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Thinking with Looped Flows

arxiv.org/abs/2609.11801

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Updated 1 h ago · first seen 11 Sept 2026

paper_01M294FPD2EEXS76CKNWF5Z9WG

Published
11 Sept 2026
T1 · 1 h ago
arXiv
2609.11801
T1 · 1 h ago
Category
cs.LG
T1 · 1 h ago

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Claim history for Abstract
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Humans and machines often solve harder problems by spending more time on computation. In deep learning, looped models implement this idea during inference by recurrently updating a hidden state. In practice, however, their training backpropagates through only one or a few updates, making it hard to train early updates to support future ones. We propose looped flows, an approach that sidesteps this issue by training the recurrence with local denoising objectives. By imposing temporal association across denoising objectives through progressively decreasing noise levels and shared noise, the model is incentivized to learn recurrent states that transfer useful computation over time, even when gradients cover only a few updates. We then formulate inference as integrating the velocity of a probability flow parameterized by the learned denoiser, coupled with recurrent states. This allows solving harder problems by spending more computation through a finer temporal grid and enables multiple valid predictions from different initial noise samples. Across six reasoning benchmarks including two multi-solution benchmarks, looped flows outperform prior state-of-the-art looped models overall, achieving 58.8% test accuracy on ARC-AGI-1 and 12.2% on ARC-AGI-2.currentcurrentarXiv (Atom API + RSS)T1highdeterministic

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