Direction, Turning, and Dispersion: A Depth-Dynamic Triad for AI-Generated Text Detection

AI-generated text detection commonly relies on output statistics or static representation features, whose effectiveness can deteriorate under shifts in generator, domain, language, and editing process. We instead study the transformation path. In a frozen backbone, human- and machine-generated content induce distinct relations among successive residual updates. We organize them into three complementary axes: directional persistence measures whether computation continues in a common direction, turning heterogeneity captures how unevenly token trajectories change course, and state dispersion tracks how token-state magnitudes spread across positions at each depth. Their relative-depth profiles form DEPTHTRIAD, a width-independent description of computation-path geometry. The representation supports DEPTHTRIAD-ZERO, a training-free analytic readout, and DEPTHTRIAD-LINEAR, a lightweight full-profile readout whose coefficients localize evidence by axis and depth. Experiments show strong training-free detection across generation, editing, and languages. The full-profile readout leads the compared cross-benchmark methods in AUROC, and the same representation supports detection in images and audio. These findings recast generative detection as measurement of computation dynamics and point toward a shared representation for multimodal provenance.