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The problem of attribution is concerned with identifying the parts of aninput that are responsible for a model's output. An important family ofattribution methods is based on measuring the effect of perturbations appliedto the input. In this paper, we discuss some of the shortcomings of existingapproaches to perturbation analysis and address them by introducing the conceptof extremal perturbations, which are theoretically grounded and interpretable.We also introduce a number of technical innovations to compute extremalperturbations, including a new area constraint and a parametric family ofsmooth perturbations, which allow us to remove all tunable hyper-parametersfrom the optimization problem. We analyze the effect of perturbations as afunction of their area, demonstrating excellent sensitivity to the spatialproperties of the deep neural network under stimulation. We also extendperturbation analysis to the intermediate layers of a network. This applicationallows us to identify the salient channels necessary for classification, which,when visualized using feature inversion, can be used to elucidate modelbehavior. Lastly, we introduce TorchRay, an interpretability library built onPyTorch.

Understanding Deep Networks via Extremal Perturbations and Smooth Masks