Editable Concept Bottleneck Models

Weaknesses:

The baseline methods are not complete. For example, there are still some methods for EBM like, probability EBM [1], etc.

Our paper proposes a CBM editing method. Probability EBM is not used as a baseline for our method, as it does not align with the primary objectives of our approach.

The influence function is only suitable for convex function. I wonder how the author applies it on the non-convex function, like deep neural network.

We disagree. While the classical influence function is most straightforwardly applied to convex functions, its principles can be adapted to non-convex functions through regularization techniques. IF has been widely studied for deep neural networks, starting from [5]. Moreover, the influence function has been successfully applied to large language models (LLMs) and diffusion models [1-4].

In ECBM, a major challenge posed by non-convexity is the singularity of the Hessian matrix, which leads to instability during matrix inversion. To address this issue, we employ EK-FAC. This method assumes that parameters across different layers are independent. For each layer, a specifically designed regularization term is introduced to prevent singularity, thereby rendering the entire Hessian matrix invertible.

[1]. Grosse, R., Bae, J., Anil, C., Elhage, N., Tamkin, A., Tajdini, A., ... & Bowman, S. R. (2023). Studying large language model generalization with influence functions. arXiv preprint arXiv:2308.03296.
[2]. Choe, S. K., Ahn, H., Bae, J., Zhao, K., Kang, M., Chung, Y., ... & Xing, E. (2024). What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions. arXiv preprint arXiv:2405.13954.
[3]. Kwon, Y., Wu, E., Wu, K., & Zou, J. (2023). Datainf: Efficiently estimating data influence in lora-tuned llms and diffusion models. arXiv preprint arXiv:2310.00902.
[4]. Xia, M., Malladi, S., Gururangan, S., Arora, S., & Chen, D. (2024). Less: Selecting influential data for targeted instruction tuning. arXiv preprint arXiv:2402.04333.
[5]. Koh, Pang Wei, and Percy Liang. "Understanding black-box predictions via influence functions." In International conference on machine learning, pp. 1885-1894. PMLR, 2017.

The approximate equal sign is mixed with the equal sign, which is not rigorous, like in Theorem 4.7. Please correct me if I have some mis-understanding.

In our theorem, the \bar indicates that the model is obtained by definition, while \tilde and \hat are the model obtained by minimizing process. We use $\approx$ in line 340 and 344, because we won't retrain the model to obtain $\tilde{f}$ and $\hat{f}$, but use $A_G$ and $B_G$ to estimate them.

Questions:

I am doubtful with the running time in Table 1. How the running time can be less 1 minute even for retraining method.

This is the averaged running time(RT), that is the actual RT/dataset size. The actual running time is much longer than 1 minute.

Dear Reviewer AK63,

We are truly grateful for the time and effort you have dedicated to reviewing our work. We would like to respectfully inform you that two reviewers have already increased their scores: Reviewer KdDJ raised the score from 5 to 6, and Reviewer Oeij raised it from 3 to 5.

We would highly appreciate your review and feedback on the responses. Should you have any questions or concerns, we would be happy to discuss and address them.

Best,
Authors

Dear Reviewer AK63,

Thank you again for your detailed and constructive review comments. We respectfully remind you that the discussion period will end in a few days. We have responded above to your concerns. We believe these address your concerns. We would appreciate it if you would take the time to read and comment on the responses.

Best,
Authors

Dear Reviewer AK63,

Thank you for your thoughtful participation and feedback in this discussion. We have addressed your concern in our response above. Additionally, we have included detailed results related to the RT in the appendix of the revision to clarify the timing method. We would greatly appreciate it if you could review these changes to confirm that they address your concerns. We respectfully request you to consider raising your rating score accordingly if your concerns are alleviated. Otherwise, we would be happy to hear the remaining concerns that prevent you from doing so and continue to discuss them.

Best,
Authors

Dear Reviewer AK63,

Thank you for your valuable contributions throughout the review process. We kindly remind you that the extended discussion period will conclude in a few days.

