Abstract: Most explanation methods are designed in an empirical manner, so exploring whether there exists a first-principles explanation of a deep neural network (DNN) becomes the next core scientific problem in explainable artificial intelligence (XAI). Although it is still an open problem, in this paper, we discuss whether the interaction-based explanation can serve as the first-principles explanation of a DNN. The strong explanatory power of interaction theory comes from the following aspects: (1) it establishes a new axiomatic system to quantify the decision-making logic of a DNN into a set of symbolic interaction concepts; (2) it simultaneously explains various deep learning phenomena, such as generalization power, adversarial sensitivity, representation bottleneck, and learning dynamics; (3) it provides mathematical tools that uniformly explain the mechanisms of various empirical attribution methods and empirical adversarial-transferability-boosting methods; (4) it explains the extremely complex learning dynamics of a DNN by analyzing the two-phase dynamics of interaction complexity, which further reveals the internal mechanism of why and how the generalization power/adversarial sensitivity of a DNN changes during the learning process.

Key words: First-principles explanation; Theory of equivalent interactions; Two-phase dynamics of interactions; Learning dynamics

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