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Deep learning has revolutionized many areas of machine learning, fromcomputer vision to natural language processing, but these high-performancemodels are generally "black box." Explaining such models would improvetransparency and trust in AI-powered decision making and is necessary forunderstanding other practical needs such as robustness and fairness. A popularmeans of enhancing model transparency is to quantify how individual inputscontribute to model outputs (called attributions) and the magnitude ofinteractions between groups of inputs. A growing number of these methods importconcepts and results from game theory to produce attributions and interactions.This work presents a unifying framework for game-theory-inspired attributionand $k^\text{th}$-order interaction methods. We show that, given modestassumptions, a unique full account of interactions between features, calledsynergies, is possible in the continuous input setting. We identify how variousmethods are characterized by their policy of distributing synergies. We alsodemonstrate that gradient-based methods are characterized by their actions onmonomials, a type of synergy function, and introduce unique gradient-basedmethods. We show that the combination of various criteria uniquely defines theattribution/interaction methods. Thus, the community needs to identify goalsand contexts when developing and employing attribution and interaction methods.

Distributing Synergy Functions: Unifying Game-Theoretic Interaction Methods for Machine-Learning Explainability