Paper: Consistency Regularization for Domain Generalization with Logit Attribution Matching (ICLR-2024)

Reviewer comment (Theory):
While I’m not an expert in causality, I hold doubt about the assumption in Figure 1, i.e., the data generation process. We certainly know that such generation process is an assumption, and other causality researchers can draw a completely different causal graph. Therefore, how can authors justify that this figure is practical and can be trusted? This is important since all analysis is based on this basic assumption.

Author response:
**1. “While I’m not an expert in causality, I hold doubt about the assumption in Figure 1, i.e., the data generation process. We certainly know that such generation process is an assumption, and other causality researchers can draw a completely different causal graph. Therefore, how can authors justify that this figure is practical and can be trusted? This is important since all analysis is based on this basic assumption.”**

Our causal model assumes that the data generation process is as follows: (1) An example input $X$ is generated from two latent variables, $X^c$ and $X^n$. (2) These two variables, $X^c$ and $X^n$, are statistically correlated. (3) The label $Y$ is generated solely from $X^c$.  

Assumption (1) is a very common and general assumption which (at least) dates back to [Tenenbaum and Freeman (1996)](https://proceedings.neurips.cc/paper_files/paper/1996/file/70222949cc0db89ab32c9969754d4758-Paper.pdf). It basically says that data is generated from some latent variables (e.g., state of the physical world). As for Assumption (2), lifting it does not affect the results of our theory at all. It is kept simply to stress one of the main challenges of DG, that is, overcoming spurious correlations between $X$ and $Y$. The last assumption is also quite frequently made in the literature, together with the previous assumptions [1,2,3,4,5]. We can effortlessly point to many more examples in top conferences or journals [6,7,8,9].

While it is sometimes more reasonable to posit a different connection between $Y$ and the other variables, the current assumption is nonetheless a very general one, encompassing a great number of real-world problems. For example, in SLAM problems, the label $Y$ is determined by the physical location of some agent in the world. As another example, in sentiment analysis, the label $Y$ is determined by the actual thought and feeling of the user.

Reviewer comment (Novelty):
I admire the effort to combine targeted augmentation with CR. But I do not think targeted augmentation is algorithmically novel since this is not general and hard to generalize to other datasets, given the wide popularity of DG in different applications. Therefore, the introduction of targeted augmentation is not efficient or general. This makes LAM deeply rely on the effectiveness of TA. I would like to know how can LAM be applied to other new domains where targeted augmentation is not realistic.

Author response:
**2. “I would like to know how can LAM be applied to other new domains where targeted augmentation is not realistic.”**

Common data augmentation (DA) methods based on basic operations such as resize, rotation, color jitter, and their random combination, RandAugment, all usually retain core factors and vary non-core factors for image classification tasks (e.g., the size of an object in an image could also be a non-core factor). After all, this is one of the most fundamental rules for data augmentation.

In Table 8 (Appendix E), we compare LAM and other consistency regularization (CR) methods on iWildCam and iWildCam-N with semantic sharing pairs created by RandAugment. Similar to when targeted augmentation is used, LAM based on RandAugment also significantly outperforms other CR-based methods and ERM baselines in terms of OOD performance on the iWildCam dataset (OOD Macro F1-score – LAM: 36.6, the second best is Prob. (JS) at 34.7 and ERM baseline at 30.2).

On the iWildCam-N dataset, with RandAugment, only LAM improves OOD performance over the ERM+DA baseline (which simply treats the augmented examples as additional training data), while other CR-based DG methods do not. This is in line with the results using targeted data augmentation and once again highlights LAM's superior ability of not suppressing features from different classes within the image.

Reviewer comment (Experiments):
See the weakness. I'm extremely curious about the practical usage of LAM without the help from TA.

Author response:
**2. “I would like to know how can LAM be applied to other new domains where targeted augmentation is not realistic.”**

Common data augmentation (DA) methods based on basic operations such as resize, rotation, color jitter, and their random combination, RandAugment, all usually retain core factors and vary non-core factors for image classification tasks (e.g., the size of an object in an image could also be a non-core factor). After all, this is one of the most fundamental rules for data augmentation.

