Probabilistic Tiny Recursive Model

TL;DR

Probabilistic TRM introduces stochastic exploration by injecting Gaussian noise during recursive reasoning, significantly improving accuracy on reasoning benchmarks without retraining or task-specific modifications.

Contribution

It proposes a task-agnostic, test-time compute scaling framework that enhances Tiny Recursive Models through stochastic exploration, leading to substantial accuracy improvements.

Findings

Achieved 98.75% accuracy on Sudoku-Extreme, up from 87.4%.

Improved puzzle-solving accuracy from 62.6% to 91.2% on Pencil Puzzle Bench.

Nearly doubled accuracy compared to frontier LLMs at minimal computational cost.

Abstract

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.