# Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning

arXiv: https://arxiv.org/abs/2610.16427 · HTML: https://mlsanity.com/paper/2610.16427/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 20 of 20)

- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Scaling Exponents Across Parameterizations and Optimizers](https://mlsanity.com/paper/2407.05872/) (2024)
- [Grokking at the Edge of Numerical Stability](https://mlsanity.com/paper/2501.04697/) (2025)
- [Path Independent Equilibrium Models Can Better Exploit Test-Time Computation](https://mlsanity.com/paper/2211.09961/) (2022)
- [Generative Recursive Reasoning](https://mlsanity.com/paper/2605.19376/) (2026)
- [Probabilistic Tiny Recursive Model](https://mlsanity.com/paper/2605.19943/) (2026)
- [Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning](https://mlsanity.com/paper/2605.21488/) (2026)
- [Are Your Reasoning Models Reasoning or Guessing? A Mechanistic Analysis of Hierarchical Reasoning Models](https://mlsanity.com/paper/2601.10679/) (2026)
- [Rethinking Deep Thinking: Stable Learning of Algorithms using Lipschitz Constraints](https://mlsanity.com/paper/2410.23451/) (2024)
- [Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth](https://mlsanity.com/paper/2608.18222/) (2026)
- [Pencil Puzzle Bench: A Benchmark for Multi-Step Verifiable Reasoning](https://mlsanity.com/paper/2603.02119/) (2026)
- [Boosting Inference with Guided Reasoning: Stochastic Exploration for Recursive Models](https://mlsanity.com/paper/2605.25230/) (2026)
- [Energy-guided Recursive Model](https://mlsanity.com/paper/2607.10128/) (2026)
- [Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning](https://mlsanity.com/paper/2609.01449/) (2026)
- [Speed is Confidence](https://mlsanity.com/paper/2601.19085/) (2026)
- [When Recursive Models Finish Computing](https://mlsanity.com/paper/2609.26487/) (2026)

## Abstract (arXiv)

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.