Explainable Artificial Intelligence
AIME²
Toward a unified algebraic theory of explainability via approximate inverse operators
AIME² formulates explainability through an approximate inverse-operator perspective and introduces an Explainability Operator for studying global, output-wise, class-wise, and local explanations within a common algebraic framework.
About
Takafumi Nakanishi
Professor at the School of Computer Science, Tokyo University of Technology. My research focuses on explainable artificial intelligence, inverse-operator approaches to explanation, data mining, and mathematical models for media and intelligent systems.
I proposed Approximate Inverse Model Explanations (AIME) and continue to develop its theoretical foundations, robust and uncertainty-aware extensions, software, and applications.
AIME
Approximate Inverse Model Explanations
AIME is a model-agnostic XAI framework that learns an approximate inverse operator from observed model behavior and uses it to construct input-side explanatory structures.
The original AIME paper introduced the method and demonstrated local and global insights across multiple data modalities. AIME² develops the broader algebraic foundation of the Explainability Operator.
AIME²
From attribution outputs to an Explainability Operator
AIME² studies explanation as an operator connecting model-output representations to explanatory structures in the input space. It does not claim that all XAI methods are identical; it provides an algebraic framework for analyzing a family of inverse-operator explanations.
Conceptual overview of the AIME² inverse-operator perspective.
Common algebraic basis
Multiple explanation queries can be studied as related evaluations of an operator-based framework.
Weighted formulation
Weighting changes the analytical scope and supports globally or locally emphasized explanations.
Regularized estimation
Regularization provides a principled response to ill-conditioning and instability in approximate inversion.
Algebraic analysis
The framework analyzes reconstruction, minimum-norm solutions, stability, and coordinate equivariance.
Publications
When should you cite AIME²?
Please consider citing AIME² when your research addresses one or more of the following:
- explainability formulated through an inverse or reconstruction problem;
- explanations represented as operators rather than isolated attribution vectors;
- a common mathematical basis for global, output-wise, class-wise, and local explanations;
- generalized inverses, minimum-norm solutions, weighting, or regularization in XAI;
- reconstruction, stability, or coordinate equivariance of explanations;
- the relationship between forward prediction and inverse explanation;
- model auditing or repeated explanation queries based on a reusable explanation operator; or
- theoretical comparisons between attribution vectors and operator-valued explanations.
In one sentence:
Cite AIME² when you need an algebraic foundation for studying explainability through a weighted and regularized approximate inverse operator.
Article
T. Nakanishi, “AIME2: toward a unified algebraic theory of explainability via approximate inverse operators,” Communications AI & Computing, vol. 1, no. 1, Art. no. 3, 2026.
BibTeX
Software
Articles, code, and implementation resources
Contact
Research collaboration and discussion
For academic discussion, collaboration, or questions about AIME and AIME², please contact me through my official website or GitHub profile.