Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
arXiv:2606.01532v1 Announce Type: new Abstract: 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
This research is emerging as AI hardware and architectural optimizations are crucial for scaling, especially amidst new insights into transformer capabilities.
This paper challenges fundamental assumptions about transformer architecture, suggesting that simpler designs may be equally powerful for reasoning tasks.
The necessity of positional encoding for Turing completeness in transformers is re-evaluated, potentially simplifying future AI model designs and reducing computational overhead.
- · AI researchers focusing on efficient transformer architectures
- · Developers of AI models for long-form reasoning
- · Hardware manufacturers focused on lower-overhead inference
- · AI researchers overly reliant on complex positional encoding schemes
Architectural simplification leads to more efficient transformer models.
Reduced computational demands could make advanced AI more accessible or allow for larger, more complex models within existing compute budgets.
New foundational models could emerge with novel capabilities that are not currently explored due to architectural constraints.
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Read at arXiv cs.LG