Guided AbsoluteGrad: Magnitude of Gradients Matters to Explanation's Localization and Saliency
Jun Huang Yan Liu





2024
370



	
	Guided AbsoluteGrad : Magnitude of Gradients 
Matters to Explanation's Localization and Saliency
    Xuming An,
        Dui Wang,
        Li Shen,
        Yong Luo,
        Han Hu,
        Bo Du,
        Yonggang Wen Fellow, IEEE,
        Dacheng Tao Fellow, IEEE

X. An and H. Hu are with the School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China (email: anxuming@bit.edu.cn; hhu@bit.edu.cn).
D. Wang, Y. Luo and B. Du are with the National Engineering Research Center for Multimedia Software, School of Computer Science, Institute of Artificial Intelligence and Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan University, Wuhan 430072, China (e-mail: wangdui@whu.edu.cn; yluo180@gmail.com; dubo@whu.edu.cn).

L. Shen and D. Tao are with the JD Explore Academy, Beijing, 100000, China (email: mathshenli@gmail.com, dacheng.tao@gmail.com).
Y. Wen is with the School of Computer Science and Engineering, Nanyang Technological University, Singapore 639798 (e-mail: ygwen@ntu.edu.sg).

    April 29, 2024
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		Jun Huang,*, Yan Liu
		

		 Concordia University, Montreal, Canada 

		

	
	
		*jun.huang@mail.concordia.ca
	
	






	This paper proposes a new gradient-based XAI method called Guided AbsoluteGrad for saliency map explanations.
	We utilize both positive and negative gradient magnitudes and employ gradient variance to distinguish the important areas for noise deduction.
	We also introduce a novel evaluation metric named ReCover And Predict (RCAP), which considers the Localization and Visual Noise Level objectives of the explanations.
	We propose two propositions for these two objectives and prove the necessity of evaluating them.
	We evaluate Guided AbsoluteGrad with seven gradient-based XAI methods using the RCAP metric and other SOTA metrics in three case studies:
	(1) ImageNet dataset with ResNet50 model;
	(2) International Skin Imaging Collaboration (ISIC) dataset with EfficientNet model;
	(3) the Places365 dataset with DenseNet161 model.
	Our method surpasses other gradient-based approaches, showcasing the quality of enhanced saliency map explanations through gradient magnitude.


Keywords:
	Explainable AI, Computer Vision, Saliency Map, Gradient-based



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§ INTRODUCTION



Saliency map <cit.> is commonly used to explain image classification tasks in computer vision.
It highlights the pixels according to their contribution to the prediction.
The work <cit.> divides saliency methods into three branches: CAM-based (Class Activation Map), gradient-based, and perturbation-based methods.
CAM-based methods such as Grad-CAM <cit.> and GradCAM++ <cit.> are commonly adopted, relying on access to the model's feature map and gradient accumulation.
These methods produce smoothed saliency maps of low resolution from the feature map.
Gradient-based methods such as Vanilla Gradient <cit.> and SmoothGrad <cit.>, on the other hand, leverage only the gradient values of the input as the explanations.
These methods reduce explanation noise by introducing randomness to the sample multiple times and aggregating the gradients into one saliency map.
Other gradient-based methods such as Integrated Gradients <cit.>, Guided Integrated Gradients <cit.>, and BlurIG <cit.> generate saliency maps by building a path between the target and baseline images.
The Guided Backpropagation <cit.> calculates the saliency map by modifying the model's backpropagation process to exclude the negative gradients on ReLU activation.
Perturbation-based methods such as RISE <cit.> and SHAP <cit.> calculate feature contribution by analyzing the prediction output and multiple modified inputs.
In this paper, we focus on developing gradient-based XAI methods for neural network models.

Interpreting the negative gradient remains a challenge during saliency map generation.
The works in <cit.> assume that the negative gradient is either noise that causes countereffect or its effect depends on the contexts of datasets and models.
The practices usually exclude negative gradients during the backpropagation or sum them with the positive gradients when generating the aggregated saliency map.
In contrast, the study in <cit.> indicates that negative gradients also play a significant role in feature attribution on remote sensing imaging.
The works in <cit.> make a similar hypothesis on negative gradients.
The above works lack comprehensive discussions and experiments on how negative gradients affect the saliency map on difference gradient-based methods.
We aim to identify the position of the negative gradient and further leverage it to generate better saliency map explanations.
Our contribution to this paper can be summarized in the following threefold.