In Table 8 (Appendix E), we compare LAM and other consistency regularization (CR) methods on iWildCam and iWildCam-N with semantic sharing pairs created by RandAugment. Similar to when targeted augmentation is used, LAM based on RandAugment also significantly outperforms other CR-based methods and ERM baselines in terms of OOD performance on the iWildCam dataset (OOD Macro F1-score – LAM: 36.6, the second best is Prob. (JS) at 34.7 and ERM baseline at 30.2).

On the iWildCam-N dataset, with RandAugment, only LAM improves OOD performance over the ERM+DA baseline (which simply treats the augmented examples as additional training data), while other CR-based DG methods do not. This is in line with the results using targeted data augmentation and once again highlights LAM's superior ability of not suppressing features from different classes within the image.

Reviewer comment (Experiments):
Over the five datasets experimented, the augmentation is handpicked based on the characteristics of each dataset. This might make the disentanglement of causal/non-causal features relatively easier (i.e., the SS pairs better fit into this paper's motivation on $X^c$ and $X^n$). I wonder how the proposed approach works when the augmentation is agnostic to the datasets, i.e., what if you apply one of RandAugment / CutMix / AugMix to all the datasets as augmentation, and use LAM for regularization? How would the performance change?

Author response:
We thank the reviewer’s valuable time and constructive feedback. We are pleased to know that you found our proposed LAM is “fairly simple” and “useful in improving the OOD performance”.

Regarding the question you've raised, we provide detailed explanations below.

**“Can the authors show how LAM works when the augmentation applied is dataset-agnostic? e.g., using augmentation methods like RandAugment / CutMix / AugMix for all the datasets?”**

Common DA methods based on basic operations such as resize, rotation, color jitter, and their random combination, RandAugment, all usually retain core factors and vary non-core factors for image classification tasks (e.g., the size of an object in an image could also be a non-core factor). After all, this is one of the most fundamental rules for data augmentation.

In Table 8 (Appendix E), we compare LAM and other consistency regularization (CR) methods on iWildCam and iWildCam-N with semantic sharing pairs created by **RandAugment**. 

Similar to when targeted augmented examples are used, when utilizing RandAugment augmented examples, LAM also significantly outperforms other CR-based methods and ERM baselines in terms of OOD performance on the iWildCam dataset (OOD Macro F1-score – LAM: 36.6, the second best is Prob. (JS) at 34.7 and ERM baseline at 30.2).

On the iWildCam-N dataset, with RandAugment, only LAM improves OOD performance over the ERM+DA baseline (which simply treats the augmented examples as additional training data), while other CR-based DG methods do not. This is in line with the results using targeted data augmentation and once again highlights LAM's superior ability of not suppressing features from different classes within the image.

***

Thank you for your reviews again. Please feel free to let us know if our responses well address your concerns, and feel free to let us know if you have any further questions or concerns. We would be more than pleased to engage in further discussion.

Reviewer comment (Experiments):
Can the authors show how LAM works when the augmentation applied is dataset-agnostic? e.g., using augmentation methods like RandAugment / CutMix / AugMix for all the datasets?

Author response:
Thank you for your response.

As you suggested, we have applied various CR-based DG methods on the *CAMELYON17-WILDS* dataset using **RandAugment** to create augmented examples. The results are as below. For comparison, the results when **Targeted DA** is used are also copied below (from Table 1).

|             Method            |      OOD Accuracy (RandAug)  |      OOD Accuracy (Targeted DA)
|:-----------------------------:|:---------------:|:---------------:|
|ERM|65.2$\pm$2.6 |65.2$\pm$2.6 
|ERM+DA| 84.3$\pm$2.2 |90.5$\pm$0.9 
|Prob. (JS)| 83.4$\pm$6.8|**94.8$\pm$1.2**
|Prob .(KL)| 86.7$\pm$5.5|92.8$\pm$1.5
|Logit| 88.0$\pm$1.4|93.4$\pm$0.3
|Feature|81.7$\pm$ 5.2|94.3$\pm$ 0.6
|LAM| **89.0$\pm$1.9**| 93.5$\pm$1.8


The result again shows that LAM can effectively the model OOD performance even when the more generic data augmentation is used. The improvement of LAM over the ERM+DA baseline (which simply treats the augmented examples as additional training data) in fact larger when RandAugment is used (84.3-->89.0) than when targeted DA is used (90.5-->93.5). 

