Kernelized Parameter Sensitivity Atlases for Amortized Conditional Interpretability

Davide Wiest, Ahanaf Hasan Ariq, Abdul Monaf Chowdhury

Gradient-based attribution provides input-specific information about model parameters, but computing it via backpropagation for many samples is expensive, while static importance scores discard input dependence. We derive KPSA (Kernelized Parameter Sensitivity Atlas) from a block decomposition of the empirical neural tangent kernel. It measures normalized parameter-group sensitivity, embeds those sources in an explicit query space, and uses a lightweight kernel to estimate sensitivities for unseen inputs. We derive bounds that separate finite-source from irreducible representation error and give margin-based top-$k$ recovery. This paper studies two interpretability applications. Firstly, KPSA identifies parameter groups with high susceptibility to perturbations across vision, forecasting, and protein-modeling setups. Across a fivefold range of parameter budgets ($0.02$-$0.1\%$), its selected groups attain $39$-$85\%$ of the perturbation susceptibility of a first-order backpropagation oracle. In vision and forecasting, these parameter groups form sparse sensitivity circuits that extend across depth and vary systematically with the input. Secondly, we use KPSA on an…