Identify the causal origin of contractivity in recurrent operators

Identify which factors—such as model scale, pretraining token volume, or recurrent-core architecture—cause the contraction mapping observed in Huginn-0125 but not in the other evaluated recurrent and dense configurations.

Background

The dynamical analysis shows that Huginn-0125 attenuates perturbations and behaves as a contraction mapping, whereas the other four evaluated configurations amplify perturbations. A controlled intervention demonstrates that sampled-depth training reduces calibration drift but does not materially change operator dynamics, so the depth schedule does not explain contractivity.

The remaining models differ simultaneously in scale, training data, and recurrent-core design. The paper therefore leaves unresolved which of these factors, or another unmeasured factor, accounts for Huginn-0125’s contractive behavior.

References

Potential explanatory factors include model scale (3.6B vs. 543M and 1.5--1.7B), pretraining token volume, or recurrent core architecture. We report the empirical observation while leaving the causal origin open.

— 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 “Contractivity Does Not Track Depth Schedule”