Thinking with Looped Flows

2026-09-10

AI Summary

该研究提出循环流方法，通过局部去噪目标训练循环模型，解决深度学习中循环模型训练时梯度仅覆盖少数更新的问题，提高推理能力。

Abstract

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.

Problem

• looped models
• recurrent updates
• backpropagation
• training difficulty
• temporal association

Innovation

• looped flows
• local denoising objectives
• temporal association
• probability flow