Towards the Linear Algebra Based Taxonomy of XAI Explanations

XAI methods need better mathematical frameworks: The paper argues that existing taxonomies of explainable AI focus too much on how they involve humans, but lack rigorous mathematical foundations that would allow researchers to systematically compare and evaluate different explanation methods.

Linear algebra offers a practical organizing principle: By grounding explanations in linear algebra concepts, this approach provides a more standardized way to categorize XAI techniques, which could help practitioners choose appropriate explanation methods for their specific applications.

Focus on "local explanations" matters for real-world use: The paper concentrates on local explanations (why a model made a specific prediction) rather than global ones, which aligns with practical needs—users typically want to understand individual decisions that affect them, not overall model behavior.

Mathematical rigor can improve transparency: A taxonomy based on mathematical properties rather than subjective criteria could make it easier to audit and verify that explanation methods are actually doing what they claim, supporting more trustworthy AI deployment.

This work addresses a gap in XAI standardization: By proposing a systematic way to classify explanations for data in real-valued spaces (ℝⁿ), the paper contributes to making XAI more standardized and comparable across different industries and applications.