu, Alexandr Andoni, Daniel Hsu |
|---|---|
| Primary category | cs.LG |
| Published | 29 May 2026 |
| Last updated at source | 1 October 2026 |
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