Scheduling Recursive Reasoning in Looped Transformers

2026-09-28

AI Summary

Recurrent Transformers struggle with test-time compute scaling due to fixed update scales, often resulting in overly conservative or aggressive inference. This work proposes TAPS, a scheduler that treats the update scale as an independent control axis and adaptively modulates recursive step sizes online via a progress-fluctuation decomposition to optimize inference trajectories. Enabling dynamic scheduling without retraining, TAPS integrates loss sensitivity analysis with an online step-size adjustment algorithm to substantially improve efficiency. Experimental results demonstrate that TAPS effectively enhances terminal accuracy, achieving up to 1.56× speedup while matching baseline precision, and exhibits strong generalization capabilities across diverse settings.

Abstract

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

Problem

• Looped Transformers
• Recurrent Reasoning
• Test-time Compute Scaling
• Update Scale Scheduling
• Step Size Adaptation

Innovation

• Looped Transformers
• Recursive Reasoning
• Adaptive Step Size
• Progress-Fluctuation Decomposition
• Test-Time Compute