In response to your remaining concerns regarding RT, we have provided additional clarifications and included further explanations in the appendix. We would greatly appreciate it if you could review these updates and consider providing additional comments or updating your score. We trust that you will evaluate our paper in light of the clarifications we have provided.

Finally, we sincerely appreciate your active participation in this thorough discussion and look forward to receiving your final decision.

Best regards,
Authors

Dear Reviewer AK63,

We hope you had a wonderful Thanksgiving. Once again, we sincerely thank you for your valuable time and effort, and we fully understand your busy schedule. We noticed that we haven’t received feedback from you following our latest revision updates in which we added explanations for running time(RT). In the meantime, we have addressed the concerns of the other two reviewers, who have expressed a positive attitude and increased their scores.

We would be truly grateful if you could let us know whether there are any additional questions or concerns we can address before the rebuttal deadline. Your feedback is invaluable and plays a crucial role in strengthening our work.

Thank you once again for your contribution to ICLR! Wishing you all the best with your current and future submissions.

Sincerely,
The Authors

Weaknesses:

Scailability: Although the authors include a relatively larger-scaled dataset (e.g., CelebA) to their evaluation... It remains unclear how well ECBMs would scale to larger datasets or more complex CBM architectures...

Our ECBM method has been specifically designed to accommodate the majority of current CBMs, including more complex architectures, such as VLMs with millions of parameters. Compared to large language model, CBMs are small. Our experiments have already cover many SOTA CBMs, so this is not an issue. By leveraging EK-FAC to accelerate computations, our approach effectively manages the Hessian computations, even for models with a large number of parameters

In [1-3], influence function has been scaled to LLM with billions of parameters, which fully validates the efficiency of EK-FAC in the inverse Hessian-vector product. As a result, CBMs, which usually have millions of parameters, are computationally feasible for EK-FAC.

[1]. Grosse, R., Bae, J., Anil, C., Elhage, N., Tamkin, A., Tajdini, A., ... & Bowman, S. R. (2023). Studying large language model generalization with influence functions. arXiv preprint arXiv:2308.03296.
[2]. Choe, S. K., Ahn, H., Bae, J., Zhao, K., Kang, M., Chung, Y., ... & Xing, E. (2024). What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions. arXiv preprint arXiv:2405.13954.
[3]. Kwon, Y., Wu, E., Wu, K., & Zou, J. (2023). Datainf: Efficiently estimating data influence in lora-tuned llms and diffusion models. arXiv preprint arXiv:2310.00902.

Questions:

Could you provide more details on how runtime efficiency scales with larger datasets or models? While your experiments show improvements over retraining on smaller datasets, it would be helpful to understand how ECBM performs with larger models like Vision-Language Models.

Regarding the scale of dataset, we have extended our method from CUB(1w) to CelebA(20w), and the results are listed in Table 1 in our paper.

You identify influential samples or concepts using influence scores. How do these rankings compare with simpler methods like analyzing weights in a linear label predictor? What additional insights do influence functions provide?

The importance derived from the weights in f emphasizes the influence of concepts on the final label during the model's prediction process, while the concept influence scores derived from ECBM based on the influence function emphasizes the impact of a concept on model parameters throughout the training process. Here the model parameters includes $g$ and $f$. Therefore, these two importance measures are relevant but different. To further explore the relevance, we conducted experiments and extracted the importance rankings under two different settings.

The results are listed in Table A. We observe that, except for the concept 'has_primary_color::black,' there is no other overlap. The important concepts recognized by label predictor weights are broader and more general, such as 'has_size,' 'has_shape,' and 'has_back_pattern.' In contrast, the concepts identified by our ECBM are more characteristic and specific, including 'has_upperparts_color,' 'has_leg_color,' and 'has_breast_color.

This observation is intuitively reasonable in the context of concept-based label prediction. The weights of the label predictor are specifically associated with predicting labels derived from concepts. When observing a bird image, its overall features—such as shape, color, and size—enable a quick determination of its general category. Additional detailed concepts are then used to refine this prediction further. In contrast, the concepts selected using the Influence score incorporate features from the input image into the selection process. Thus, the selected concepts are those that provide a more direct and definitive basis for determining the category.

