We study causal interactions for payoff allocation in cooperative game theory, including quantifying feature attribution for deep learning models. Most feature attribution methods mainly stem from the criteria of the Shapley value, which assigns fair payoffs to players based on their expected contribution in a cooperative game. However, interactions between players in the game do not explicitly appear in the original formulation of the Shapley value. In this work, we reformulate the Shapley value to clarify the role of interactions and discuss implicit assumptions from a game-theoretical perspective. Our theoretical analysis demonstrates that when negative interactions exist—common in deep learning models—the efficiency axiom can lead to the undervaluation of attributions or payoffs. We suggest a new allocation rule that decomposes contributions into interactions and aggregates positive parts for non-convex games. Furthermore, we propose an approximation algorithm to reduce the cost of interaction computation which can be applied to differentiable functions such as deep learning models. Our approach mitigates counterintuitive attribution outcomes observed in existing methods, ensuring that features critical to a model’s decision receive appropriate attribution.

Understanding intermediate representations of the concepts learned by deep learning classifiers is indispensable for interpreting general model behaviors. Existing approaches to reveal learned concepts often rely on human supervision, such as pre-defined concept sets or segmentation processes. In this paper, we propose a novel unsupervised method for discovering distributed representations of concepts by selecting a principal subset of neurons. Our empirical findings demonstrate that instances with similar neuron activation states tend to share coherent concepts. Based on the observations, the proposed method selects principal neurons that construct an interpretable region, namely a Relaxed Decision Region (RDR), encompassing instances with coherent concepts in the feature space. It can be utilized to identify unlabeled subclasses within data and to detect the causes of misclassifications. Furthermore, the applicability of our method across various layers discloses distinct distributed representations over the layers, which provides deeper insights into the internal mechanisms of the deep learning model.

Even though Generative Adversarial Networks (GANs) have shown a remarkable ability to generate high-quality images, GANs do not always guarantee the generation of photorealistic images. Occasionally, they generate images that have defective or unnatural objects, which are referred to as `artifacts'. Research to investigate why these artifacts emerge and how they can be detected and removed has yet to be sufficiently carried out. To analyze this, we first hypothesize that rarely activated neurons and frequently activated neurons have different purposes and responsibilities for the progress of generating images. In this study, by analyzing the statistics and the roles for those neurons, we empirically show that rarely activated neurons are related to the failure results of making diverse objects and inducing artifacts. In addition, we suggest a correction method, called `Sequential Ablation’, to repair the defective part of the generated images without high computational cost and manual efforts.

Deep neural networks have demonstrated competitive performance in classification tasks for sequential data. However, it remains difficult to understand which temporal patterns the internal channels of deep neural networks capture for decision-making in sequential data. To address this issue, we propose a new framework with which to visualize temporal representations learned in deep neural networks without hand-crafted segmentation labels. Given input data, our framework extracts highly activated temporal regions that contribute to activating internal nodes and characterizes such regions by prototype selection method based on Maximum Mean Discrepancy. Representative temporal patterns referred to here as Prototypes of Temporally Activated Patterns (PTAP) provide core examples of subsequences in the sequential data for interpretability. We also analyze the role of each channel by Value-LRP plots using representative prototypes and the distribution of the input attribution. Input attribution plots give visual information to recognize the shapes focused on by the channel for decision-making.