Just as you suggested, we will appropriately highlight the results with the generic data augmentation methods in the revised version of the paper.

We appreciate your time in reviewing our paper. We hope the additional experiment results could enhance your confidence in our proposed LAM when used with the  dataset-agnostic augmentation methods.

Reviewer comment (Theory):
Theorem 1 contains the very strong assumption that the target distribution of $X^c$ lies within the support of corresponding source distribution (Assumption 3) of the theorem. It is highly suspicious if in reality such a condition would hold true in conjunction with the first two assumptions. It seems that such a condition would only hold in a regime where transfer learning is easy.

Author response:
**1. “Theorem 1 contains the very strong assumption that the target distribution of $X^c$ lies within the support of corresponding source distribution (Assumption 3) of the theorem. It is highly suspicious if in reality such a condition would hold true in conjunction with the first two assumptions.
”**

We respectfully disagree that Assumption 3 of Theorem 1 is strong. On the contrary, we believe that this is one of the most fundamental assumptions required by DG. The reason is as follows:

Imagine that a model had never seen certain $x^c$ during training, then it would not learn the corresponding $y$ of this $x^c$ unless we assume certain structures of $X^c$ that would allow us to infer the $y$ of the *unseen* $x^c$ from other *seen* $x^c$ (and their $y$).  However, such structural assumptions differ from task to task, and it is impossible to know the true underlying structure by only partially observing it without prior domain knowledge. Consequently, Assumption 3 is in fact a minimal assumption for optimal DG in general problems.

Reviewer comment (Reproducibility):
In the description of LAM, it is not clear to me if the weights $\{w_{uy_k}\}$ are hyperparameters or if they are learned during training. If they are hyperparameters, how are they decided? and why not set them to 1 for each $(u, y_k)$?. If they are learned, what mechanism would force them to satisfy the two conditions listed on page 6 (lines 8 and 9)? Note that these weights and $f_\phi$ are learned together.

Author response:
**2. “In the description of LAM, it is not clear to me if the weights are hyperparameters or if they are learned during training. If they are hyperparameters, how are they decided? and why not set them to 1 for each (u, y_k)? If they are learned, what mechanism would force them to satisfy the two conditions listed on page 6 (lines 8 and 9)?”**

The weights are learned during training. Moreover, they are *not* additional parameters introduced by LAM. They are just the weights of the classifier (assumed to be linear, so effectively the last layer) of the model. Consequently, the term $w_{uy_k}f_{\phi}^{u}(x_k)$  is exactly the attribution from a feature unit $u$ to the logit of certain class $y_k$ in the model. That is why we call it Logit Attribution Matching.

To understand how the two conditions listed on page 6 are satisfied, note that the LAM regularization term is minimized if and only if either:

 $w_{uy_k} = 0$ or  $f_{\phi}^{u}(x_k) = f_{\phi}^{u}(\tilde{x}_k)$, 

for every $u$ and $k$. This means that either the weight $|w_{uy_k}|$ is small or the feature difference $|f_{\phi}^{u}(x_k) - f_{\phi}^{u}(\tilde{x}_k)|$ is small (or both). 

In the final algorithm, the regularization term and the cross-entropy loss term are combined to establish the training objective as given in Equation (3).  This combination encourages the model to assign high weights to feature unit $u$ that are predictive and exhibit small feature difference $|f{\phi}^{u}(x_k) - f_{\phi}^{u}(\tilde{x}_k)|$. The core features are exactly such features. At the same time, the difference of features associated with higher weights would tend to be smaller than those associated with lower weights because of LAM. These are the driving forces behind the two conditions listed on page 6.

Reviewer comment (Theory):
Theory is not connected to LAM. Since the condition is $\hat{P}(y | x) = \hat{P}(y | \tilde{x})$, why does probability matching not work well? Why does LAM work better?