Table A: The most influential cocnepts selected by the weights of label predictor $f$ and influence function(IF).

Dear Reviewer sqUB,

We are truly grateful for the time and effort you have dedicated to reviewing our work. We would like to respectfully inform you that two reviewers have already increased their scores: Reviewer KdDJ raised the score from 5 to 6, and Reviewer Oeij raised it from 3 to 5.

We would highly appreciate your review and feedback on the responses. Should you have any questions or concerns, we would be happy to discuss and address them.

Best,
Authors

Dear Reviewer sqUB,

Thank you again for your detailed and constructive review comments. We respectfully remind you that the discussion period will end in a few days. We have responded above to your concerns. We believe these address your concerns. We would appreciate it if you would take the time to read and comment on the responses.

Best,
Authors

Dear Reviewer sqUB,

Thank you again for your detailed and constructive review comments. We respectfully remind you that the discussion period will end in a few days. We have responded above to your concerns. We believe these address your concerns. We would appreciate it if you would take the time to read and comment on the responses.

Best, Authors

Dear Reviewer sqUB,

We sincerely appreciate your valuable contributions to ICLR. As the extended discussion period will conclude in a few days, we kindly remind you to share any final input.

Having addressed the concerns you raised, we respectfully request that you review our clarifications and consider providing further comments or updating your score. We trust that you will re-evaluate our paper based on the additional details provided.

Thank you once again for your thoughtful contributions. We look forward to receiving your final decision.

Best regards,
Authors

Dear Reviewer sqUB,

We hope you had a wonderful Thanksgiving. Once again, we sincerely thank you for your valuable time and effort, and we fully understand your busy schedule. We noticed that we haven’t received any feedback from you yet. In the meantime, we have addressed the concerns of the other two reviewers, who have expressed a positive attitude and increased their scores.

We would be truly grateful if you could let us know whether there are any additional questions or concerns we can address before the rebuttal deadline. Your feedback is invaluable and plays a crucial role in strengthening our work.

Thank you once again for your contribution to ICLR! Wishing you all the best with your current and future submissions.

Sincerely,
The Authors

Dear Reviewer sqUB,

I hope this message finds you well. I am writing to kindly follow up, as today marks the final day to provide feedback on our rebuttal discussions. Your insights are invaluable in addressing any remaining concerns and refining our submission to its best possible version.

If there are any aspects of the rebuttal that require further clarification or discussion, please do not hesitate to let us know. We will address them promptly. If your concerns have already been addressed, we kindly ask that you consider reflecting this in your review score.

Thank you for your time and effort during this review process. We sincerely appreciate your valuable feedback and look forward to hearing from you.

Best regards,
Authors

General questions and comments

Q1 lines 145-146: please reword "usually, here the map $f$ is linear"...

It is not misleading. Linear predictors are often preferred in CBMs due to their better interpretability, which allows for straightforward understanding of the relationships between concepts and outcomes. Consequently, most CBMs utilize linear predictors. However, linear models are limited in their ability to capture complex, nonlinear relationships between different concepts. To address this limitation, alternative CBM architectures featuring more complex, nonlinear label predictors have been proposed such as [1]. Thus, we use the term 'usually' to accurately reflect the common but not universal use of linear predictors in CBMs. Thus, we think it is unnecessary to focus on one word "usually".

[1]. Xu, X., Qin, Y., Mi, L., Wang, H., & Li, X. (2024). Energy-based concept bottleneck models: unifying prediction, concept intervention, and conditional interpretations. arXiv preprint arXiv:2401.14142.

Q2: notation of loss functions throughout the paper:

We use different notation for convenience, and we believe there is no confusion for the equations you mentioned. Please carefully read our paper.

In Equations (1) and (2), the symbol '=' is interpreted as 'denotes' or ≜, meaning 'is defined as' for the purposes of this discussion.

In (1), $L_{C}(g^j(x_i),c_i^j)$ represents the loss function for the $j$-th concept of the $i$-th data point, while $L_{C_j}(g(x_i),c_i)$ provides a simplified notation of the same concept. Both notations convey the same idea of measuring loss for concept prediction.