Firstly, we propose a gradient-based method called Guided AbsoluteGrad that considers the magnitude of positive and negative gradients.
Our method works as follows:
(1) for each sample, we obtain multiple saliency maps from different modifications of the original image;
(2) we absolutize the gradient values to measure the gradient magnitude as the feature attribution;
(3) we calculate the gradient variance as a guide to the target area;
(4) we sum the absolute gradients multiplied by the guide as the explanation.

Secondly, we identify the limitation of the existing saliency map evaluation techniques and define the ReCover And Predict (RCAP) that focuses on Localization and Visual Noise Level objectives of the explanations.
We collect multiple recovered images on a baseline image based on different partitions of the ranked saliency map values.
We get the prediction scores of these recovered images.
For each partition and its recovered image, we multiply
(1) the ratio saliency value of the partition against the entire explanation,
and (2) the prediction score of the recovered image as the evaluation result.

Finally, we conduct experiments involving three datasets, three models, and seven state-of-the-art (SOTA) gradient-based XAI methods.
The result shows that, for RCAP and other SOTA metrics, the Guided AbsoluteGrad method outperforms other gradient-based XAI methods. 
We also propose two propositions and provide experiments to discuss and validate how RCAP evaluates the two objectives.
The code of this paper is released in GitHub[<https://github.com/youyinnn/Guided-AbsoluteGrad>].



§ RELATED WORKS


In this section, we discuss the existing negative gradient interpretations and our assumptions based on them.
We also discuss the saliency map evaluation metrics and their drawbacks, therefore proposing a new metric.



 §.§ Interpretation of Negative Gradients.



We summarize three groups of negative gradient interpretations from the existing works.

Group 1: Negative Gradient Can Not Indicate Target Class Attribution.
Guided Backpropagation <cit.> argues that the negative gradients stem from the neurons deactivated regarding the targeted class;
Grad-CAM <cit.> thinks that negative gradients might belong to other categories.
Both methods rule out the negative gradient from their saliency explanations.
Based on <cit.>, the XRAI <cit.> states that regions unrelated to the prediction should have near-zero attribution,
and regions with competing classes should have negative attribution.
That is saying the negative gradient is not used to explain the target class.

Group 2: The Indication of Negative Gradient Depends on the Data Context.
SmoothGrad <cit.> suggests that whether to keep the negative gradient depends on the context of the dataset or individual sample.
DeepLift <cit.> addresses the limitations of <cit.> by considering the effects of positive and negative contributions at nonlinearities separately.

Group 3: Negative Gradient Indicates Target Class Attribution.
The work in  <cit.> hypothesizes that negative gradients form around the important features and further complement the positive gradient for better visualization.
The study <cit.> found that the magnitude may be far more telling feature importance than the direction of the gradient.
Another work <cit.> provides supporting experiments and proposes the BiGradV, which verifies that the negative gradients also play a role in saliency map explanation in the remote sensing images.

The above interpretations are limited to the direction of the gradient based on their own XAI methods, 
handling negative gradients differently.
There is a lack of empirical experiments on how the negative gradients solely affect the explanations.
With this regard, we propose an assumption that could be applied to any gradient-based method, that is, the magnitude of both positive and negative gradients matters to feature attribution.
Based on the assumption, we develop a gradient-based XAI method that leverages the gradient magnitude.
Moreover, we modify the existing gradient-based methods by taking the negative gradient direction and conducting empirical experiments to verify our assumption.



