An axiomatization of the interactions between the palyers of any coalition is given. It is based on three axioms: linearity, dummy and symmetry. These interaction indices extend the Banzhaf and Shapley values when using in addition two equivalent recursive axioms. Lastly, the authors give an expression of the Banzhaf and Shapely interaction indices in terms of pseudo-Boolean functions.

An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games

This paper aims to understand and improve the utility of the dropout operation from the perspective of game-theoretic interactions. We prove that dropout can suppress the strength of interactions between input variables of deep neural networks (DNNs). The theoretic proof is also verified by various experiments. Furthermore, we find that such interactions were strongly related to the over-fitting problem in deep learning. Thus, the utility of dropout can be regarded as decreasing interactions to alleviate the significance of over-fitting. Based on this understanding, we propose an interaction loss to further improve the utility of dropout. Experimental results have shown that the interaction loss can effectively improve the utility of dropout and boost the performance of DNNs.

Interpreting and Boosting Dropout from a Game-Theoretic View

In this study, we define interaction components of different orders between two input variables based on game theory. We further prove that interaction components of different orders satisfy several desirable properties.

Game-Theoretic Interactions of Different Orders.

Technical Note: Game-Theoretic Interactions of Different Orders.

This paper aims to understand adversarial attacks and defense from a new perspecitve, i.e., the signal-processing behavior of DNNs. We novelly define the multi-order interaction in game theory, which satisfies six properties. With the multi-order interaction, we discover that adversarial attacks mainly affect high-order interactions to fool the DNN. Furthermore, we find that the robustness of adversarially trained DNNs comes from category-specific low-order interactions. Our findings provide more insights into and make a revision of previous understanding for the shape bias of adversarially learned features. Besides, the multi-order interaction can also explain the recoverability of adversarial examples.

Game-theoretic Understanding of Adversarially Learned Features.

This paper aims to explain deep neural networks (DNNs) from the perspective
of multivariate interactions. In this paper, we define and quantify the
significance of interactions among multiple input variables of the DNN. Input
variables with strong interactions usually form a coalition and reflect
prototype features, which are memorized and used by the DNN for inference. We
define the significance of interactions based on the Shapley value, which is
designed to assign the attribution value of each input variable to the
inference. We have conducted experiments with various DNNs. Experimental
results have demonstrated the effectiveness of the proposed method.

Interpreting Multivariate Interactions in DNNs

This paper proposes a method to disentangle and quantify interactions among words that are encoded inside a DNN for natural language processing. We construct a tree to encode salient interactions extracted by the DNN. Six metrics are proposed to analyze properties of interactions between constituents in a sentence. The interaction is defined based on Shapley values of words, which are considered as an unbiased estimation of word contributions to the network prediction. Our method is used to quantify word interactions encoded inside the BERT, ELMo, LSTM, CNN, and Transformer networks. Experimental results have provided a new perspective to understand these DNNs, and have demonstrated the effectiveness of our method.

Building Interpretable Interaction Trees for Deep NLP Models.

This paper aims to explain deep neural networks (DNNs) from the perspective of multivariate interactions. In this paper, we define and quantify the significance of interactions among multiple input variables of the DNN. Input variables with strong interactions usually form a coalition and reflect prototype features, which are memorized and used by the DNN for inference. We define the significance of interactions based on the Shapley value, which is designed to assign the attribution value of each input variable to the inference. We have conducted experiments with various DNNs. Experimental results have demonstrated the effectiveness of the proposed method.

Die Zhang

Papers

Interpreting Multivariate Interactions in DNNs

Building Interpretable Interaction Trees for Deep NLP Models.

Interpreting Multivariate Shapley Interactions in DNNs

Game-theoretic Understanding of Adversarially Learned Features.

Interpreting Hierarchical Linguistic Interactions in DNNs.