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.
Limits of deep learning: Sequence modeling through the lens of complexity theory
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
verdicts
UNVERDICTED 2representative citing papers
LRMs exhibit complete accuracy collapse beyond certain puzzle complexities, with reasoning effort rising then declining, outperforming standard LLMs only on medium-complexity tasks.
citing papers explorer
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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.
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The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity
LRMs exhibit complete accuracy collapse beyond certain puzzle complexities, with reasoning effort rising then declining, outperforming standard LLMs only on medium-complexity tasks.