 §.§ Existing Saliency Map Evaluation Metric


The Log-Cosh Dice Loss <cit.> evaluates the loss between the ground-truth segmentation and the saliency map regarding the target object.
Similarly, the work in <cit.> uses Mean Absolute Error (MAE) to evaluate the performance based on ground-truth segmentation.
The works of <cit.> employ humans to evaluate their work with questionnaires.
However, collecting ground-truth segmentation or conducting human studies, in most cases, is unavailable and expensive.
Deletion and Insertion Area Under Curve (DAUC&IAUC) are widely adopted <cit.> to evaluate the saliency map by getting the prediction from the gradually removing or inserting the important pixels of the input.
Likewise, the RemOve And Retrain (ROAR) <cit.> evaluates the saliency map by assessing the performance of the retrained model on the modified datasets.
Such modified datasets are generated by gradually removing features based on saliency.
However, the ROAR lacks the theoretical and empirical basis to justify the necessity of retraining.
We argue that the retraining process brings more uncertainty due to different training strategies that involve hyperparameter optimization, machine learning model selection, and data processing strategies.
Existing work <cit.> also reveals the contradictory evaluation result against ROAR and discusses that the mutual information between the input and the target label can lead to biased attribution results during the ROAR retraining.
Moreover, both DAUC&IAUC and ROAR evaluate how accurately the explanation can locate the important features but ignore the visual noise level of the explanations.
Therefore, we propose ReCover And Predict (RCAP) that focuses on the Localization and Visual Noise Level objectives at the same time.
We define propositions followed by theoretical proof and conduct experiments to describe 
how RCAP guarantees these objectives are evaluated correctly.




§ DEFINE GUIDED ABSOLUTEGRAD


In this section, we summarize the algorithm from the SOTA gradient-based methods into three parts and present the existing implementation of each part.
Then, we present how we leverage the gradient magnitude to define the proposed method.



 §.§ Gradient-based XAI Method Abstraction


In general, the gradient-based methods are based on the Vanilla Gradient <cit.> and can be summarized into three parts:
(1) Input Modification, (2) Gradient Interpretation, and (3)  Gradient Aggregation from multiple modifications.
We represent the input modification with the generated saliency map as follows:

    M_c(x, γ) = ∇ f_c(γ(x)) = ∂ f_c(γ(x))/∂ (γ(x))

where f_c(x) is the activation function regarding class c of the input image x and γ is the modification function for saliency explanation noise removal.
SmoothGrad <cit.> achieves this by introducing the Gaussian noise to the input.
Integrated Gradients <cit.> samples multiple modifications from the evolution path between the baseline image and the original input.

For gradient interpretations, we can rule out the negative gradient <cit.> or take the summation <cit.>, considering the negative gradient as the disturbance of explanations.
We can also take the absolute gradient, leveraging the magnitude as feature importance.

And finally, there are different aggregation strategies to generate the final saliency map explanations.
Suppose M_c^n(x, γ) = {M_c(x, γ_i) | i ∈ 1,2,…,n} indicates the resulting  n variant of the saliency maps and the γ_i is the i^th modification of function γ.

We can take the saliency mean <cit.>, considering the average saliency represents the best of the explanation.
We can also use the saliency variance <cit.>, leveraging the magnitude of saliency values' changes as explanations.




 §.§ Leveraging the Gradient Magnitude by Absolutization and Variance Guide


Now, we define our Guided AbsoluteGrad method.
We first define AbsoluteGrad by absolutizing the gradient values and taking the mean aggregation:

    M^AG = |M_c^n|(x, γ) = 1/n∑_i=1^n |M_c(x, γ_i)|


Since the absolutization might also magnify the saliency value of the features that do not represent the target object,
we leverage the variance of M_c^n(x, γ) to filter the features.
This is based on the idea that features with fierce gradient variation determine if they are important or not.
The more important the feature is, the larger the gradient variation from negative to positive due to the modification.
We calculate the gradient variance with:

    𝕍(M_c^n(x, γ)) = 1/n - 1∑_i=1^n (M_c(x, γ_i) - M_c^n(x, γ))^2


We define a variance guide 𝔾 to filter the feature based on a threshold percentile p.

    𝔾 = 
    		1                               𝕍(M_c^n(x, γ))  ≥ p^th percentile
    𝕍(M_c^n(x, γ))    otherwise


Finally, we multiply the variance guide 𝔾 with M^AG as the saliency explanations.
In summary, the absolute gradient and the mean aggregation determine how much contribution the feature has; the gradient variance guide determines if the feature is important or not.



