Understanding Mamba-3 through Oscillatory Dynamics

Mamba-3 introduces input-dependent rotations into recurrent state updates, but their contribution beyond state retention remains unclear. We interpret these rotations as **underdamped second-order dynamics**, providing a framework for investigating the role of oscillation in sequence modeling. Controlled comparisons show that underdamped dynamics outperform non-oscillatory damping regimes on state-tracking tasks, while language-model pretraining demonstrates benefits for long-context prediction and length generalization. Interventions in pretrained models further establish the importance of learned phase, and state analysis suggests that rotation regulates how retained information combines with incoming updates. Taken together, these findings identify underdamped dynamics as a useful mechanism for recurrent computation and suggest that oscillation supports long-context processing by regulating how information accumulates.