Answer resampling improves recursive reasoning in puzzles
Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning
Machine Learning
Summary
The paper looks at how AI models that solve puzzles by thinking repeatedly can get stuck on wrong answers. The authors find that tweaking the model’s guessed answer during testing helps fix errors better than changing other internal parts. They create a new method that resamples answers only when the model is uncertain, vastly improving success rates on tough puzzles without extra training. It also beats previous methods that use much more computing power.
What this means in practice
- •For ai model engineers: Improve puzzle-solving AI accuracy by applying answer resampling during test-time to fix errors efficiently without retraining.
- •For software developers for game ai: Enhance computational resource use in recursive puzzle solvers, enabling better performance on complex logic games like Sudoku variants.
Authors
Maxime Illouz
Abstract
Recursive reasoning models such as the Tiny Recursive Model (TRM) iteratively refine two latent states: an answer state y, decoded into the output, and a reasoning state z, which is never decoded. Many of their failures have been attributed to bad basins, regions of latent space that trap the recursion on wrong answers. Recent test-time approaches perturb y, z or both to recover these failures, but the impact of this choice on performance, test-time compute efficiency and scaling properties remains unclear. Through controlled experiments on TRM, we find that a failed trajectory carries its failure in its answer state. At equal compute, in depth and in width, resampling y recovers more failures than any perturbation of z we tested, and the performance gap widens as the test-time compute budget grows. Our approach, Gated Answer Resampling (GAR), pairs this resampling of the answer state with the model's own halting head and restarts only the puzzles that the head rejects. With at most 64 restarts per puzzle and no training or hyperparameter search, GAR takes TRM from 85.9% to 99.4% on Sudoku-Extreme and from 68.8% to 85.6% on Pencil Puzzle Bench validation. On the same checkpoints, GAR also outperforms Probabilistic TRM (PTRM), which perturbs z at each step, even when PTRM uses 42 to 197 times as much compute.