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

2026-05-26

AI Summary

This work addresses the instability and performance degradation commonly observed in recurrent language models during test-time scaling, where deeper inference often leads to collapse rather than improvement. To overcome this limitation, the authors propose the STARS framework, which introduces, for the first time, a stability-driven recursive scaling mechanism. By conceptualizing inference as a process of uncertainty reduction, STARS guides hidden states toward an asymptotically stable fixed point. Stability is enforced through Jacobian spectral radius regularization and stochastic recurrent sampling, effectively constraining the dynamics of hidden states. Experimental results demonstrate that this approach enables reliable test-time scaling on arithmetic tasks, substantially mitigates performance deterioration with increasing depth in complex mathematical reasoning, and achieves higher peak performance.

Abstract

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.

Problem

• Looped Language Models
• test-time scaling
• recurrent dynamics
• stability
• latent reasoning

Innovation

• Looped Language Models
• Test-Time Scaling
• Stability
• Fixed Points
• Jacobian Spectral Radius Regularization