CoT transformers simulate any Word RAM algorithm with poly-logarithmic overhead in three architectures, improving on quadratic TM overhead.
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cs.LG 4years
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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.
Low-precision softmax transformers with chain-of-thought simulate Turing machines at logarithmic depth and width; summarized CoT improves this to logarithmic space scaling.
LOTUS uses a looped padded Transformer with parallel cross-entropy supervision on gold CoT tokens to match explicit CoT performance at 3B parameters while reducing thought-phase latency 2.5x-6.9x.
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 Expressive Power of Low Precision Softmax Transformers with (Summarized) Chain-of-Thought
Low-precision softmax transformers with chain-of-thought simulate Turing machines at logarithmic depth and width; summarized CoT improves this to logarithmic space scaling.
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Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers
LOTUS uses a looped padded Transformer with parallel cross-entropy supervision on gold CoT tokens to match explicit CoT performance at 3B parameters while reducing thought-phase latency 2.5x-6.9x.