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

arXiv: https://arxiv.org/abs/2504.02016 · HTML: https://mlsanity.com/paper/2504.02016/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 53 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 30 of 40)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Full-Gradient Representation for Neural Network Visualization](https://mlsanity.com/paper/1905.00780/) (2019)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective](https://mlsanity.com/paper/2202.01602/) (2022)
- [Debugging Tests for Model Explanations](https://mlsanity.com/paper/2011.05429/) (2020)
- [Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practice](https://mlsanity.com/paper/2203.05962/) (2022)
- [Do Feature Attribution Methods Correctly Attribute Features?](https://mlsanity.com/paper/2104.14403/) (2021)
- [Impossibility Theorems for Feature Attribution](https://mlsanity.com/paper/2212.11870/) (2022)
- [GraphFramEx: Towards Systematic Evaluation of Explainability Methods for Graph Neural Networks](https://mlsanity.com/paper/2206.09677/) (2022)
- [Towards better understanding of gradient-based attribution methods for Deep Neural Networks](https://mlsanity.com/paper/1711.06104/) (2017)
- [IROF: a low resource evaluation metric for explanation methods](https://mlsanity.com/paper/2003.08747/) (2020)

## Built on by (most cited first, 1 of 1)

- [The Second LoViF 2026 Challenge on Real-World All-in-One Image Restoration: Methods and Results](https://mlsanity.com/paper/2607.21118/) (2026)

## Abstract (arXiv)

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.