Deeper Understanding of Black-box Predictions via Generalized Influence Functions

Influence functions (IFs) elucidate how learning data affects model behavior. However, growing non-convexity and the number of parameters in modern large-scale models lead to imprecise influence approximation and instability in computations. We highly suspect that the first-order approximation in large models causes such fragility, as IFs change all parameters including possibly nuisance parameters that are irrelevant to the examined data. Thus, we attempt to selectively analyze parameters associated with the data. However, simply computing influence from the chosen parameters can be misleading, as it fails to nullify the subliminal impact of unselected parameters. Our approach introduces generalized IFs, precisely estimating target parameters' influence while considering fixed parameters' effects. Unlike the classic IFs, we newly adopt a method to identify pertinent target parameters closely associated with the analyzed data. Furthermore, we tackle computational instability with a robust inverse-Hessian-vector product approximation. Remarkably, the proposed approximation algorithm guarantees convergence regardless of the network configurations. We evaluated our approach on ResNet-18 and VGG-11 for class removal and backdoor model recovery. Modifying just 10\% of the network yields results comparable to the network retrained from scratch. Aligned with our first guess, we also confirm that modifying an excessive number of parameters results in a decline in network utility. We believe our proposal can become a versatile tool for model analysis across various AI domains, appealing to both specialists and general readers. Codes are available at https://github.com/hslyu/GIF.