通过随机探索提升小模型推理能力，零成本实现高精度解题。
Probabilistic Tiny Recursive Model
- 在递归步骤注入高斯噪声，实现多路径并行探索。
- Sudoku-Extreme准确率从87.4%提升至98.75%，谜题集达91.2%。
- 无需重训练，700万参数媲美大模型，成本不足其万分之一。
Tiny Recursive Models (TRM) 以极少参数实现复杂推理，通过迭代优化隐状态与答案。但其确定性递归易陷入次优解，缺乏逃离机制。现有方法依赖任务特异性输入扰动与投票聚合，成本高且不通用。本文提出概率化TRM（PTRM），一种无需重训练、无需任务定制的测试时计算扩展框架。在每层深层递归中注入高斯噪声，使多条并行轨迹探索不同解空间，并利用原TRM的Q头选择最优路径。在多个基准上显著提效：Sudoku-Extreme准确率由87.4%升至98.75%；在Pencil Puzzle Bench上从62.6%提升至91.2%。该模型仅用700万参数，成本不足前沿大模型的0.0001倍，准确率接近其两倍（91.2% vs. 55.1%）。
原文摘要 · Abstract (English)
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can lead to convergence at suboptimal solutions, without escape mechanism. A common workaround relies on task-specific input perturbations at test time combined with answer aggregation via voting. We introduce Probabilistic TRM (PTRM), a task-agnostic framework for test-time compute scaling that addresses this limitation through stochastic exploration. PTRM injects Gaussian noise at each deep recursion step, enabling parallel trajectories to explore diverse solution basins, and selects among them using the model's existing Q head (used for early stopping in the original TRM). Without requiring retraining or task-specific augmentations, PTRM enables substantial accuracy gains across benchmarks, including Sudoku-Extreme (87.4% to 98.75%) and on various puzzles from Pencil Puzzle Bench (62.6% to 91.2%). On the latter, PTRM achieves nearly double the accuracy of frontier LLMs (91.2% vs. 55.1%) at less than 0.0001x the cost, using only 7M parameters.
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