GRALIS Framework Unifies XAI Attribution Methods via Riesz Representation

A novel mathematical framework known as GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley) introduces a cohesive canonical representation for linear attribution techniques in explainable AI. Documented in arXiv:2605.05480, this framework employs the Riesz Representation Theorem to demonstrate that every additive, linear, and continuous attribution functional on L^2(Q,mu) has a distinct canonical form (Q, w, Delta). This framework encompasses methods such as SHAP, Integrated Gradients, LIME, and linearized GradCAM, while excluding nonlinear functionals like standard GradCAM or attention maps. GRALIS presents seven formal theorems that ensure guarantees such as necessary canonical form, exact completeness, and Monte Carlo convergence O(1/sqrt(m))+O(1/k), among others, facilitating formal comparisons across previously unconnected methods.