Why Training-Free Token Reduction Collapses: The Inherent Instability of Pairwise Scoring Signals

Training-free token reduction methods for Vision Transformers (ToMe, ToFu, PiToMe, and MCTF) employ different scoring mechanisms, yet they share a closely matched cliff-like collapse at high compression. This paper explains \emph{why}. We develop a diagnostic framework with two tools, ranking consistency $\rho_s$ and off-diagonal correlation $\rho_\text{off}$, that decomposes the collapse into (1)a signal-agnostic error amplifier inherent to layer-wise reduction, predicting convex Pareto curves and $r_{\text{crit}} \propto 1/L$; and (2)shared reliance on \emph{pairwise} similarity signals whose ranking consistency degrades from $\rho_s{=}0.88$ to $0.27$ in deep layers. Pairwise rankings are inherently unstable ($O(N_p^2)$ joint perturbations) while unary signals enjoy greater stability ($O(N_p)$ perturbations, CLT). From three design principles derived from this diagnosis, we construct CATIS as a constructive validation: unary signals raise the trigger threshold, triage suppresses the gain. On ViT-Large at 63% FLOPs reduction, CATIS retains 96.9% of vanilla accuracy (81.0%) on ImageNet-1K where all baselines collapse to 43--65%.