Extending Recursive Model Inference to 512 Steps Raises Cumulative Sudoku Solve Rates

The study *When Recursive Models Finish Computing*, submitted on September 22, suggests that small recursive models that answer incorrectly within a fixed number of steps may still benefit from further computation. On 1,000 difficult Sudoku puzzles, the authors extended outer recursion from 16 to 512 steps. The attention model’s cumulative full-puzzle solve rate rose from 59.2% to 87.5%, while the MLP version’s rose from 74.4% to 91.9%. [Paper abstract](https://arxiv.org/abs/2609.26487)

These Tiny Recursive Models repeatedly reuse a small network, alternating between updates to the latent state and the answer representation. The original project provides attention and MLP training configurations for Sudoku, allowing computational depth to increase through repeated computation. The engineering value lies in considering parameter capacity and inference budget separately: a model can retain the same weights, while the number of updates each puzzle requires remains a separate cost that must be measured. [Original implementation](https://github.com/SamsungSAILMontreal/TinyRecursiveModels)

The new experiments kept weights and inputs unchanged and observed that changes in the latent state decreased after a puzzle was solved. Local Jacobian analysis showed that perturbations along the model’s own direction of computation generally contract, while those in other directions may still grow. Apparent state stability therefore describes a particular trajectory and cannot directly establish robustness to arbitrary perturbations. [Methods and analysis](https://arxiv.org/html/2609.26487v1)

Reproduction also requires attention to dataset definitions. The Sudoku-Extreme dataset card lists multiple sources of puzzle difficulty, requires every digit on the board to be correct for a solution to count as successful, and states that training and test puzzles are not mathematically equivalent. In engineering evaluations, the puzzle list, checkpoint, and decoding method should be held fixed to avoid directly comparing scores from different subsets. The dataset’s difficulty scores use the number of backtracking steps taken by a symbolic solver; these should not be treated as estimates of the number of steps a neural network needs. [Dataset documentation](https://huggingface.co/datasets/sapientinc/sudoku-extreme)

The study’s cumulative metric counts puzzles that were answered correctly at any point, which differs from output accuracy at a specified step. The main analysis covers only two attention-model checkpoints and one MLP checkpoint, and the findings remain preprint evidence. [Evaluation definitions and limitations](https://arxiv.org/html/2609.26487v1)

For inference systems, a next step worth testing is whether computation can stop reliably without knowing the answer. Changes in state could be combined with an external rule-based verifier, with separate measurements of average steps per puzzle, tail latency, and erroneous stopping rates, then compared with deployment under a fixed computation budget. This is an engineering direction suggested by the results. Increasing the allowed number of steps alone does not demonstrate improved service throughput or cost efficiency, and the findings cannot be directly extrapolated to open-ended language tasks.