Unbiased Attribution with Intrinsic Information

Since the Weaknesses and Questions raised are similar, we have primarily addressed Reviewer kTtj's questions.

Response to Question 1: Extra Information and Class Information

We appreciate the reviewer’s observation regarding the clarity of the "Extra Information" concept. In Global Response 1, we have provided a detailed explanation, including mathematical definitions, to clarify the concepts of "Information Ignorance" and "Extra Information."

To summarize briefly:
"Extra Information" occurs when attribution methods accumulate gradients under the assumption of a specific target class, leading to the inclusion of irrelevant features. In Fig.2, this manifests as attribution to superfluous regions, highlighting how predefined class assumptions can bias the results. This explanation will be expanded upon in the revised manuscript.

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Response to Question 2: Description of the AII Algorithm

Thank you for highlighting the need for a more detailed discussion of how AII mitigates the issues of "Information Ignorance" and "Extra Information." Unlike existing methods, AII introduces adversarial attack strategies to remove the dependency on predefined target classes, a key source of "Extra Information." While averaging methods such as Integrated Gradients rely on class information, AII attributes features without such dependency, offering a novel contribution. Furthermore, we propose improvements to the commonly used Insertion and Deletion Scores to address their limitations, ensuring a more robust evaluation of attribution methods. Our experimental results consistently demonstrate the superior performance of AII across multiple metrics and dimensions.

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Response to Question 3: Comparisons with CEM

We appreciate the reviewer's comment on the similarity between our method and contrastive explanation methods such as CEM. However, CEM does not satisfy the attribution axioms, whereas AII strictly adheres to them. Additionally, CEM relies on introducing samples similar to the current one, which risks adding "Extra Information." This makes it unclear whether the explanation pertains to the original sample or is influenced by the added samples. Our experiments ensure fairness by comparing methods that do not involve external sampling, demonstrating the effectiveness of AII. We will include a discussion on CEM in the revised paper for completeness.

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Response to Question 4: Computational Cost of CFA

Thank you for your concern regarding the computational cost of CFA. In practice, the cost is not significant: CFA typically requires only 20 seconds per calculation and at most 90 seconds in extreme cases. Moreover, the null pixel values are computed once per model and reused, avoiding repeated calculations. This computational expense is negligible compared to the hundreds or thousands of hours required for model training.

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Response to Question 5: Null Value for Feature Removal

While the use of black pixels or average pixel values as null values has been explored, our main contribution lies in addressing "Information Ignorance" and "Extra Information." Our entropy-maximization approach ensures that the chosen null value represents maximum uncertainty, aligning with mathematical definitions of entropy. This provides a theoretically grounded method for feature removal, which we believe is more robust than other heuristics.

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Response to Question 6: Typographical Issues in Equation 2

Thank you for pointing out the errors in Equation 2. We have corrected the summation index from $i=1$ to $j=1$ and will provide more detailed descriptions for terms such as $x_1, \ldots, x_n$ and $x_t$. The iterative relationship for $x^0$ is already defined, ensuring the equation is complete. These revisions will be included in the updated manuscript.

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Response to Question 7: Timing Results for AII and CFA

We agree that computational efficiency is important. To address this, we measured the FPS (frames per second) for AII and other baseline methods. The results are as follows:

As shown, AII has comparable computational costs to AGI, while achieving significant performance improvements. Given that explainability prioritizes faithfulness and accuracy, we believe the additional computational expense is justified.

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Response to Minor Comment: Absolute Value of Attribution

We agree with the reviewer’s suggestion and will revise the statement to clarify that larger absolute values of attributions indicate more important features for the model’s decision.

Response to Weakness 1: Illustration for Key Concepts

Thank you for the suggestion to provide a more intuitive and visual illustration of the key concepts. We have already provided detailed textual definitions of "Information Ignorance" and "Extra Information" in Section 1 (Introduction, lines 52-54) and Section 3.2 (lines 160 and 210). In brief, "Information Ignorance" refers to features that should be attributed but are omitted, while "Extra Information" involves attributing irrelevant features.

To further enhance understanding, we will include diagrams (e.g., Venn diagrams) in a future revision to better illustrate the differences between traditional methods and AII in terms of what features they attribute.

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Response to Weakness 2: Resolving Extra Information

We have elaborated on the causes and resolution of "Extra Information" in Global Response 1, including a mathematical formalization. In summary:

• Cause of Extra Information: Traditional attribution methods accumulate gradients based on predefined target classes. This introduces assumptions about task-relevant features, leading to the inclusion of irrelevant information.
• How AII Resolves It: AII eliminates the reliance on target class-specific gradients by redefining gradient accumulation to consider all class outputs, ensuring task-irrelevant features are excluded.

We hope this explanation addresses the reviewer's concern.

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Response to Weakness 3: Additional Examples

Figures 1–4 in the manuscript provide comprehensive examples of how our method addresses "Information Ignorance" and "Extra Information." Moreover, additional examples can be found in our supplementary materials at [https://anonymous.4open.science/r/AII-787D/rebuttal/]. These examples further demonstrate the effectiveness of AII in resolving these issues.

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Response to Weakness 4: Typographical Errors

Thank you for pointing out the typographical error in the caption of Table 2. We have corrected "U-INS, U-DEL" to "F-INS, F-DEL" and conducted a thorough review of the manuscript to eliminate other potential typos.

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Response to Weakness 5: Dataset and Model Bias

Our method is designed as a general attribution algorithm, and we chose well-known datasets and models to ensure transparency and reproducibility. Additionally, the baseline methods we compared against were also evaluated on these datasets, ensuring fairness in our experimental comparisons. The use of publicly available datasets and models is intended to provide a reliable and unbiased evaluation of our approach.

