Fast Fourier Correlation is a Highly Efficient and Accurate Feature Attribution Algorithm from the Perspective of Control Theory and Game Theory

The study of neural networks from the perspective of Fourier features has garnered significant attention. While existing analytical research suggests that neural networks tend to learn low-frequency features, a clear attribution method for identifying the specific learned Fourier features has remained elusive. To bridge this gap, we propose a novel Fourier feature attribution method grounded in signal decomposition theory. Additionally, we analyze the differences between game-theoretic attribution metrics for Fourier and spatial domain features, demonstrating that game-theoretic evaluation metrics are better suited for Fourier-based feature attribution. Our experiments show that Fourier feature attribution exhibits superior feature selection capabilities compared to spatial domain attribution methods. For instance, in the case of Vision Transformers (ViTs) on the ImageNet dataset, only $8\%$ of the Fourier features are required to maintain the original predictions for $80\%$ of the samples. Furthermore, we compare the specificity of features identified by our method against traditional spatial domain attribution methods. Results reveal that Fourier features exhibit greater intra-class concentration and inter-class distinctiveness, indicating their potential for more efficient classification and explainable AI algorithms.