A Universal Metric and O(1) Framework for Disentangling Feature-Level Privacy Risk in Machine Learning Models

This paper introduces the Residual Information Index (RII), a universal, model-agnostic metric that is designed to quantify the clarity of the functional residue that survives a machine learning (ML) model's compression process. Grounded in the Information Bottleneck principle, the RII establishes a mathematically precise Critical Residual Boundary at 𝑒 −1 ≈ 0.37 to identify representational leakage definitively across disparate data modalities. To operationalize this metric, we develop the Residual Information Auditor (RIA), an inverse multi-task learning architecture that resolves the long-standing Audit Scalability Gap in ML privacy auditing. Experimental results across 30 trials demonstrate that the RIA framework achieves amortized 𝑂(1) efficiency by collapsing the traditional 𝑂(𝑁) auditing process into a single-pass training objective, achieving speedups of up to 91x over generative adversarial batteries while maintaining strong diagnostic alignment. The framework's robustness across deep neural networks and gradient-boosted decision trees validates the RII as a fundamental, architecture-independent measure of informational persistence that is empirically grounded in information-theoretic bitrates.