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arXiv:2609.11801LGAI10 sep 2026

Thinking with Looped Flows

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LOOPED FLOWS58.8%GRAM52%FPRM47.5%TRM44.6%0100% ARC-AGI-1 PASS@2
fig. arc-agi-1 pass@2Looped flows top single-trajectory looped models on ARC

Train looping reasoning models as step-by-step denoisers so more loops at test time help.

58.8%

ARC-AGI-1 test accuracy

Same 7M architecture as TRM, much higher score

How it works

  1. Loops train poorly

    Looped models backprop through only one or a few updates, so early steps never learn to help later ones.

  2. Denoise, step by step

    Each loop step denoises a noisy solution, with noise shrinking over steps and the same noise sample shared.

  3. Better, scalable reasoning

    Beats prior looped models on five of six benchmarks; finer time grids add compute, different noise gives varied answers.

updatenext steppredictionflow stateat t=1Problem+ noiseStatefuldenoiserRecurrentstateODE/SDE stepSolutionupdatenext steppredictionflow stateat t=1Problem+ noiseStatefuldenoiserRecurrentstateODE/SDE stepSolution

What they found

Which comes out on top on ARC-AGI-1 pass@2?

More integration steps, better answers

try it

Drag the number of inference steps up and watch accuracy change.

Inference stepsAccuracycoarse, rough solvefine, near ceiling
Accuracy
low
here
coarse, rough solve
A finer time grid spends more compute and lifts accuracy, then gains level off.Illustrative model, not the paper's data

Terms

6 terms

Looped model Network reusing the same weights repeatedly to update a hidden state.'

Like restoring a photo through progressively clearer versions, each pass keeping notes for the next, instead of guessing the whole picture at once.

Where it breaks
Here the notes are learned hidden features, trained only with local losses.

Limits

  • Models are tiny (5–7M) and tested only on puzzle-style grid tasks.
  • Sharing noise allows a shortcut the model could learn in theory.
  • Needs extra regularization to avoid overfitting on Sudoku and ARC-AGI-2.
From the paper