Algorithm <ref> and Figure <ref> describe the detailed implementation of the above process.
The algorithm can leverage any modification function.
We conduct experiments on XAI methods with different modifications: 
SmoothGrad <cit.>, Integrated Gradients <cit.>, Guided Integrated Gradients <cit.>, and BlurIG <cit.>.
We find that introducing the Gaussian noise performs the best for stimulating the gradient variation.
Hence, in this paper, we add the Gaussian noise to modify the input.
Figure <ref> shows the examples of saliency explanations from the Guided AbsoluteGrad method with p = 85^th and other SOTA gradient-based methods.
We also include the CAM-based method of Grad-CAM <cit.>.
Our method explains high saliency to the area of the frog and low saliency to the background.

[t]0.43
	
	


[t][][b]0.5
	
	






§ DEFINE THE RECOVER AND PREDICT

In this section, we define the ReCover And Predict (RCAP) metric with notations and formulas.
We then discuss two propositions to describe the idea behind RCAP.



 §.§ Area Separation for Evaluation


Metrics of DAUC&IAUC <cit.> or ROAR <cit.> evaluate all features' saliency, whereas the RCAP could be more focused on the important area.
We first define the Focus Area and Noise Area of the saliency explanations.
Features with saliency values higher than the lower_bound percentile value in Focus Area; otherwise, in Noise Area.
We then define the Ground-truth Area and Background Area.
Features that only describe the target object are in the Ground-truth Area; otherwise, in Background Area.
For instance, the ground-truth segmentation annotated by humans is the perfect representation of the Ground-truth Area.
We will define these areas in detail with notations in the next section.

Figure <ref> shows the area separation of two images.
We use a lower_bound of 60^th percentile to separate the areas.
The white pixels in the area indicate where we keep the saliency value.
The first row shows the Focus Area of SmoothGrad is sparse, whereas the Guided AbsoluteGrad is dense.
We argue that the saliency map evaluation can be done in just the Focus Area.
Both DAUC&IAUC and ROAR evaluations are based on the prediction score of the gradually recovered samples.
Therefore, including more features from the Noise Area will bring two results:
(1) prediction scores vary in a small range, indicating the most important features are explained already;
(2) prediction scores increased a lot, indicating the highest 40 of saliency can not well cover the target object.
Both results are considered poor explanations and, thus, can be skipped.
We argue that evaluating the Noise Area can be done without model prediction calls by just taking the saliency ratio of the Focus Area with the entire saliency map.
The second row shows the saliency values in the Focus Area of method AbsoluteGrad and Guided AbsoluteGrad are close to each other,
but the AbsoluteGrad assigns more saliency value in the Noise Area.
It showcases that when the two saliency maps explain the target object equally well, we should consider the noise level.





 §.§ Metric Definition


Based on the Ground-truth/Background Area in Section <ref> and the discussion of Figure <ref>fig:areas in Section <ref>,
we define two objectives of the saliency map evaluation as follows.

	
  * Localization: 
	It evaluates if the explained Focus Area covers more on the Ground -truth Area and less on the Background Area.
	      
	
  * Visual Noise Level: 
	It evaluates if the saliency map can explain more saliency values in the Focus Area and less in the Noise Area.


Suppose the range of the saliency value is normalized to [0,1], and M is the saliency value matrix where ∑ M > 0.
We take features from the highest salience value to lower_bound and partition them with the given interval interval.
Then, starting from a baseline image (a black image, for instance), we recover the features multiple times with these partitions and obtain multiple recovered images.
With these partitions, we present the following notations:

	
  * P = {p_k | k ∈{1,2,…,j}} where p_k is the (100 - k * interval)^th percentile of the saliency values, interval indicates a fixed difference of the adjacent percentile, and k is the ordinal number of elements in P.
	      Note that 100 ≥ k * interval≥lower_bound≥ 0 where lower_bound is lowest percentile p_k we take into consideration.
	      Then, we get the number of elements j = (100 - lower_bound)/interval.
	      