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Response to Question 1: High-Confidence vs. Low-Confidence

High-confidence data refers to instances where the model is confident in its decision, implying fewer features interfere with the decision-making process. Low-confidence data, on the other hand, represents cases where the model's confidence is low, indicating that more features may be influencing the decision. This distinction is illustrated in Fig.1 of the manuscript.

To address the question, we conducted additional experiments using a 50% confidence threshold as a dividing line. The results, summarized below, demonstrate that AII consistently achieves superior performance compared to other methods, even under this threshold:

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Response to Question 2: Mathematical Formalization

We appreciate the suggestion to include more formal definitions of the issues. As discussed in Global Response 1, we have provided mathematical descriptions of "Information Ignorance" and "Extra Information." These definitions will be incorporated into the main text in a future revision to further clarify and strengthen the paper.

Response to Weakness 1: Fig.2 Settings and Irrelevant Regions

Thank you for pointing out the concern regarding Fig.2. The issue raised has been discussed in the work by Shah et al. [1], which highlights the phenomenon of "feature leakage" and how attribution methods may mistakenly highlight irrelevant features.

In addition, the confidence score for this example is only 0.5786, while most examples in the MNIST dataset typically exhibit confidence scores above 0.95. Therefore, it is not appropriate to attribute this instance solely based on the current class, as traditional attribution methods require a predefined class to operate.

Reference:
[1] Shah, Harshay, Prateek Jain, and Praneeth Netrapalli. "Do input gradients highlight discriminative features?" Advances in Neural Information Processing Systems 34 (2021): 2046-2059.

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Response to Weakness 2: Metrics and Low-Confidence Examples

We appreciate your suggestion to include more examples like Fig.1 in the paper. Additional examples demonstrating similar low-confidence scenarios are provided in our supplementary materials and can be accessed at [https://anonymous.4open.science/r/AII-787D/rebuttal/]. These examples further illustrate how our method effectively handles ambiguity in attribution.

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Response to Weakness 3: Intuition Behind Entropy Maximization

Entropy represents uncertainty in a model's decision. Increasing entropy during feature replacement simulates a process where the model becomes progressively uncertain about its predictions. We believe this better approximates the removal of a feature compared to directly replacing it with a zero value, as zero replacement can inadvertently introduce biases depending on the model's learned features. This approach aligns better with the intuition that higher uncertainty indicates the effective removal of the feature's influence.

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Response to Weakness 4: Less Ambiguous Figures and Fig.3

Regarding the concern about Fig.3, it is indeed based on the original MNIST resolution (32×32). The original image used in Fig.3 is available in our open-source code repository at [https://anonymous.4open.science/r/AII-787D/rebuttal/]. While the MNIST dataset predominantly consists of less ambiguous examples, Fig.3 demonstrates a broader limitation of existing attribution methods: reliance on predefined classes. Our method addresses this limitation by eliminating the need for such specifications, resulting in more robust and generalized attributions.

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Response to Question 1: Observations in Fig.3 and Implications for Fig.1

The issue highlighted in Fig.3 reflects a limitation in current attribution methods, not a feature of the model itself. These methods assume that specifying a class will yield meaningful attribution for that class, which we demonstrate to be problematic. For instance, in Fig.3, the attribution results for a digit labeled "7" remain highly similar across all other class labels, suggesting that the process of class specification is redundant.

Our AII algorithm avoids this limitation by performing attribution without requiring class specification, achieving superior results as shown in our experiments. In the context of Fig.1, it would not be reasonable to highlight only the dog area, as the confidence for the "dog" label is 0.53, with the remaining 0.47 confidence likely associated with the "cat." Simply focusing on the dog or cat alone would fail to explain why the "dog" confidence is only 0.53. Our method effectively addresses this issue by incorporating contributions from all relevant features, resulting in more faithful explanations.

Response to Weakness 1 (W1): Definitions of Key Concepts

We acknowledge the reviewer's concern about the clarity of the definitions for "Information Ignorance" and "Extra Information." In response, we have provided detailed explanations in Global Response 1, where the definitions and mathematical formalizations of these concepts are presented. To summarize briefly:

• Information Ignorance refers to the omission of features from non-target classes, leading to biased attribution.
• Extra Information denotes the erroneous inclusion of irrelevant features in the attribution process.

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Response to Weakness 2 (W2): Explanation of Mitigation

Our method addresses the problems of "Information Ignorance" and "Extra Information" by removing the dependency on a predefined target class during attribution. As highlighted in the manuscript, traditional methods rely on a specified class for attribution, which inherently excludes information from other classes, leading to "Information Ignorance." Additionally, if the chosen class is imperfect (e.g., has low confidence), the attribution process introduces "Extra Information," contaminating the results, as illustrated in Figure 1.

The Attribution with Intrinsic Information (AII) algorithm avoids these issues by using a gradient accumulation method that considers the contributions of all class outputs without prioritizing a single class. This ensures a more balanced and unbiased attribution, as shown in our experimental results.

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Response to Weakness 3 (W3): Clarification on Loss Function

The statement in lines 157-158 refers to the predominant focus of the loss function $L(f(x), y)$ on the target class $y$. While it is true that cross-entropy loss considers the logits for all classes, its primary optimization direction is to increase the output for the target class $y$ while suppressing the outputs for all other classes. This can be understood from the gradient perspective: the gradient of the loss function with respect to $f(x)_y$ increases $f(x)_y$

However, the gradients with respect to $f(x)_{j \neq y}$ decrease those outputs. Thus, the optimization is inherently dominated by the target class $y$, which can lead to "Information Ignorance" by neglecting contributions from other classes.

We appreciate the reviewer's attention to detail and hope this explanation clarifies the intended meaning of our statement.