Determine how the contractivity coefficient evolves with extended training

Determine how the perturbation-response coefficient of the evaluated depth-recurrent language model evolves during training beyond the 40,000-step checkpoint and through the planned 110,000 training steps.

Background

The paper measures perturbation response at a checkpoint trained for 40,000 of 110,000 planned steps. This coefficient is used to characterize whether recurrent operators attenuate or amplify perturbations, but the reported measurement provides only a snapshot of the training trajectory.

The authors explicitly state that its evolution under longer training is unknown. Tracking it across later checkpoints could reveal whether operator dynamics change with optimization even though the 1,000-step depth-sampling intervention did not materially alter contractivity.

References

We also do not know how this coefficient evolves with extended training: our evaluated checkpoint reached $40{,}000$ out of $110{,}000$ planned steps.

— Beyond Depth Truncation: Controlled Evaluation of Depth Utilization in Recursive Language Models  (2609.19934 - Dau et al., 17 Sep 2026) in Section 4, “Dynamics of Recurrence,” subsection “Limitations”