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文章背景与核心概要

无论是人类还是机器，在应对更复杂的难题时，最直观的策略往往是投入更多的计算与思考时间。在深度学习领域，传统的循环模型试图通过在推理阶段不断循环更新隐藏状态来实现这一目标，但其训练过程常受限于反向传播算法的有效步数，导致早期的循环计算无法有效为后续推理步骤铺路。针对这一瓶颈，本文提出了名为“循环流” (Looped Flows) 的全新方法，通过局部去噪目标与递减噪声水平巧妙引导循环状态的演进。在推理时，模型将计算过程转化为对概率流速度的积分，能够通过更精细的时间网格投入额外算力，并在 ARC-AGI-1 上取得了 58.8% 的高准确率，为深度模型在测试期自适应扩展推理算力提供了全新思路。

基于循环流的思考：通过动态计算分配提升深度推理能力

Thinking with Looped Flows

概要

Summary

《基于循环流的思考》 (Thinking with Looped Flows) 提出了一种新颖的机器学习方法，旨在通过动态分配计算时间来增强深度学习模型处理复杂推理任务的能力。传统的循环模型在训练时往往面临严重瓶颈，因为其反向传播通常仅能覆盖极少数的循环更新步骤，这导致模型在早期阶段难以学习到有利于后续计算的特征表示。

"Thinking with Looped Flows" introduces a novel machine learning approach to improve how deep learning models handle complex reasoning tasks by dynamically allocating computation time. Traditional looped models suffer during training because backpropagation is typically restricted to only a few recurrent updates, making it difficult for early steps to learn representations that benefit future computations.

作者提出了循环流 (looped flows) 方法，该方法利用带有共享噪声且噪声水平逐步降低的局部去噪目标，在时间维度上无缝训练循环状态。通过将这种训练策略与概率流速度积分相结合，模型不仅能够借助更精细的时间网格扩展其推理能力，还能基于不同的初始噪声样本生成多样化的预测结果。实验结果表明，循环流在六个推理基准测试中全面超越了以往的最优循环模型，在 ARC-AGI-1 上斩获了 58.8% 的准确率，在 ARC-AGI-2 上取得了 12.2% 的优异成绩。

The authors propose looped flows, which utilize local denoising objectives with shared noise and progressively decreasing noise levels to seamlessly train recurrent states over time. By combining this training strategy with probability flow velocity integration, the model can scale its reasoning capacity through finer temporal grids and generate diverse predictions from initial noise samples. Demonstrating exceptional performance, looped flows outperform previous state-of-the-art looped models across six reasoning benchmarks, achieving 58.8% accuracy on ARC-AGI-1 and 12.2% on ARC-AGI-2.

论文元数据

Paper Metadata

  • arXiv ID： arXiv:2609.11801 [cs.LG]
  • 研究领域： 机器学习 (cs.LG)，人工智能 (cs.AI)
  • 提交日期： 2026年9月10日
  • 作者：
  • Ayhan Suleymanzade
  • Chanhyuk Lee
  • Floor Eijkelboom
  • Nicholas M. Boffi
  • İsmail İlkan Ceylan
  • Jinwoo Kim
  • arXiv ID: arXiv:2609.11801 [cs.LG]
  • Subject Areas: Machine Learning (cs.LG), Artificial Intelligence (cs.AI)
  • Submission Date: September 10, 2026
  • Authors:
  • Ayhan Suleymanzade
  • Chanhyuk Lee
  • Floor Eijkelboom
  • Nicholas M. Boffi
  • İsmail İlkan Ceylan
  • Jinwoo Kim

摘要

Abstract

面对更具挑战性的问题，人类和机器通常都会选择在计算上投入更多时间。在深度学习中，循环模型在推理阶段通过反复更新隐藏状态来实现这一理念。然而在实际训练中，反向传播往往只能贯穿一次或极少数几次更新，这使得早期的更新步骤难以被充分训练以有效支撑后续计算。为此，我们提出了循环流 (looped flows) 方法，通过利用局部去噪目标来训练循环结构，巧妙地避开了这一难题。我们通过逐步递减的噪声水平和共享噪声，在去噪目标之间施加了时间关联性，从而促使模型学会传递随时间累积有益计算的循环状态，即便梯度的回传仅覆盖少数更新步骤亦是如此。随后，我们将推理过程形式化为对由学得去噪器与循环状态耦合参数化的概率流速度进行积分。这种机制允许模型通过设定更精细的时间网格投入更多计算来解决复杂难题，并支持从不同的初始噪声样本中生成多个有效预测。在涵盖两个多解基准在内的六个推理基准测试中，循环流全面超越了以往的最优循环模型，在 ARC-AGI-1 测试集上达到了 58.8% 的准确率，在 ARC-AGI-2 测试集上达到了 12.2%。

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.

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