# Probabilistic Tiny Recursive Model

arXiv: https://arxiv.org/abs/2605.19943 · HTML: https://mlsanity.com/paper/2605.19943/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 15 of 15)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [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)
- [Pencil Puzzle Bench: A Benchmark for Multi-Step Verifiable Reasoning](https://mlsanity.com/paper/2603.02119/) (2026)
- [Form Follows Function: Recursive Stem Model](https://mlsanity.com/paper/2603.15641/) (2026)

## Built on by (most cited first, 19 of 19)

- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [Energy-guided Recursive Model](https://mlsanity.com/paper/2607.10128/) (2026)
- [Quantizing Recursive Reasoning Models](https://mlsanity.com/paper/2607.16237/) (2026)
- [Reassessing Muon for Matrix Factorization](https://mlsanity.com/paper/2607.13246/) (2026)
- [Steering Recurrent Reasoners at Inference Time with Readout Feedback](https://mlsanity.com/paper/2608.24136/) (2026)
- [Recursive Vision Language Models for General Symbolic Reasoning](https://mlsanity.com/paper/2608.01534/) (2026)
- [Dissecting Hierarchical Reasoning Models: A Mechanistic Study](https://mlsanity.com/paper/2609.22197/) (2026)
- [Compute Time Scaling with Recursive Models for Combinatorial Optimization](https://mlsanity.com/paper/2609.34585/) (2026)
- [Reasoning with Neural Cellular Automata](https://mlsanity.com/paper/2609.36126/) (2026)
- [Scheduling Recursive Reasoning in Looped Transformers](https://mlsanity.com/paper/2609.36653/) (2026)
- [A Tilted Bowl Is Not a Slippery Slope: Compressing Looped Models](https://mlsanity.com/paper/2609.39277/) (2026)
- [Random Recursive Models](https://mlsanity.com/paper/2610.00541/) (2026)
- [On-the-fly Weight Generation: A Hypernetwork Proof of Concept on ARC-1D](https://mlsanity.com/paper/2610.00820/) (2026)
- [Unrolled Flow Models for Reasoning](https://mlsanity.com/paper/2610.09759/) (2026)
- [Invariant-Measure Reasoners: Stable Representations for Latent Reasoning](https://mlsanity.com/paper/2610.10996/) (2026)
- [RELAGRAM: Recursive Latent Graph Model for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2610.15106/) (2026)
- [Resample the Answer: Where to Spend Test-Time Compute in Recursive Reasoning](https://mlsanity.com/paper/2610.16427/) (2026)
- [Tiny Recursive Message Passing](https://mlsanity.com/paper/2610.18649/) (2026)

## Abstract (arXiv)

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.