Decay Signatures: Measuring Domain-Dependent Degradation and the Boundaries of Anchor Prediction

Training on degraded inputs is a standard route to robust representations, yet choosing the degradation intensity remains empirical: existing approaches scan, search, or offer qualitative principles — none compute a schedule from measurable properties of its operators. Working in cross-modal molecule image–graph retrieval, where structure is discrete and verifiable, we introduce decay signatures: per-operator decay rates measured on task, structure, and frequency channels. Signatures overturn conventional operator labels — operator class is a measured, domain-dependent fact, not a priori intuition — and reveal a non-monotone, U-shaped response of fixed-anchor training to intensity, which decomposes into a mild-anchor penalty and a deployment-conditional optimum. Stress-testing a first-order transition-landmark predictor (product of per-operator survival curves, threshold calibrated once) on ten held-out schedules under pre-registration yields a boundary map: the primary criterion is not met (2/4 under the plateau reading, 1/4 under strict argmax scoring); prediction is exact at bracket resolution on a restricted subset, with the caveat that one exact hit rests on a near-cancellation of two measured error terms; and failures decompose into three observed structural sources — saturation, interaction error, and compensability. Degradation intensity is measurable — but only to first order; we report this boundary with the same fidelity as the hits.