Author response:
**1. "Theory is not connected to LAM. Why does probability matching not work well? Why does LAM work better?"**

Thank you very much for pointing this out. As you kindly suggested, we provide below a clear and concise explanation of how the logit attribution matching (LAM) is connected to the theory and why LAM works better than probability matching.

In LAM, the labelled pair $(x_k, \tilde{x}_k: y_k)$ is used whereas the unlabelled pair $(x_k, \tilde{x}_k)$ is used in prior CR-based methods. The key here is to realize that the pairing of $x_k$ and $\tilde{x}_k $ in the labelled pair $(x_k, \tilde{x}_k: y_k)$ is *less informative* than the corresponding unlabelled pair $(x_k, \tilde{x}_k)$. In fact, $(x_k, \tilde{x}_k)$ means that $x_k$ and $\tilde{x}_k$ contain the same semantic information about ALL classes, while $(x_k, \tilde{x}_k: y_k)$ means that $x_k$ and $\tilde{x}_k$ contain the same semantic information about ONE PARTICULAR class $y_k$. 

This distinction between labelled and unlabelled pairs matters because, in practice, it is much harder to ensure that $x_k$ and $\tilde{x}_k$ hold identical information about all classes of interest than a single class $y_k$, especially when the total number of classes is large. For instance, images labelled with class $y_k$ may include small objects of other classes $y_k'$ in the background. This kind of label noise is pervasive in machine learning datasets [1]. When creating the augmented example $\tilde{x}_k$ from $x_k$, it is much easier to retain information about only $y_k$ since we do not need to care about features of other classes when augmenting the data to randomize non-core features $x^n_k$. 

In the aforementioned realistic scenarios, matching the probability distributions over ALL classes is not justified and would lead to sub-optimal solutions (the same can be said about matching the entire feature vectors, $f(x_k)$ and $f(\tilde{x}_k)$). Instead, the logical thing to do is to match only the features that are important for the $y_k$ class. Those considerations lead to LAM. In LAM, regularization is applied only to the labelled pairs $(x_k, \tilde{x}_k: y_k)$, with the assumption that $x_k$ and $\tilde{x}_k$ share the same information of $y_k$. As explained earlier, this assumption is much more practically reasonable since it significantly lowers the requirement on the quality of SS pairs. The advantage of LAM in this respect is specifically demonstrated through the iWildCam-N dataset with amplified label noise. As shown in Table 1 and discussed in Section 5.4 of the paper, on this dataset, only LAM can improve OOD performance over the ERM+DA baseline (which simply use the augmented examples as additional training data), while all previous CR-based methods that regularize across the entire feature, logit, or probability vector fall short of the baseline.

To summarize, the theory essentially provides us with a general understanding of optimal DG under ideal conditions where probability matching across all classes works best. However, when practical aspects of the problem are also considered, we must relax the condition. Under the relaxed condition, LAM is the best choice that we currently have in the literature (to the best of our knowledge).

Reviewer comment (Theory):
The theoretical model's connection to data augmentation is also rather weak. Can you show that your choice of data augmentation is retaining $x^c$ and changing $x^n$?

Author response:
**2. "The theoretical model's connection to data augmentation is also rather weak. Can you show that your choice of data augmentation is retaining $x^c$ and changing $x^n$?"**

Targeted augmentation incorporates human knowledge to control and vary non-core factors while retaining core factors. Take the iWildCam dataset as an example. Since different animals usually live in different habitats, the non-core factors that the models tend to exploit are the backgrounds in the images. So, for this dataset, we can retain $x^c$ and change $x^n$ by copying the animals from one image to another image taken at a different location where the animals might appear. This choice of data augmentation effectively changes spurious background factors while preserving robustly predictive animal traits in the training examples [2]. This fact is reflected by the results in Table 1, showing that by simply adding these augmented examples to the training data, the learned model already significantly outperforms its counterpart trained without the augmented examples (OOD Macro F1-score: 36.5 vs. 30.2). In addition to that, LAM further improves the performance to 41.2. Similar results are also observed on various datasets. Such significant improvements cannot be explained if $x^c$ is not retained or $x^n$ is not changed by the chosen augmentation.

