Transform Coordinates Separate Vulnerability from Compensatory Capacity under Deployment Perturbations

Local sensitivity identifies functional directions vulnerable to deployment perturbations without necessarily revealing which can compensate for the induced error. A three-parameter Iwasawa representation of the linear canonical transform (LCT), together with a real-valued quadrature of its complex kernel, yields a token-mixing matrix whose derivatives with respect to these parameters can be obtained analytically. Analog in-memory computing (AIMC) supplies a controlled post-training perturbation, followed by hardware-aware fine-tuning to measure adaptation. These differentials capture pronounced anisotropy across coordinates, with additional variation remaining unexplained. After mapping, fractional order retains the highest sensitivity yet exhibits the smallest displacement during adaptation, while the relative contributions of scale and shear change with depth. A local response estimate produces candidate-subset rankings that align more closely with restricted recovery than sensitivity-based selection, and comparison with unrestricted fine-tuning shows that the LCT parameters account for only part of the available recovery. Transform coordinates thereby separate vulnerability from compensatory capacity and provide an interpretable basis for prioritizing post-deployment adaptation.