While standard evaluation scores for generative models are mostly reference-based, a reference-dependent assessment of generative models could be generally difficult due to the unavailability of applicable reference datasets. Recently, the reference-free entropy scores, VENDI and RKE, have been proposed to evaluate the diversity of generated data. However, estimating these scores from data leads to significant computational costs for large-scale generative models. In this work, we leverage the random Fourier features framework to reduce the computational price and propose the Fourier-based Kernel Entropy Approximation (FKEA) method. We utilize FKEA's approximated eigenspectrum of the kernel matrix to efficiently estimate the mentioned entropy scores. Furthermore, we show the application of FKEA's proxy eigenvectors to reveal the method's identified modes in evaluating the diversity of produced samples. We provide a stochastic implementation of the FKEA assessment algorithm with a complexity $O(n)$ linearly growing with sample size $n$. We extensively evaluate FKEA's numerical performance in application to standard image, text, and video datasets. Our empirical results indicate the method's scalability and interpretability applied to large-scale generative models. The codebase is available at https://github.com/aziksh-ospanov/FKEA.

翻译：尽管生成模型的标准评估分数大多基于参考数据，但由于适用参考数据集的不可得性，依赖参考的生成模型评估通常较为困难。近期，无参考熵分数VENDI与RKE被提出用于评估生成数据的多样性。然而，从数据中估计这些分数会导致大规模生成模型产生显著的计算成本。本工作中，我们利用随机傅里叶特征框架降低计算代价，提出了基于傅里叶的核熵近似方法。我们利用FKEA所近似的核矩阵特征谱来高效估计上述熵分数。此外，我们展示了FKEA代理特征向量的应用，以揭示该方法在评估生成样本多样性时所识别的模态。我们提供了复杂度为$O(n)$的FKEA评估算法随机实现，其计算量随样本量$n$线性增长。我们在标准图像、文本和视频数据集上广泛评估了FKEA的数值性能。实证结果表明该方法应用于大规模生成模型时具有可扩展性与可解释性。代码库发布于https://github.com/aziksh-ospanov/FKEA。