Besides, common DA methods based on basic operations such as resize, rotation, color jitter, and their random combination, RandAugment, all usually retain core factors and vary non-core factors for image classification tasks (e.g., the size of an object in an image could also be a non-core factor). After all, this is one of the most fundamental rules for data augmentation. In Table 8 (Appendix E), we compare LAM and other consistency regularization (CR) methods on top of RandAugment. It shows that CR on top of RandAugment also significantly outperforms the ERM baseline on the iWildCam dataset.

Reviewer comment (Novelty):
Having trouble understanding why CR on top of DA is a contribution. In the related work you say that CR can use different data augmentation strategies as well as alternate ways to pair up samples.

Author response:
**3. "Having trouble understanding why CR on top of DA is a contribution? In the related work you say that CR can use different data augmentation strategies as well as alternate ways to pair up samples."**

We would like to take this great opportunity to clarify the first contribution of our paper. By “empirically showing that CR, if done properly, can improve OOD performance when combined with DA”, we do not claim that we are the first to propose CR methods for DG. Instead, we were referring to the fact that there had not been an extensive discussion and comparison of existing CR methods for DG until our work. We believe this is **the first time** that multiple methods are systematically evaluated together under the same evaluation protocol and data. By benchmarking existing CR methods and showing their effectiveness (as well as limitations), we hope that our work draws more attention from the research community to this promising but relatively unexplored direction. We will carefully revise the introduction of our paper to better reflect the above points.

Reviewer comment (Writing):
Minor nit: this paper has many abbreviations (DG, DA, OOD, CR, CLD). I found that use of DG and DA were a bit confusing the first time I read the paper, and would prefer having more sentences with the full words, at least in the introduction.

Author response:
**4. "I found that use of DG and DA were a bit confusing the first time I read the paper, and would prefer having more sentences with the full words, at least in the introduction."**

Thanks for your kind advice. You are absolutely right. We will pay attention to it and address it in the revised version of the paper.

Reviewer comment (Presentation):
Unclear how contributions in the introduction are related. It reads like a list of ways to improve performance but don't feel well-motivated.

Author response:
**5. "Unclear how contributions in the introduction are related. It reads like a list of ways to improve performance but don't feel well-motivated."**

The starting point of our paper is that data augmentation (DA) is quite important and effective for DG. A recent study shows that targeted augmentations can significantly improve OOD performance in various real-world datasets [2]. Furthermore, DA creates abundant semantic sharing pairs which can be naturally utilized in consistency regularization (CR). To better understand and harness CR for DG, we first theoretically show that CR on top of DA can lead to optimal DG and then systematically evaluate existing CR approaches on a scale and rigor that has not seen before. In addition, we propose a new CR method, LAM, to achieve even better performance compared to previous CR-based DG methods and other representative DG methods. Finally, the connection between LAM and our theory is discussed in the answer to the Question 1 above. If you find the added discussions are appropriate and helpful, we will revise the introduction section of the paper to reflect this connection better.

Reviewer comment (Novelty):
The contributions may not be very significant because consistency regularization for DG has already been extensively studied in previous research and the proposed method only makes simple modifications to the existing feature matching method. Several concepts in this paper are borrowed from previous ideas, such as targeted augmentation and causal-invariant prediction.

Author response:
**1. "The contributions may not be very significant. Consistency regularization for DG has already been extensively studied. Several concepts in this paper are borrowed from previous ideas, such as targeted augmentation and causal-invariant prediction."**

- We greatly appreciate the chance to clarify the contributions of our paper; however, we respectfully disagree that consistency regularization (CR) for DG has been extensively studied. Considering the sheer volume of DG literature, CR for DG is relatively unexplored. In fact, it is not even considered as an established category of DG methods in recent DG survey papers (see Table 3 of [1] and Figure 3 of [2]).   

