Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence. Through latent dynamics analysis, we find an inherent trade-off between stability and effectiveness in existing architectures and strategies. By conceptualizing reasoning as uncertainty reduction, we propose that convergence toward stable fixed points while preserving effectiveness represents a promising way. To this end, we propose STARS (STAbility-driven Recurrent Scaling), a training framework that constrains latent states to approach asymptotically stable fixed points. This is realized via efficient Jacobian Spectral Radius Regularization with random loop sampling, enabling STARS to maximize effectiveness while ensuring rigorous stability. Experiments on arithmetic tasks show that STARS achieves reliable test-time scaling, and on complex mathematical reasoning it substantially mitigates performance degradation as recurrence depth increases while also improving peak performance.

Large language models typically grow by adding more layers, which increases computational cost. LoopLMs offer an alternative by reusing the same layer repeatedly. However, instead of improving steadily with more loops, their performance often peaks at a certain point and then crashes when looped too many times. This paper investigates why this happens and finds a fundamental tension: too few loops leave reasoning incomplete, while too many make the model’s internal state drift into confusion. Inspired by the idea that thinking reduces uncertainty, we propose STARS that gently guides the model’s internal representations toward stable anchor points. This stability prevents the model from spiraling into nonsense when looped many times, while preserving its ability to reason effectively. The result is a step toward making looped language models both efficient and predictable at test time.