	      
	      
	
  * I_P = {I_p_k | k ∈{1,2,…,j}} where I_p_k is the recovered image, which recovers the features that hold saliency value greater or equal to the p_k^th percentile.
	
  * M_P = {M_p_k | k ∈{1,2,…,j}} where M_p_k is the subset of the saliency value of the recovered portion.
	      The last element M_p_j indicates the Focus Area.
	      Moreover, we use the hat notion M̂_p_j = (M - M_p_j) to represent the Noise Area.
	
  * σ(f_c(I_p_k)) indicates softmax operation on prediction score of I_p_k in class c.
	      
	      
	
  * ∑ M_p_k/∑ M is the saliency ratio of the recovered part and the entire saliency map.


We then formulaize our RCAP metric as RCAP(M) as:

    RCAP(M) = 1/j∑_k=1^j [(·∑ M_p_k/∑ M)^Visual Noise Level×·σ(f_c(I_p_k))_Localization]


We interprate that the first term ∑ M_p_k/∑ M = ∑ M_p_k/(∑ M_p_k + ∑M̂_p_k) measures the Visual Noise Level with the saliency ratio of partition and the saliency map M.
If ∑ M_p_k gets larger, the ratio will get higher and approach 1, indicating less Visual Noise Level of the explained Focus Area.
The second term σ(f_c(I_p_k)) is the prediction confidence that measures the Localization.
If more features from the Background Area are recovered,
it means the explained saliency deviates from the target object, resulting in a smaller prediction score.



 §.§ Metric Proposition for Explanation Performance


We propose two propositions to describe how RCAP evaluates the saliency map.
We denote the Ground-truth Area as matrix M^T.
Additional high saliency value assigned outside M^T is considered a noise.
We start by presenting the case in Figure <ref> to help understand the propositions better.
Suppose we use the lower_bound = 60^th for area separation,
indicating the highest 40 of the saliency values are in the Focus Area M_p_j.



Figure <ref> presents an ideal case where four saliency maps conform to Gaussian distribution.
M^1 is the best explanation with more precise Localization and low Visual Noise Level.
M^2 has the same distribution center as M^1 but with a higher standard deviation, resulting in higher noise levels.
M^3 has the same standard deviation, but its center deviates from the M^T with a 30 of the total width and height towards the lower right.
M^4 has the same standard deviation as M^2 and same center as M^3, resulting in the worst explanation.


We now define two propositions utilizing Figure <ref>.
Suppose we have two saliency maps M^a and M^b for class c and evaluate them with the same interval and lower_bound.

[label=prop:1]
	For any k ∈{1,2,…,j},
	if ∑ M^a_p_k≊∑ M^b_p_k and ∑ M^a ≊∑ M^b,
	then we have:∑ M^a_p_k/∑ M^a ≊∑ M^b_p_k/∑ M^b.
	If the Focus Area of M^a covers more Ground-truth Area than M^b does,
	we should get RCAP(M^a) > RCAP(M^b).



Proposition 1 describes how to evaluate the saliency map when they have similar Visual Noise Levels.
This can be described by the ∑ M^1_p_k/∑ M^1 ≊∑ M^3_p_k/∑ M^3 from Figure <ref>.
Now, the evaluation depends on the coverage M_p_j∩ M^T.
As can be observed, M^1's Focus Area (gray area) covers more Ground-truth Area (yellow area) than M^3.
However, ground-truth explanation collection is not always available.
We hypothesize that the prediction confidence σ(f_c(I_p_k)) of the recovered partitions is approximate to this coverage.
We design experiments to validate this hypothesized measurement with the following steps.
Given the saliency map, we generate a reversed variant that swaps between the high and low saliency values.
Firstly, we retain the highest l of saliency values to ensure a certain level of explanation accuracy.
Secondly, we swap the saliency value in [0, m^th] percentile with the saliency values in [(100 - l - m)^th, (100 - l)^th] percentile.
With such modification, we make the Focus Area of this saliency map cover more on the Background Area and less on the Ground-truth Area.
This results in a lower probability on σ(f_c(I_p_k)) than its original.