  In addition, there has not been an extensive discussion and comparison of existing CR methods for DG until our work. We believe this is **the first time** that multiple methods are systematically evaluated together under the same evaluation protocol and data. The results under targeted augmentation and a more generic form of data augmentation (RandAugment) are presented in Table 1 and Table 8 respectively. Discussion of the results is also made in Section 5.3 and Appendix E. By benchmarking existing CR methods and showcasing the effectiveness of CR when done properly for DG, we hope that it draws more attention from the research community to this promising direction.

- Almost every paper borrows some concepts from previous ideas. We genuinely do not think this is an originality issue of our paper as what we propose is quite different from targeted augmentation [3] and invariant causal prediction (ICP) [4]. 

  To be specific, our causal DG model differs fundamentally from ICP: in our model, $X^c$ is unobserved, unlike ICP which assumes that $X^c$ is observed and disentangled from $X^n$. This is a very important difference as our model is thereby compatible with unstructured data modalities like vision and text. With this more practical assumption, our causal DG model and theorem provide more general insights on the performance gains of consistency regularization (CR) for DG. Besides, the focus of this work is the generalization effect brought by CR between original and augmented data. Targeted augmentation is just one of the possible ways to create augmented examples. Other data augmentation methods also work to certain extents (e.g., RandAugment in Table 8).

- Our final contribution is that we introduced a new CR approach: Logit Attribution Matching (LAM), following the theoretical discussion and empirical evaluation of prior CR-based DG methods. Empirically, LAM surpasses other CR methods and representative DG methods on multiple real-world datasets as shown in Table 1 and 2. In response to your third question below, we will delve deeper into the connection between LAM and our theorem and explain why it provides superior performance compared to previous CR-based DG methods.

Reviewer comment (Theory):
The theorem does not serve as a supporting foundation for the proposed logit attribution matching method. It seems that the theorem and the techniques are divided and tell two different stories. Concretely, the theorem just reveals that consistency regularization can be an optimal solution for DG. It is not connected to why logit attribution matching is needed to deal with core and non-core factors. Before this paper can be accepted, it is necessary that it undergoes revision to ensure a clear and concise explanation of how the theorem serves as a driving force behind the techniques employed.

Author response:
**3. "Before this paper can be accepted, it is necessary that it undergoes revision to ensure a clear and concise explanation of how the theorem serves as a driving force behind the techniques employed."**

Thank you very much for pointing this out. As you kindly suggested, we provide below a clear and concise explanation of why logit attribution matching (LAM) is needed - as a practical implication of the theorem.  

In LAM, the labelled pair $(x_k, \tilde{x}_k: y_k)$ is used whereas the unlabelled pair $(x_k, \tilde{x}_k)$ is used in prior CR-based methods. The key here is to realize that the pairing of $x_k$ and $\tilde{x}_k $ in the labelled pair $(x_k, \tilde{x}_k: y_k)$ is *less informative* than the corresponding unlabelled pair $(x_k, \tilde{x}_k)$. In fact, $(x_k, \tilde{x}_k)$ means that $x_k$ and $\tilde{x}_k$ contain the same semantic information about ALL classes, while $(x_k, \tilde{x}_k: y_k)$ means that $x_k$ and $\tilde{x}_k$ contain the same semantic information about ONE PARTICULAR class $y_k$. 

This distinction between labelled and unlabelled pairs matters because, in practice, it is much harder to ensure that $x_k$ and $\tilde{x}_k$ hold identical information about all classes of interest than a single class $y_k$, especially when the total number of classes is large. For instance, images labelled with class $y_k$ may include small objects of other classes $y_k'$ in the background. This kind of label noise is pervasive in machine learning datasets [5]. When creating the augmented example $\tilde{x}_k$ from $x_k$, it is much easier to retain information about only $y_k$ since we do not need to care about features of other classes when augmenting the data to randomize non-core features $x^n_k$. 

