Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models
For practitioners of looped language models, this work addresses the critical bottleneck of unreliable test-time scaling, enabling deeper latent reasoning without performance degradation.
Looped Language Models suffer from performance collapse with increased recurrence depth. STARS, a training framework using Jacobian Spectral Radius Regularization, stabilizes latent dynamics, achieving reliable test-time scaling and improved peak performance on arithmetic and mathematical reasoning tasks.
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.