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arXiv · 2512.06341

Interpretive Efficiency: Information-Geometric Foundations of Data Usefulness

Ronald Katende
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Abstract

Interpretability is central to trustworthy machine learning, yet existing metrics rarely quantify how effectively data support an interpretive representation. We propose Interpretive Efficiency, a normalized, task-aware functional that measures the fraction of task-relevant information transmitted through an interpretive channel. The definition is grounded in five axioms ensuring boundedness, Blackwell-style monotonicity, data-processing stability, admissible invariance, and asymptotic consistency. We relate the functional to mutual information and derive a local Fisher-geometric expansion, then establish asymptotic and finite-sample estimation guarantees using standard empirical-process tools. Experiments on controlled image and signal tasks demonstrate that the measure recovers theoretical orderings, exposes representational redundancy masked by accuracy, and correlates with robustness, making it a practical, theory-backed diagnostic for representation design.

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Ronald Katende. 2025-12-06. Interpretive Efficiency: Information-Geometric Foundations of Data Usefulness. https://arxiv.org/abs/2512.06341

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