09-15-2026, 03:51 PM
The article “Explainable artificial intelligence and mathematics: What lies behind?” by Massimiliano Ferrara examines how mathematics can make increasingly complex AI systems more understandable and trustworthy. As modern neural networks become “black boxes,” explainable AI (XAI) seeks to clarify why a model produces a particular prediction—especially in sensitive areas such as healthcare and finance.
The author emphasizes that XAI is deeply mathematical: linear algebra underlies techniques such as PCA and SVD, calculus and optimization explain learning through gradients and Hessians, while information theory provides concepts such as entropy and mutual information for measuring uncertainty and information.
A major focus is game theory, particularly Shapley values, which provide a principled way to measure how much each feature contributes to an AI prediction and form the basis of SHAP explanations. The article also discusses LIME, decision trees, Bayesian networks, gradient-based explanations and attention mechanisms. Looking ahead, Ferrara argues that areas such as topological data analysis, causal inference, information geometry, and multi-objective optimization could further improve explainability. The central message is that mathematics is not merely useful for explaining AI after it has been built; it is likely to be a fundamental tool for designing AI systems that balance accuracy, transparency, simplicity, and accountability. [/url]
[url=https://ems.press/content/serial-article-files/50491]ARTICLE [PDF]
The author emphasizes that XAI is deeply mathematical: linear algebra underlies techniques such as PCA and SVD, calculus and optimization explain learning through gradients and Hessians, while information theory provides concepts such as entropy and mutual information for measuring uncertainty and information.
A major focus is game theory, particularly Shapley values, which provide a principled way to measure how much each feature contributes to an AI prediction and form the basis of SHAP explanations. The article also discusses LIME, decision trees, Bayesian networks, gradient-based explanations and attention mechanisms. Looking ahead, Ferrara argues that areas such as topological data analysis, causal inference, information geometry, and multi-objective optimization could further improve explainability. The central message is that mathematics is not merely useful for explaining AI after it has been built; it is likely to be a fundamental tool for designing AI systems that balance accuracy, transparency, simplicity, and accountability. [/url]
[url=https://ems.press/content/serial-article-files/50491]ARTICLE [PDF]
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