In the aforementioned realistic scenarios, matching the probability distributions over ALL classes is not justified and would lead to sub-optimal solutions (the same can be said about matching the entire feature vectors, $f(x_k)$ and $f(\tilde{x}_k)$). Instead, the logical thing to do is to match only the features that are important for the $y_k$ class. Those considerations lead to LAM. In LAM, regularization is applied only to the labelled pairs $(x_k, \tilde{x}_k: y_k)$, with the assumption that $x_k$ and $\tilde{x}_k$ share the same information of $y_k$. As explained earlier, this assumption is much more practically reasonable since it significantly lowers the requirement on the quality of semantic sharing pairs. The advantage of LAM in this respect is specifically demonstrated through the iWildCam-N dataset with amplified label noise. As shown in Table 1 and discussed in Section 5.4 of the paper, on this dataset, only LAM can improve OOD performance over the ERM+DA baseline (which simply use the augmented examples as additional training data), while all previous CR-based methods that regularize across the entire feature, logit, or probability vector fall short of the baseline.

To summarize, the theorem essentially provides us with a general understanding of optimal DG under ideal conditions where probability matching across all classes works best. However, when practical aspects of the problem are also considered, we must relax the condition. Under the relaxed condition, LAM is the best choice that we currently have in the literature (to the best of our knowledge).

***
We plan to appropriately include the points discussed above in the revised version of the paper. Please feel free to let us know if our responses well address your concerns, and feel free to let us know if you have any further questions or concerns. We would be more than pleased to engage in further discussion.

Reviewer comment (Theory):
Is it possible to build logit attribution matching upon probability matching or logit matching models?

Author response:
**2. "Is it possible to build logit attribution matching upon probability matching or logit matching models? Are they better or worse than building upon a feature matching model? Can the authors provide more analysis and explanations of why you just choosing feature matching methods?"**

Thank you for your questions, but we suspect that there might be some misunderstanding. To facilitate better understanding, we will make the following point clearer in the paper: LAM does *not* introduce additional weights into the model or the learning process. Instead, it simply uses the weights of the classifier as a natural indicator of the importance of each feature dimension to each class. In other words, here the weights are not newly added parameters, but just from the classification head of the original model. So, LAM is not simply built upon a feature matching model. As a matter of fact, the term $w_{uy_k}f_{\phi}^{u}(x_k)$ in the formulation of LAM is exactly the attribution from a feature unit to the logit of certain class in the model. That is why we call it Logit Attribution Matching.

Reviewer comment (Experiments):
Are they better or worse than building upon a feature matching model?

Author response:
**2. "Is it possible to build logit attribution matching upon probability matching or logit matching models? Are they better or worse than building upon a feature matching model? Can the authors provide more analysis and explanations of why you just choosing feature matching methods?"**

Thank you for your questions, but we suspect that there might be some misunderstanding. To facilitate better understanding, we will make the following point clearer in the paper: LAM does *not* introduce additional weights into the model or the learning process. Instead, it simply uses the weights of the classifier as a natural indicator of the importance of each feature dimension to each class. In other words, here the weights are not newly added parameters, but just from the classification head of the original model. So, LAM is not simply built upon a feature matching model. As a matter of fact, the term $w_{uy_k}f_{\phi}^{u}(x_k)$ in the formulation of LAM is exactly the attribution from a feature unit to the logit of certain class in the model. That is why we call it Logit Attribution Matching.

Reviewer comment (Experiments):
Can the authors provide more analysis and explanations of why you just choosing feature matching methods?

Author response:
**2. "Is it possible to build logit attribution matching upon probability matching or logit matching models? Are they better or worse than building upon a feature matching model? Can the authors provide more analysis and explanations of why you just choosing feature matching methods?"**

Thank you for your questions, but we suspect that there might be some misunderstanding. To facilitate better understanding, we will make the following point clearer in the paper: LAM does *not* introduce additional weights into the model or the learning process. Instead, it simply uses the weights of the classifier as a natural indicator of the importance of each feature dimension to each class. In other words, here the weights are not newly added parameters, but just from the classification head of the original model. So, LAM is not simply built upon a feature matching model. As a matter of fact, the term $w_{uy_k}f_{\phi}^{u}(x_k)$ in the formulation of LAM is exactly the attribution from a feature unit to the logit of certain class in the model. That is why we call it Logit Attribution Matching.