\( Xpression \) : A Unifying Metric to Optimize Compression and Explainability Robustness of AI Models

Trustworthiness and efficiency have recently become crucial aspects of applied AI. The intersection of interpretability and model compression, however, still poses significant challenges. As models undergo compression for improved efficiency, maintaining explainability needs to remain a priority. In this paper, we propose a novel metric to evaluate both aspects simultaneously and help practitioners navigate this trade-off. In particular, we delve into the effect that knowledge distillation, quantization, and pruning have on the Infidelity explainability metric. Our goal is for \( Xpression \) metric to guide the optimization of compression whilst the model keeps its infidelity robustness. Experimental results across several neural network architectures show the effectiveness of the proposed metric in combining efficiency and relative interpretability with respect to the original model. This work contributes to advancing the understanding of compression techniques and provides a valuable framework for evaluating their implications on model interpretability.