On the Existence of Universal Simulators of Attention

• URL: http://arxiv.org/abs/2506.18739v1
• Date: Mon, 23 Jun 2025 15:15:25 GMT
• Title: On the Existence of Universal Simulators of Attention
• Authors: Debanjan Dutta, Faizanuddin Ansari, Anish Chakrabarty, Swagatam Das,
• Abstract summary: We present solutions to identically replicate attention outputs and the underlying elementary matrix and activation operations via RASP.<n>Our proofs, for the first time, show the existence of an algorithmically achievable data-agnostic solution, previously known to be approximated only by learning.
• Score: 17.01811978811789
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Prior work on the learnability of transformers has established its capacity to approximate specific algorithmic patterns through training under restrictive architectural assumptions. Fundamentally, these arguments remain data-driven and therefore can only provide a probabilistic guarantee. Expressivity, on the contrary, has theoretically been explored to address the problems \emph{computable} by such architecture. These results proved the Turing-completeness of transformers, investigated bounds focused on circuit complexity, and formal logic. Being at the crossroad between learnability and expressivity, the question remains: \emph{can transformer architectures exactly simulate an arbitrary attention mechanism, or in particular, the underlying operations?} In this study, we investigate the transformer encoder's ability to simulate a vanilla attention mechanism. By constructing a universal simulator $\mathcal{U}$ composed of transformer encoders, we present algorithmic solutions to identically replicate attention outputs and the underlying elementary matrix and activation operations via RASP, a formal framework for transformer computation. Our proofs, for the first time, show the existence of an algorithmically achievable data-agnostic solution, previously known to be approximated only by learning.

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