Fixed Universal Transformers
Fixed universal transformers simulate any target transformer via input embeddings with frozen internal parameters, and random initialization achieves universality almost surely.
Published 2026Atlanta Poster Session 3 · Thu, Dec 10, 10:00 AM–1:00 PM local time · Hall C1arXiv ↗OpenReview ↗
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Abstract
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 reasoning. Our results suggest that much of a transformer's expressive power may reside in its input representation rather than its learned weights.