[label=prop:2]
	For any k ∈{1,2,…,j}, assuming I^a_p_k recovers similar feature areas as I^b_p_k does,
	then we have: σ(f_c(I^a_p_k)) ≊σ(f_c(I^b_p_k)).
	If M^b is visually noisier than M^a, we should get RCAP(M^a) > RCAP(M^b).


Proposition 2 describes how to evaluate the saliency map explanations when map M^a and map M^b perform close on covering the Ground-truth Area.
We leverage M^1 and M^2 from Figure <ref> to define the noise level.
Figure <ref> reveals that
(1) both maps have full coverage on M^T, resulting σ(f_c(I_p_k^1)) ≊σ(f_c(I_p_k^2));
(2) the ratio of the area under the curve of ∑ M^1_p_k/(∑ M^1_p_k + ∑M̂^̂1̂_p_k) is greater than ∑ M^2_p_k/(∑ M^2_p_k + ∑M̂^̂2̂_p_k);
(3) the map M^2 has a higher saliency deviation, resulting in increased saliency in the Noise Area.
Moreover, (2) and (3) are sufficient and necessary conditions for each other.
We therefore derive (∑ M^1_p_k / ∑ M^1) ×σ(f_c(I_p_k^1)) > ∑ (M^2_p_k / ∑ M^2) ×σ(f_c(I_p_k^2)).
Hence RCAP(M^1) > RCAP(M^2) is guaranteed based on Equation <ref>. Thus, the Proposition 2 is proved.


Existing recovering/removing-based metrics such as DAUC&IAUC <cit.> or ROAR <cit.> also hold the Proposition 1.
However, they are not sensitive to the Visual Noise Level change as is described in the Proposition 2.
They only consider the rank of the partitional saliency map.
In the extreme case of Figure <ref>, M^1 and M^2 get the same evaluation from DAUC&IAUC,
regardless of the difference of saliency deviation,
as long as the same ranked saliency covers the same feature partitions.
We will showcase this limitation of DAUC&IAUC in the experiment section.
We argue that Proposition 2 is also crucial to the saliency map evaluation.





§ EXPERIMENT SETUP



We use ReCover And Predict (RCAP) with lower_bound = 50^th and interval = 10 and the DAUC&IAUC <cit.> for all the cases.
Additionally, we use metric Log-Cosh Dice Loss (L_lc-dce) <cit.> and Mean Absolute Error (MAE) for ImageNet-S case that has available ground-truth segmentation.
We select the samples that have over 90% prediction confidence on the ground-truth class since poor performance on the prediction might lead to uninterpretable explanation <cit.>.
We conduct experiments on the following three cases.

Case 1: ImageNet-S with ResNet-50.
We select the ImageNet-S <cit.> that provides the ground-truth segmentation for the benchmark dataset ImageNet <cit.>.
A total of 3,976 images with 256× 256 resolution are used in the experiments.
We select the ResNet-50 <cit.> model pre-trained by Pytorch.

Case 2: ISIC with EfficientNet.
We select the combined dataset <cit.> of the International Skin Imaging Collaboration (ISIC) challenge for the years 2018 to 2020.
A total of 3,000 images with 448× 448 resolution are used in the experiments.
Accordingly, we select the pre-trained EfficientNet from <cit.>.

Case 3: Places365 with DenseNet-161.
We select the Plac­es365 <cit.> dataset along with its pre-trained DenseNet-161 model.
A total of 5,432 images with 224× 224 resolution are used in the experiments.




 §.§ Ablation Study for Parameter p of the Guided AbsoluteGrad

We explore the performance of the Guided AbsoluteGrad methods with different percentile p from 15^th (GAG-15) to 85^th (GAG-85).
The Guided AbsoluteGrad method with no variance guide (p=0) is the AbsoluteGrad (GAG-0).
From Table <ref>, we observe that when the p is 85^th (GAG-85),
the Guided AbsoluteGrad achieves the best performance on the RCAP metric against GAG-0 by increasing
41.66 (ImageNet-S), 51.38 (ISIC), and 44.24 (Places365).
For the MAE metric, the performance trends are the same as the RCAP metric.
In general, the more saliency we filter by the variance guide, the more RCAP performance we gain.
In contrast, the performance of DAUC&IAUC remains stable, indicating that they are insensitive to the noise level change and only focus on the Localization of the saliency map.
This also indicates that applying the variance guide won't lose much performance of Localization but improves the Visual Noise Level of the explanations.




