Quantifying Privacy Leakage in Split Inference via Fisher-Approximated Shannon Information Analysis

Split inference (SI) partitions deep neural networks into distributed sub-models, enabling privacy-preserving collaborative learning. Nevertheless, it remains vulnerable to Data Reconstruction Attacks (DRAs), wherein adversaries exploit exposed smashed data to reconstruct raw inputs. Despite extensive research on adversarial attack-defense games, a shortfall remains in the fundamental analysis of privacy risks. This paper establishes a theoretical framework for privacy leakage quantification using information theory, defining it as the adversary's certainty and deriving both average-case and worst-case error bounds. We introduce Fisher-approximated Shannon information (FSInfo), a novel privacy metric utilizing Fisher Information (FI) for operational privacy leakage computation. We empirically show that our privacy metric correlates well with empirical attacks and investigate some of the factors that affect privacy leakage, namely the data distribution, model size, and overfitting.