When Geometry Misleads: Evaluating Hidden-State Stopping Signals Beyond Accuracy

We investigate the assumption underlying geometry-based adaptive stopping: that low hidden-state alignment during autoregressive generation indicates redundant computation. We introduce Geometric Alignment (GA), a training-free second-order metric, and deploy a forced-truncation intervention across 2,000 reasoning traces on four open-weight architectures, finding that truncation at low GA regions degrades accuracy by up to 81.3% (Clopper–Pearson 95% CIs, all lower bounds positive). However, a six-step evaluation protocol reveals that this value is driven by truncation timing, not content-specific detection: a position-only model achieves nearly identical predictive accuracy (AUROC delta +0.024, bootstrap 95% CI [−0.036, +0.227], includes zero); GA fires at 83% on content-free text (N=100) versus 80% on reasoning; and random triggers at equivalent positions degrade accuracy comparably (Fisher’s exact p=0.745). Applying the same protocol to entropy-based stopping reveals a structurally different failure mode: entropy is a near-fixed position threshold (mean trigger token 22.6±7.5), firing at 100% on content-free text. We propose this six-step evaluation checklist—illustrated on two representative threshold-based signals with distinct failure modes—as a recommended evaluation procedure before deploying any trajectory-based stopping criterion, and release all code and data.