Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
Positional encoding (PE) is widely viewed as necessary for transformers to process ordered sequences: without them, the next-token map appears permutation-invariant in its context tokens. This intuition underlies all prior universality results, which rely on positional information to prove that transformers with chain-of-thought can perform arbitrary computation, i.e., they are Turing complete. We revisit this belief in the regime most relevant to long-form reasoning, where generation proceeds through a finite sliding context window. Our opening perception is that the window mechanism itself (mildly) breaks the permutation symmetry. To distill and precisely capture the degree of this adde...
| Authors | Qian Li, Xinyu Mao, Shang-Hua Teng |
|---|---|
| Primary category | cs.LG |
| Published | 1 June 2026 |
| Last updated at source | 2 June 2026 |
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