In (2), $L_{Y}(f(\hat{g}(x_i)), y_i)$ represents the loss function of the $i$-th data in the training set, where $f(\hat{g}(x_i)$ denotes the predicted label, and $y_i$ the true label. And $L_{Y_i}(f, \hat{g})$ is a simplified notation, omitting $x_i$ and $y_i$ for brevity as the context makes their roles clear.

In Appendix D, similar notation is used for clarity. $L_{Y_l}$ denotes the label loss for the $l$-th data. $L_{Y_{ir}}$ specifies the label loss for the $ir$-th data point that is under consideration.

Q3: lines 170-172: the derivative should be of $\hat{\theta}_{\epsilon,-z_m}$, not $\hat{\theta}$ as it does not depend on $\epsilon$.

We corrected it.

Q4: difference with test-time intervention.

Let's first clarity the secondary editing. If an input of the concept predictor has the k-th concept mispredicted, test-time intervene will correct this concept, and we can observe the predicted label directly. However, the concept predictor may still mispredicted the k-th concept when it receive a similar input. This is because the flaws in the concept predictor have not been rectified at all. Therefore, if these misprediction have taken place several times, our method, ECBM, can help to edit the concept model to remove the concept at all, or to correct the mislabeled data resulting in these wrong predictions.

"This process extends the rectification from the data level to the model level": Test-time intervene only correct one prediction, and our method can correct the model, and thereby correct all the latter similar predictions. Our focus is not only the interpretability Of CBM but also the correction of the model.

Q5: lines 246-249: "This is because the ..." this sentence is very confusing.

Note that this sentence should be considered in conjunction with the previous statement. If several concepts, indexed by M, need to be removed due to incorrect attribution or spurious associations, we must adjust the concept predictor. This adjustment decreases the output dimension and alters the predictor's dimensionality. Under these circumstances, applying IF becomes particularly challenging due to changes in the predictor's dimensional structure. This is because Influence Functions rely on the same dimension of output to assess the impact of small perturbations, and alterations in the dimensional structure disrupt the assumptions necessary for IF to function effectively. See our preliminaries on the influence function for details.

Q6: line 254: "by inserting a zero-row vector into the $r$-th row of the matrix in the final layer of". This sentence makes several implicit assumptions...They are reasonable, but they should be stated clearly in order not to confuse readers.

Note that the primary assumption we've made is that the final layer of the encoder g is a linear layer, which is a common configuration in neural network architectures. We agree that this assumption should be explicitly stated to avoid any potential confusion for the readers. We will revise the manuscript to include this clarification.

Q7: line 264: I do not understand why "the value of 00" is written several times instead of simply 0. Also, what is "MM"?

We have corrected these errors.

Basic questions:

all equations should be numbered.

As only some of the equations are referred. We think it is unncessary to number all equation (in fact, most theoretical papers do not number all equation). Numbering all equations will definitely makes the paper unreadable.

proofs should be explicitly referenced after theorems.

We have included all proofs in Appendix. In fact, there are many papers do not explicitly refer proofs after theorems. There is no such a requirement for all papers, right?

line 27: "large multimodal models" (include "models").

"modal" is not model. Please refer to MLLM(multi-modal LLM).

line 493: There is no need to report results with 6 decimals.

We agree, but this is not a typo, right?

Explanation for specific wording:

line 80: it is unclear what erroneous or poisoned data mean.

Poisoned data is a commonly used word in adversarial machine learning, and we have illustated in Figure 1. If the reviewer cannot understand it, we can add some explaination.

line 94: the sentence "and the concept for all data on model parameters" is incomplete and should be rephrased.

No, please read the whole sentence "Leveraging the influence function (Cook, 2000; Cook & Weisberg, 1980), we quantify the impact of individual data points, individual concept labels, and the concept for all data on model parameters."

lines 96-97: it is unclear what "due to their composite structure, i.e. the intermediate representation layer" means. All neural networks have intermediate representation layers, why is this a specific limitation about CBMs?

The layer means the concept layer. This is the essential difference between CBM and other neural network.

line 131-132: "thereby deciphering the interaction of concept models and providing an adaptive solution to concept editing" is a confusing sentence. What does it mean to decipher an interaction?

