Junyeob Baek and colleagues introduce Generative Recursive reAsoning Models (GRAM) that convert deterministic recursive reasoning into stochastic latent trajectories and report 97.0% accuracy on Sudoku-Extreme with 10 million parameters

Original post

🧠We introduce "Generative Recursive Reasoning"!

Recursive Reasoning Models like HRM, TRM, and Looped Transformers are deterministic — same input, same reasoning, every time. They collapse the entire space of plausible reasoning paths into a single attractor.

Our model GRAM (Generative Recursive reAsoning Models) turns recursion itself into a stochastic latent trajectory. Multiple hypotheses, alternative solution strategies, and inference-time scaling not just by depth, but by width — parallel trajectory sampling.

And here's the kicker: the same formulation that gives us conditional reasoning p(y|x) also makes GRAM a general generative model p(x).

With only 10M params: • Sudoku-Extreme: 97.0% (TRM 87.4%) • ARC-AGI-1: 52.0% • ARC-AGI-2: 11.1% • N-Queens coverage: 90%+

📄 Paper: https://arxiv.org/abs/2605.19376 🌐 Project page: https://ahn-ml.github.io/gram-website

w/ Junyeob Baek @JunyeobB (KAIST), Mingyu Jo @pyross0000 (KAIST), Minsu Kim @minsuuukim (KAIST & Mila), Mengye Ren @mengyer (NYU), Yoshua Bengio @Yoshua_Bengio (Mila), Sungjin Ahn @SungjinAhn_ (KAIST)

6:10 AM · May 20, 2026 · 160.7K Views

2605.19376

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billy bubba bingus-drumpfus@wgrathwohl

You know shits gonna be fire when fig1 is MNIST

Sungjin Ahn@SungjinAhn_

🧠We introduce "Generative Recursive Reasoning"!

And here's the kicker: the same formulation that gives us conditional reasoning p(y|x) also makes GRAM a general generative model p(x).

With only 10M params: • Sudoku-Extreme: 97.0% (TRM 87.4%) • ARC-AGI-1: 52.0% • ARC-AGI-2: 11.1% • N-Queens coverage: 90%+

📄 Paper: https://arxiv.org/abs/2605.19376 🌐 Project page: https://ahn-ml.github.io/gram-website

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Rohan Paul@rohanpaul_ai

A 10 million parameter model just outperformed deterministic rivals 3 times its size by doing something regular recursive AI dont do: exploring multiple reasoning paths at the same time.

Most AI reasoning models are trapped on a single train of thought, and GRAM ("Generative Recursive Reasoning") is the first to break that by letting the model think in parallel universes simultaneously.

The problem is that all existing recursive models are fully deterministic, meaning given the same input they always follow the exact same reasoning path and can never escape a wrong trajectory or discover more than 1 valid answer.

GRAM fixes this by injecting learned randomness at each refinement step, so the model samples a slightly different direction each time rather than snapping to 1 fixed next state, which produces a spread of diverse reasoning trajectories.

At test time the model runs many of these paths in parallel and selects the best one using a small reward predictor trained alongside the main model, adding a "width" scaling axis on top of the usual "depth" axis of running more recursion steps.

On hard Sudoku puzzles, GRAM with 10M parameters hits 97% accuracy versus 87.4% for the best prior recursive model, and with only 20 parallel samples it outperforms every deterministic baseline even at 320 recursion steps.

On tasks with many valid answers like N-Queens, deterministic recursive models collapse as the number of solutions grows, while GRAM maintains near-perfect accuracy throughout.

The same stochastic framework also acts as a generator: given a blank board, GRAM produces valid Sudoku puzzles 99% of the time using 16 steps, versus 1,000 steps and 55M parameters for the best diffusion baseline at just 91%.

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Paper Link – arxiv. org/abs/2605.19376v1

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Sungjin Ahn@SungjinAhn_

🧠We introduce "Generative Recursive Reasoning"!

And here's the kicker: the same formulation that gives us conditional reasoning p(y|x) also makes GRAM a general generative model p(x).

With only 10M params: • Sudoku-Extreme: 97.0% (TRM 87.4%) • ARC-AGI-1: 52.0% • ARC-AGI-2: 11.1% • N-Queens coverage: 90%+

📄 Paper: https://arxiv.org/abs/2605.19376 🌐 Project page: https://ahn-ml.github.io/gram-website

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Taelin@VictorTaelin

@SungjinAhn_ this makes me unreasonably happy, keep going

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Biosemiote@biosemiote

@SungjinAhn_ Cool work. Also dropping this here, closely related: https://arxiv.org/abs/2605.08605

100% on sudoku extreme with 4 minutes of training on 800k params by computing the trajectory in a lattice, similar to a constraint solver.

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Sungjin Ahn@SungjinAhn_

Generating Sudoku map. GRAM generates valid maps in less than 10 recursion steps. Diffusion (D3PM) takes much more steps and often leaves incorrect cells.

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asfaan murthyulas@AMurthyulas

@SungjinAhn_ How much different from this work.?

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//TODO: fix later 🐳@enjoyingthewind

@SungjinAhn_ Rigggght right, branching vs just wiggling a bit. Thanks for taking time to respond. This is a very interesting research direction.

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Sungjin Ahn@SungjinAhn_

@biosemiote Cool. Thank you for sharing!

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송준 Jun Song@jun_song

@SungjinAhn_ Amazing work from KAIST! 👍

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James@JamesNguyen868

@rohanpaul_ai @grok so this is better than https://arxiv.org/abs/2510.04871 and hrm https://arxiv.org/abs/2506.21734?

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Junyeob Baek@JunyeobB

@enjoyingthewind @SungjinAhn_ Pls check our ablation study. Only Stochasticity fails at multi-solution tasks and generations.

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//TODO: fix later 🐳@enjoyingthewind

@SungjinAhn_ How is it different from

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Rohan Ahluwalia@r0hanahluwalia

@wgrathwohl "age of research" they say

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Super Watcher@superaiwatcher

@SungjinAhn_ Deterministic reasoning is a feature, not a bug. Within 18 months, non-deterministic generative agents will be abandoned for production-critical workflows.

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