The Geometry of Narrow Fine-Tuning Degradation: Trajectory Lock-in and Spectral Bifurcation

Magnitude-based stability proxies such as parameter drift are widely used in narrow-task fine-tuning, yet they do not reliably indicate degradation of broad capabilities. We identify trajectory lock-in: under fixed training conditions for narrow adaptation, the joint evolution of task loss and broad generalization collapses onto a shared low-dimensional degradation curve, so many stabilizers primarily change the rate of progress along this curve rather than altering the curve itself. This yields a drift paradox, in which comparable Euclidean displacement can still correspond to divergent generalization outcomes. To diagnose the underlying structure, we introduce objective-agnostic geometric probes that track the effective update subspace, together with an online harm signal that reflects curvature-dominated channeling toward directions associated with broad degradation. Finally, we show that escaping lock-in requires a spectral bifurcation, namely a qualitative reorientation of the update subspace toward softer curvature modes, thereby improving broad generalization while maintaining matched training performance. We validate these findings across model scales and modalities in narrow-task settings, and report practical deployment procedures and overhead measurements.