The interaction refers to the ones between the concept predictor and the label predictor in CBMs.

line 161: "thus capturing the essence of the original CBMs" should be rephrased. What does it mean to capture the essence of a model? Eqs. (1) and (2) are the standard definition of a CBM, what is the "original CBM" being referred to here?

In this paper, our focus is editing the CBM to remove the harmful data/concept/concept label, while preserve the essence of the original CBM. To understand this sentence, the title of this paper should be taken into account.

abstract: "elucidate the prediction process". It is unclear what prediction process this sentence is referring to. abstract: "affirming their adaptability within the realm of CBMs" this sentence sounds very unnatural and should be rephrased.

The terms used here are scientific terms. If we use simplified language to explain these terms in detail, our abstract could become unnecessarily lengthy.

line 328: I do not understand the sentence "with the original loss before unlearning in equation 2".

The "unlearning" means we remove the data and retrain the model. Before unlearning means the original model.

line 1248: "We can see that there is a huge gap between $\hat{f}_{-z_G}$ and $\hat{f}$". Could the authors clarify in what sense they are characterizing the gap between the two functions as huge?

This hug gap is the form difference between equation (11) and equation (2), and that's why we use equation (12) as an intermediate.

Grammatical issues:

lines 35-36: ".. for placing human-understandable concepts. In the process ...". This sentence is not grammatical.

line 311: the sentence "... due to different reasons, such as the training data involving poisoned or erroneous issues" is not grammatical.

line 193: "estimating the changes in the parameters of the retraining model holds significance" is not grammatical and should be rephrased.

We have checked all the above grammatical issues with ChatGPT, there is not grammar error in this line.

Typos:

line 189: "for certain concepts, we may opt to" is incomplete. These two sentences should be linked by a connector.

line 197-198: "the retrained concept predictor label predictor" is not grammatical and should be rephrased.

-line 208-209: "a two-stage edition approach", typo in "edition" -> "editing".

line 256: typo in "is the subset of is the subset of $T$".

line 312: $G$ is overloaded, it was already used to define the Fisher information matrix.

line 424: "we conducted experiments ... removed." is unclear and should be rephrased.

line 455-456: typos in "11-1010", "0.0250.025".

line 517: "1010" is a typo.

line 128: the sentence "CBMs work on the image field also includes" is incomplete and should be rephrased.

line 323: typo in "loss function with respect to".

line 82: it is not clear what "the learning models" means.

Answer:"the learning models" is the model we learned. We changed it to "the learned models"

We have modified all the above minor typo issues.

Dear Reviewer,

We sincerely appreciate your thorough review of our paper and the time you have dedicated to it. Based on your suggestions, we have made minor revisions to the paper. Given that the paper considers the comprehensive application scenarios of our method, a certain level of reading difficulty is inevitable. The current structure of the paper is sufficiently clear, and therefore, no major modifications are necessary. Note that other three reviewers did not encounter significant difficulties in understanding the content of our article.

Additionally, regarding the suggestions in writing comments and minor comments, we believe that certain scientific terms and phrasing are essential to maintain the conciseness and professionalism of the paper's language. If the language of our paper is overly simplistic and the content is introduced in excessive detail, to the extent that beginners can fully comprehend every sentence, it may adversely affect the readability for the majority of readers.

We appreciate your understanding. If there is anything unclear in the paper, please feel free to let us know. Considering your recognition of the contribution in our paper, we hope you will reconsider the rating of our work.

Dear Reviewer,

Regarding the issues related to mathematical notations, we have included a notation table in Appendix A of the revision to address this concern. We are open to your suggestions and willing to make further improvements.

You also raised concerns regarding writing style and grammatical issues. For the grammatical points, we have thoroughly reviewed them and conducted additional checks by Grammerly and ChatGPT, confirming that the issues you mentioned do not constitute actual grammatical errors. With regard to the writing style, we believe that our work is adhere to standard practices in scientific writing.

