# DART: Distributional Adversarial Recurrent Training for Algorithm Learning

arXiv: https://arxiv.org/abs/2609.05988 · HTML: https://mlsanity.com/paper/2609.05988/

## 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 27 references that are in the map.
- First posted on arXiv 5 Sep 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)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [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)
- [PonderNet: Learning to Ponder](https://mlsanity.com/paper/2107.05407/) (2021)
- [The pitfalls of next-token prediction](https://mlsanity.com/paper/2403.06963/) (2024)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoning](https://mlsanity.com/paper/2511.22570/) (2025)
- [End-to-end Algorithm Synthesis with Recurrent Networks: Logical Extrapolation Without Overthinking](https://mlsanity.com/paper/2202.05826/) (2022)
- [Encoding Robustness to Image Style via Adversarial Feature Perturbations](https://mlsanity.com/paper/2009.08965/) (2020)
- [Differentiable Adaptive Computation Time for Visual Reasoning](https://mlsanity.com/paper/2004.12770/) (2020)
- [Structure-Guided Adversarial Training of Diffusion Models](https://mlsanity.com/paper/2402.17563/) (2024)
- [Rethinking Deep Thinking: Stable Learning of Algorithms using Lipschitz Constraints](https://mlsanity.com/paper/2410.23451/) (2024)
- [Adaptive recurrent vision performs zero-shot computation scaling to unseen difficulty levels](https://mlsanity.com/paper/2311.06964/) (2023)

## Abstract (arXiv)

Recurrent reasoning models (RRMs) can solve structured problems, achieving easy-to-hard generalization through iterative computation in hidden space. These models are typically trained with instance-level supervision, which becomes increasingly problematic as task difficulty grows: valid solutions occupy a tiny region of the solution space, while invalid solutions proliferate rapidly. We propose Distributional Adversarial Recurrent Training (DART), a training framework that replaces single-point supervision with a local target distribution around the ground-truth solution and aligns model outputs with this distribution through an adversarial objective. DART provides a richer learning signal and encourages more stable iterative trajectories toward valid solutions. When evaluated on Maze, Chess, and masked Sudoku with multiple RRMs, including Deep Thinking Systems and Tiny Recursive Models, DART improves solution quality, stability, and robustness under the evaluated distribution shifts. Comparisons with label smoothing, Gaussian softened targets, and progressive training show that DART is not explained by target softening alone and is complementary to training schemes that stabilize long-horizon recurrence. These results identify DART as a promising approach for improving robustness across the evaluated recurrent reasoning models.