Recent years have witnessed an explosion in the development of novel
prediction-based attribution methods, which have slowly been supplanting older
gradient-based methods to explain the decisions of deep neural networks.
However, it is still not clear why prediction-based methods outperform
gradient-based ones. Here, we start with an empirical observation: these two
approaches yield attribution maps with very different power spectra, with
gradient-based methods revealing more high-frequency content than
prediction-based methods. This observation raises multiple questions: What is
the source of this high-frequency information, and does it truly reflect
decisions made by the system? Lastly, why would the absence of high-frequency
information in prediction-based methods yield better explainability scores
along multiple metrics? We analyze the gradient of three representative visual
classification models and observe that it contains noisy information emanating
from high-frequencies. Furthermore, our analysis reveals that the operations
used in Convolutional Neural Networks (CNNs) for downsampling appear to be a
significant source of this high-frequency content -- suggesting aliasing as a
possible underlying basis. We then apply an optimal low-pass filter for
attribution maps and demonstrate that it improves gradient-based attribution
methods. We show that (i) removing high-frequency noise yields significant
improvements in the explainability scores obtained with gradient-based methods
across multiple models -- leading to (ii) a novel ranking of state-of-the-art
methods with gradient-based methods at the top. We believe that our results
will spur renewed interest in simpler and computationally more efficient
gradient-based methods for explainability.

预测基于的归因方法相对于梯度基于的方法表现更好的原因是因为前者的高频信息更少，通过优化低通滤波器可以改善梯度基于的归因方法的表现。

梯度反击：滤除高频率如何改善解释性

Gradient strikes back: How filtering out high frequencies improves  explanations

Cardiac diseases are one of the main reasons of mortality in modern,
industrialized societies, and they cause high expenses in public health
systems. Therefore, it is important to develop analytical methods to improve
cardiac diagnostics. Electric activity of heart was first modeled by using a
set of nonlinear differential equations. Latter, variations of cardiac spectra
originated from deterministic dynamics are investigated. Analyzing the power
spectra of a normal human heart presents His-Purkinje network, possessing a
fractal like structure. Phase space trajectories are extracted from the time
series graph of ECG. Lower values of fractal dimension, D indicate dynamics
that are more coherent. If D has non-integer values greater than two when the
system becomes chaotic or strange attractor. Recently, the development of a
fast and robust method, which can be applied to multichannel physiologic
signals, was reported. This manuscript investigates two different ECG systems
produced from normal and abnormal human hearts to introduce an auxiliary phase
space method in conjunction with ECG signals for diagnoses of heart diseases.
Here, the data for each person includes two signals based on V_4 and modified
lead III (MLIII) respectively. Fractal analysis method is employed on the
trajectories constructed in phase space, from which the fractal dimension D is
obtained using the box counting method. It is observed that, MLIII signals have
larger D values than the first signals (V_4), predicting more randomness yet
more information. The lowest value of D (1.708) indicates the perfect
oscillation of the normal heart and the highest value of D (1.863) presents the
randomness of the abnormal heart. Our significant finding is that the phase
space picture presents the distribution of the peak heights from the ECG
spectra, giving valuable information about heart activities in conjunction with
ECG.

研究了应用辅助相空间方法和心电信号诊断心脏疾病的两种不同 ECG 系统，通过分析时间序列图和相空间轨迹来计算分形维度 D， 并发现较高的 D 值表明更多的随机性和信息，从而提供了有关心脏活动的有价值的信息。

心脏谱的相空间分析

Phase Space Analysis of Cardiac Spectra

Cardiac diseases are one of the leading mortality factors in modern,
industrialized societies, which cause high expenses in public health systems.
Due to high costs, developing analytical methods to improve cardiac diagnostics
is essential. The heart's electric activity was first modeled using a set of
nonlinear differential equations. Following this, variations of cardiac spectra
originating from deterministic dynamics are investigated. Analyzing a normal
human heart's power spectra offers His-Purkinje network, which possesses a
fractal-like structure. Phase space trajectories are extracted from the time
series electrocardiogram (ECG) graph with third-order derivate Taylor Series.
Here in this study, phase space analysis and Convolutional Neural Networks
(CNNs) method are applied to 44 records via the MIT-BIH database recorded with
MLII. In order to increase accuracy, a straight line is drawn between the
highest Q-R distance in the phase space images of the records. Binary CNN
classification is used to determine healthy or unhealthy hearts. With a 90.90%
accuracy rate, this model could classify records according to their heart
status.

本研究旨在应用相空间分析和卷积神经网络方法对来自 MIT-BIH 数据库的 44 个记录进行分类识别，以提高对心脏健康状况的诊断精度，结果表明该方法可以达到 90.90% 的准确率。