Additionally, it is worth noting that other reviewers did not express significant concerns regarding the writing style, grammar, or clarity of the paper's structure. We believe that rejecting the paper solely because you may not prefer or be accustomed to this common scientific writing style would be extremely unreasonable.

Given your overall recognition of our work, we strongly request that you reconsider your rating. If you have further suggestions, we are prepared to discuss them with you at any time.

Sincere,
Authors

232 35 0 4 11.3090
221 35 0 4 30.2400
181 35 0 3 6.3280
209 35 0 4 3.2440
188 35 0 3 2.2210
235 35 0 4 2.0460
197 35 0 2 2.7910
213 35 0 4 4.7770
184 35 0 4 15.0440
238 35 0 4 2.7580
230 35 0 4 1.7970
216 35 0 4 8.9130
222 35 0 1 0.8450
189 35 0 4 6.9700
195 35 0 4 7.5280
194 35 0 4 6.8940
203 35 0 1 0.5630
228 35 0 3 25.5060
206 35 0 4 5.6110
227 35 0 4 18.0670
218 35 0 1 0.5310
187 35 0 4 1.5230
215 35 0 2 11.8400
220 35 0 1 2.8280

Dear Reviewer,

Thanks for your questions.

Question

Q1:

The top-10 most important concepts according to Retrain are not the concepts with the highest coefficients in the edited linear label predictor. We have explained this in the last comment:"Each concept is removed through retraining or ECBM. Based on the observed decrease in F1 score, we ranked the concepts and presented the top-10 in Figure 5". Please read our comments carefully.

The purpose of our experiment to identify the most influential concepts is not primarily aimed at intuitively explaining which concept plays a decisive role in predicting a specific image. Rather, our aim is to identify the concepts that are most critical for the CBM's accurate label predictions, thereby improving interpretability in terms of model accuracy. The images in Figure 5 are intended to provide an intuitive understanding, rather than being used to directly assist in predicting that specific image.

We provide a detailed explanatoin in Appendix H.3.1 in the revision. And to clarify the misunderstanding, we reword the "how they determine the predicted label" into "how they assist the predictoin".

Q2:

As stated in lines 375-376 of the manuscript, "we follow the same network architecture and settings outlined in Koh et al. (2020)." Thus, the dataset we use is the CUB dataset processed according to [1], rather than the original CUB dataset. This is a standard preprocessing step commonly employed in CBM studies.

The concept you mentioned is labeled as "0" in the original CUB dataset but is transformed to "1" after processing. If needed, you may refer to the following link for the specific dataset used in our study.

[1]. Pang Wei Koh, Thao Nguyen, Yew Siang Tang, Stephen Mussmann, Emma Pierson, Been Kim, and Percy Liang. Concept bottleneck models. In International conference on machine learning, pp. 5338–5348. PMLR, 2020.

link for CUB dataset: https://worksheets.codalab.org/rest/bundles/0x5b9d528d2101418b87212db92fea6683/contents/blob/

link for CBM: https://github.com/yewsiang/ConceptBottleneck

Q3:

We have made minor adjustments to the wording and replaced 'with their correct concept labels' with 'within them,' in the hope that this will improve your understanding.

Dear Reviewer,

We sincerely appreciate your acknowledgment of our revisions, your efforts in clarifying the issues in the CUB processing procedure, and your decision to increase the score.

We have revised our paper based on your suggestions. We added an explanation of the CUB processing steps in Appendix H.

Thank you very much for your detailed review and for the time and effort you have dedicated to helping us improve our paper. If you have any further questions or concerns, we would be more than happy to discuss and address them. If everything is clear, we would be deeply grateful if you could kindly consider further improving the score.

Best regards,
Authors

Dear Reviewer oeij,

Thank you for participating in the discussion. We have addressed your concerns in the above response and in our general comments, aside from the suggestions on grammar and writing style, which were not raised by other reviewers.

We respectfully request you to consider raising your rating score accordingly if your concerns are alleviated. Otherwise, we would be happy to hear the remaining concerns that prevent you from doing so and continue to discuss them.

