The rapid advancement of Generative Adversarial Networks (GANs) necessitates the need to robustly evaluate these models. Among the established evaluation criteria, the Fr\'{e}chet Inception Distance (FID) has been widely adopted due to its conceptual simplicity, fast computation time, and strong correlation with human perception. However, FID has inherent limitations, mainly stemming from its assumption that feature embeddings follow a Gaussian distribution, and therefore can be defined by their first two moments. As this does not hold in practice, in this paper we explore the importance of third-moments in image feature data and use this information to define a new measure, which we call the Skew Inception Distance (SID). We prove that SID is a pseudometric on probability distributions, show how it extends FID, and present a practical method for its computation. Our numerical experiments support that SID either tracks with FID or, in some cases, aligns more closely with human perception when evaluating image features of ImageNet data.

翻译：生成对抗网络（GAN）的快速发展要求对这些模型进行稳健评估。在已有的评估标准中，弗雷歇初始距离（FID）因其概念简单、计算速度快以及与人类感知高度相关而得到广泛应用。然而，FID存在固有限制，主要源于其假设特征嵌入服从高斯分布，因此可通过前两阶矩定义。由于这一假设在实际中并不成立，本文探索了图像特征数据中三阶矩的重要性，并利用这一信息定义了一种新度量——我们称之为偏度初始距离（SID）。我们证明了SID是概率分布上的伪度量，展示了其如何扩展FID，并提出了一种实用的计算方法。数值实验表明，SID要么与FID趋势一致，要么在某些情况下，在评估ImageNet数据的图像特征时与人类感知更为吻合。