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This paper presents a theoretical framework for looped transformers that interpolate between chain-of-thought reasoning and latent thought via recurrence in hidden states, offering significant reductions in context window and token generation resources. By simulating Turing machines with softmax attention at constant bit-size, the work advances our understanding of how architectural constraints influence computational efficiency in large language models.
Internalizing Chain-of-thought into Looped Transformers
arXiv:2610.25998v1 Announce Type: cross Abstract: Chain-of-thought (CoT) enables constant-bit-size transformers to perform general-purpose computation through generated tokens (Li and Wang, 2025a), whereas looped transformers carry out the same computation by recurrence in hidden states (latent thought). We construct a family of constant-bit-size looped transformers that interpolates between CoT and latent thought. For a prescribed loop count $L=L(n)$ and a fixed integer $k\ge1$ satisfying $s(n)^{1/k}=\Omega(L)$, our transformer simulates a time-$t(n)$, space-$s(n)$ Turing machine using a context window of $O(s(n)/L)$ and $O(t(n)s(n)^{1/k}/L)$ generated tokens, reducing both resources by a factor of $L$ relative to the corresponding unlooped queue-machine simulation. The construction also holds with softmax attention at constant bit-size, under the finite-precision kernel specified in this paper.
Abstract:Chain-of-thought (CoT) enables constant-bit-size transformers to perform general-purpose computation through generated tokens (Li and Wang, 2025a), whereas looped transformers carry out the same computation by recurrence in hidden states (latent thought). We construct a family of constant-bit-size looped transformers that interpolates between CoT and latent thought. For a prescribed loop count $L=L(n)$ and a fixed integer $k\ge1$ satisfying $s(n)^{1/k}=\Omega(L)$, our transformer simulates a time-$t(n)$, space-$s(n)$ Turing machine using a context window of $O(s(n)/L)$ and $O(t(n)s(n)^{1/k}/L)$ generated tokens, reducing both resources by a factor of $L$ relative to the corresponding unlooped queue-machine simulation. The construction also holds with softmax attention at constant bit-size, under the finite-precision kernel specified in this paper.
Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG)
arXiv:2610.25998 [cs.CC]
(or arXiv:2610.25998v1 [cs.CC] for this version)
https://doi.org/10.48550/arXiv.2610.25998 Focus to learn more arXiv-issued DOI via DataCite
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