§ EXPERIMENT RESULTS

We compare the Guided AbsoluteGrad (GAG) with seven SOTA gradient-based methods along with the Grad-CAM <cit.>,
including SmoothGrad (SG) <cit.>, VarGrad <cit.>,
Guided Backpropagation (GB) <cit.>,
Guided Integrated Gradients (Guided IG) <cit.>,
Integrated Gradients (IG) <cit.>, BlurIG <cit.>,
Vanilla Gradient (VG) <cit.>.
We use the same number of modifications for all methods as 20.
Based on the ablation studies of Table <ref>,
we set p=85^th for all methods that use our variance guides in all cases.





 §.§ Gradient-based Method Comparison and Proposition Observation


Part 2 of Table <ref> shows that our GAG method outperforms other gradient-based methods with regards to RCAP, L_lc-dce, and MAE evaluations in all cases, without considering the Grad-CAM.
For IAUC, the GAG method ranks first (ImageNet-S), third (ISIC), and second (Places365), respectively.
Whereas the DAUC of GAG outperforms others for ISIC case, it ranks lower than the average in other cases.
When comparing with the Grad-CAM method,
our GAG method gets the closest L_lc-dce evaluation and IAUC against other gradient-based methods for case ImageNet-S.
Moreover, the GAG gets a better RCAP in the case ImageNet-S and the closest RCAP in the other two cases against other gradient-based methods.

As is discussed in Section <ref>, we aim to observe the proposition 1.
We alter methods SG, IG, Guided IG, BlurIG, and GB to their reversed variants with superscript R.
From part 2&3 of Table <ref>,
we observe that all reversed variants get significantly worse performance in all metrics against their original methods, which matches the description of proposition 1.





 §.§ Ablation Study on Different Gradient Processing

We discuss how the different gradient processing approaches affect explanations in different contexts (dataset and model).
For methods SG, IG, Guided IG, BlurIG, and GB,
we make five variants of gradient processing:
(+) use positive gradients only;
(-) use negative gradients only;
(A) use absolute gradients;
(G) use our proposed gradient variance guide for noise deduction;
(GA) use both absolute gradients and our variance guide.
After evaluating different variants, we divide them by their original method's evaluation to measure how much improvement/deterioration they make.
We then average the evaluations of all methods case by case for each metric.
Table <ref> shows the results where 1.0 indicates the performance is almost the same as its original methods.
The positive gradient generally enhances performance, while the negative gradient leads to minimal degradation.
On the other hand, utilizing the absolute gradient, applying the variance guide, or a combination of both tends to have more performance improvement in general.
It also shows that our RCAP metric is more sensitive to the noise level changes against the DAUC&IAUC metric.
In the ISIC case, the IAUC metric can barely recognize the improvement of gradient processing variants (4) and (5) indicated by DAUC and our RCAP metrics.






§ CONCLUSION

In this paper, we propose a novel gradient-based XAI named Guided AbsoluteGrad.
The approach utilizes both positive and negative gradient magnitudes to aggregate saliency maps, employing gradient variance as a guide to reduce the noise of explanations.
We conduct ablation studies to reveal the performance influence of difference gradient processing approaches.
The result indicates that our assumption on the gradient magnitude matters to the saliency map explanation is valid.
Additionally, we propose a novel evaluation metric called ReCover And Predict (RCAP).
We introduce two evaluation objectives: Localization and Visual Noise Level.
We further present how the RCAP evaluates these objectives with proven propositions and empirical experiments.
We compare the Guided AbsoluteGrad method with seven SOTA gradient-based methods.
The experiment results show that the Guided AbsoluteGrad outperforms other SOTA gradient-based methods in the RCAP metric and ranks in the front-tier in other metrics.













[heading=subbibintoc]

