Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
arXiv preprint arXiv:2411.01992 , year=
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Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.