From Spectral Saliency to Finite Deletion: Evaluating Selective Language Model Edits

Deleting singular components offers a precise way to remove a capability from a language model, yet the first-order spectral saliency used to rank components predicts only a local loss change, whereas deletion is a finite intervention. In this paper, we study how prediction error affects selective editing, where selective editing requires degradation of a target task while preserving others. We decompose the error into derivative transfer across item splits and nonlinear response along the deletion path. We establish that outer interval screening retains every feasible candidate when every candidate's intervals contain its finite validation loss changes on every task. We evaluate these effects using one answer-only negative log-likelihood objective for search, validation, and test, with disjoint calibration and evaluation masks. The primary configuration targets arithmetic in Mistral-7B-Instruct-v0.3 while preserving code and question answering; extensions cover Llama-3.1-8B-Instruct and reversed target roles. In the primary study, which deletes 1024 coordinates from a support of 7168, calibrated intervals cover 968 of 1024 evaluation masks. Outer screening reaches the direct-selected edit after 25 verification checks, whereas direct verification abstains at a 32-check cap, but it rejects 4 of 74 feasible masks. All three selected edits pass validation, yet only one meets every test constraint. Interval coverage, feasible-candidate retention, and independent test preservation are therefore distinct properties and require separate assessment.