A Compositional Theory of Causally Masked Transformers
What types of decision problems can a causally masked, finite-precision transformer solve for inputs of arbitrary length? Existing answers often rely on idealized arithmetic, but under finite precision, rounding and evaluation order can change what information attention retains and therefore what the model can compute. We develop an algebraic formalization that derives expressivity directly from the model's implemented dynamics. Its central object is its memory; the finite internal state computed by attention that summarizes the information from the prefix available to all future queries. Each attention head updates its own state independently within a layer, while layers compose hierarch...
| Authors | Franz Nowak, Ryan Cotterell, Reda Boumasmoud |
|---|---|
| Primary category | cs.FL |
| Published | 29 July 2026 |
| Last updated at source | 29 July 2026 |
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