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<p>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<sup>2</sup>). 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<sup>2</sup> as a structured algebraic inverse-operator perspective on explainability.</p>

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AIME2: toward a unified algebraic theory of explainability via approximate inverse operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月14日

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  • Takafumi Nakanishi

摘要

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 (AIME2). 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 AIME2 as a structured algebraic inverse-operator perspective on explainability.