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As deep learning (DL) efficacy grows, concerns for poor model explainabilitygrow also. Attribution methods address the issue of explainability byquantifying the importance of an input feature for a model prediction. Amongvarious methods, Integrated Gradients (IG) sets itself apart by claiming othermethods failed to satisfy desirable axioms, while IG and methods like ituniquely satisfy said axioms. This paper comments on fundamental aspects of IGand its applications/extensions: 1) We identify key differences between IGfunction spaces and the supporting literature's function spaces whichproblematize previous claims of IG uniqueness. We show that with theintroduction of an additional axiom, \textit{non-decreasing positivity}, theuniqueness claims can be established. 2) We address the question of inputsensitivity by identifying function classes where IG is/is not Lipschitz in theattributed input. 3) We show that axioms for single-baseline methods haveanalogous properties for methods with probability distribution baselines. 4) Weintroduce a computationally efficient method of identifying internal neuronsthat contribute to specified regions of an IG attribution map. Finally, wepresent experimental results validating this method.

A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions