Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.

Multimodal AI models have achieved impressive performance in tasks that require integrating information from multiple modalities, such as vision and language. However, their "black-box" nature poses a major barrier to deployment in high-stakes applications where interpretability and trustworthiness are essential. How to explain cross-modal interactions in multimodal AI models remains a major challenge. While existing model explanation methods, such as attention map and Grad-CAM, offer coarse insights into cross-modal relationships, they cannot precisely quantify the synergistic effects between modalities, and are limited to open-source models with accessible internal weights. Here we introduce MultiSHAP, a model-agnostic interpretability framework that leverages the Shapley Interaction Index to attribute multimodal predictions to pairwise interactions between fine-grained visual and textual elements (such as image patches and text tokens), while being applicable to both open- and closed-source models. Our approach provides: (1) instance-level explanations that reveal synergistic and suppressive cross-modal effects for individual samples - "why the model makes a specific prediction on this input", and (2) dataset-level explanation that uncovers generalizable interaction patterns across samples - "how the model integrates information across modalities". Experiments on public multimodal benchmarks confirm that MultiSHAP faithfully captures cross-modal reasoning mechanisms, while real-world case studies demonstrate its practical utility. Our framework is extensible beyond two modalities, offering a general solution for interpreting complex multimodal AI models.

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates.

Abstract: Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature importance scores for any black box model. Shapley interaction indices extend the Shapley value to define any-order feature interaction scores. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. We, however, propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for all three definitions, as well as all other that satisfy the linearity, symmetry and dummy axiom.

This paper explores the bottleneck of feature representations of deep neural networks (DNNs), from the perspective of the complexity of interactions between input variables encoded in DNNs. To this end, we focus on the multi-order interaction between input variables, where the order represents the complexity of interactions. We discover that a DNN is more likely to encode both too simple interactions and too complex interactions, but usually fails to learn interactions of intermediate complexity. Such a phenomenon is widely shared by different DNNs for different tasks. This phenomenon indicates a cognition gap between DNNs and human beings, and we call it a representation bottleneck. We theoretically prove the underlying reason for the representation bottleneck. Furthermore, we propose a loss to encourage/penalize the learning of interactions of specific complexities, and analyze the representation capacities of interactions of different complexities. The revolution from shallow to deep models is a crucial step in the development of artificial intelligence. Deep neural networks (DNNs) usually exhibit superior performance to shallow models, which is generally believed as a result of the improvement of the representation power (Pascanu et al., 2013; Montúfar et al., 2014).