---
title: "KAIST's GRAM Beats 671B DeepSeek-R1 on Sudoku With a 10M Model"
subtitle: "GRAM makes recursive reasoning probabilistic, letting a 10M-parameter model beat deterministic baselines on Sudoku, ARC-AGI, and multi-solution puzzles by sampling multiple latent reasoning paths in parallel."
url: "https://alphasignal.ai/news/kaist-s-gram-beats-671b-deepseek-r1-on-sudoku-with-a-10m-model"
author: "AlphaSignal Newsroom"
author_url: "https://alphasignal.ai/editorial-team"
company: "AlphaSignal"
company_url: "https://alphasignal.ai/company/alphasignal"
published: "2026-05-19T05:20:56.000Z"
updated: "2026-06-09T07:32:01.306Z"
type: "Paper"
topics:
  - "Reasoning"
  - "Post Training"
subtopics:
  - "Test Time Compute"
  - "Math Reasoning"
  - "Rl"
upvotes: 1333
source_url: "https://arxiv.org/abs/2605.19376"
comments: 0
truncated: true
---

# KAIST's GRAM Beats 671B DeepSeek-R1 on Sudoku With a 10M Model

> GRAM makes recursive reasoning probabilistic, letting a 10M-parameter model beat deterministic baselines on Sudoku, ARC-AGI, and multi-solution puzzles by sampling multiple latent reasoning paths in parallel.

Most of the recent excitement around reasoning models has focused on one axis: making models think longer by generating more tokens. Chain-of-thought, tree-of-thought, and latent reasoning approaches all extend computation by appending to a sequence. But a quieter research thread has been exploring a fundamentally different mechanism: **recursive latent refinement**, where a compact model repeatedly updates a hidden state rather than growing an output. A new paper from KAIST, NYU, and Mila introduces [GRAM (Generative Recursive reAsoning Models)](https://ahn-ml.github.io/gram-website), which takes this idea further by making the recursive process probabilistic.

## The single-trajectory problem

Recursive Reasoning Models (RRMs) like HRM, TRM, and Looped Transformers work by repeatedly applying a shared transition function to a latent state. Each pass refines the state, and the final state is decoded into an answer. The appeal is efficiency: a small model can do deep computation by reusing the same weights many times, decoupling reasoning depth from parameter count.

The catch is that these models are entirely deterministic. Given the same input and the same initialization, they always follow the same latent trajectory and converge to the same prediction. This is fine when a problem has one right answer, but it creates a structural failure mode: the model has no way to explore alternative solution strategies, maintain uncertainty, or recover from a bad early trajectory. On problems with multiple valid solutions, deterministic recursive models exhibit **mode collapse**, converging to one answer and ignoring the rest of the solution space.

![Comparison of deterministic RRM versus GRAM latent trajectories on N-Queens puzzle](https://arxiv.org/html/2605.19376v2/x1.png) 

## Stochastic guidance at every step

GRAM's core idea is to inject learned stochasticity into the recursive transition itself. Instead of computing a deterministic next state, GRAM computes a deterministic proposal `u_t`, then samples a Gaussian perturbation `ε_t` conditioned on that proposal, and adds them together:

_Preview only. Full text requires an AlphaSignal Pro account._

## Sources

- [Generative Recursive Reasoning (arXiv)](https://arxiv.org/abs/2605.19376)
- [GRAM Project Page](https://ahn-ml.github.io/gram-website)
- [GRAM Full Paper HTML](https://arxiv.org/html/2605.19376)