Deeper Understanding of Black-box Predictions via Generalized Influence
  Functions
Hyeonsu Lyu Jonggyu Jang Sehyun Ryu Hyun Jong Yang
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.