Abstract Explainable artificial intelligence (XAI) encompasses diverse families of methods, from perturbation-based surrogates such as local interpretable model-agnostic explanations and Shapley additive explanations to rule- and utility-based frameworks including Anchors and contextual importance and utility. These approaches rely on different assumptions and contain multiple partially overlapping theoretical lines rather than a single broadly adopted framework. This study reformulates XAI as an inverse problem in vector spaces and introduces an algebraic framework termed approximate inverse model explanations squared (AIME 2 ). The framework expresses explanations as solutions to a weighted generalized inverse that links model outputs to input features. It provides a common perspective from which several existing XAI paradigms can be interpreted within a shared inverse-operator structure. Theoretical analyses confirm the framework’s stability and coordinate equivariance. Controlled experiments demonstrate near-machine-precision equivariance, low perturbation sensitivity (0.2%), and competitive reconstruction fidelity. These results position AIME 2 as a structured algebraic inverse-operator perspective on explainability.
Takafumi Nakanishi (Tue,) studied this question.