Best,
Authors

Dear Reviewer oeij,

We hope you had a wonderful Thanksgiving. Once again, we sincerely thank you for your valuable time and effort, and we fully understand your busy schedule. We noticed that we haven’t received feedback from you following our latest revision updates. In the meantime, we have addressed the concerns of Reviewer KdDJ, who has expressed a positive attitude and increased the score.

We would be truly grateful if you could let us know whether there are any additional questions or concerns we can address before the rebuttal deadline. Your feedback is invaluable and plays a crucial role in strengthening our work.

Thank you once again for your contribution to ICLR! Wishing you all the best with your current and future submissions.

Sincerely,
Authors

Dear Reviewer oeij,

Thank you for your valuable contributions during this review process. We wish to kindly remind you that the extended discussion period will end in a few days.

Since we have addressed your remaining concerns about Figure 5 above and included additional explanations in the appendix, we kindly request that you consider updating your score or providing additional comments. We trust that you will re-evaluate our paper based on our additional clarifications.

Finally, we deeply appreciate your participation in this thorough discussion and look forward to hearing your final thoughts.

Best,
Authors

Weaknesses

W1: The related work section could be expanded. Other existing methods for model editing without retraining (if available) should be discussed.

We agree that discussing existing methods for model editing without retraining would enrich the related work section. However, after thorough research, we found that there are currently no established methods specifically for CBM editing without retraining.

There have been some works on model unlearning; they can remove the influence of certain data without the need for retraining. To further support this, we will include relevant works on model unlearning in the appendix as part of our revision.

W2: The experiments do not fully support the claims made in earlier sections...The authors might consider intentionally introducing some noise (at different levels) to their training data, and then use their model editing strategy to remove their impacts and see if the model’s performance/interpretability benefits from their methods...

We do not agree. Our focus is on removing the influence of certain data points with erroneous labels, spurious concepts, and incorrect concept annotations from the model through editing. The experiments presented in the section titled “ECBMs can erase data influence” have already demonstrated that the influence of the removed data points is effectively eliminated. These results provide evidence of the effectiveness of ECBMs in editing the model to remove specific samples.

We expects to see an improvement in model performance after removing erroneous or false concepts. However, in practice, an increase in accuracy does not necessarily indicate that the data has truly been removed. The MIA method is currently one of the most reliable approaches to determine whether data has been removed. Therefore, we chose to use MIA rather than testing the F1 score after removing artificially synthesized noisy data.

To further strengthen the validation of our claims, we conducted additional experiments where varying levels of noise (i.e., noisy labels, noisy concepts) are introduced into the data. We then applied our ECBM method to assess its effectiveness in mitigating these issues and evaluate whether the model's performance benefit as expected.

Firsly, we introduce noises under three levels. In concept level, we choose 10% of the concepts and flip these concept labels for a portion of the data. In data level, we choose 10% of the data and flip their labels. In concept-label level, we choose 10% of the total concepts and flip them. Then we conduct the following experiments.

After that, we remove the noise and obtain the retrained mdoel, which is the ground truth(gt) of this harmful data removal task. In contrast, we use ECBM to remove the harmful data. The results are shown in Table A.

Table A: Harmful Data Removal on Nosiy CUB Dataset.

From Table A, it can be observed that the model performance improves across all three settings after noise removal and subsequent retraining or ECBM editing.

This confirms that the performance of ECBM is nearly equivalent to retraining in various experimental scenarios, further providing evidence of the robustness of our method.

W3: The presentation needs further improvement. There are several inconsistent notations in the paper. Some terms are used before they are defined. Some equations are numbered but some are not. See more details in the Questions section. Some important proof/deviations are in the appendix, but not referenced appropriately in the main text (e.g., Appendix A).

As only some of the equations are referred, we think it is unncessary to number all equation (in fact, most theoretical papers do not number all equation). Numbering all equations will definitely makes the paper unreadable. We have included all proofs in Appendix. In fact, there are many theoretical papers do not explicitly refer proofs after theorems.

Dear Reviewer KdDJ,

Thank you again for your thoughtful participation and feedback in this discussion. We have carefully addressed your primary concern as well as the additional points you raised. We kindly request your review of these changes to confirm that they effectively address your concerns. We would also appreciate it if you could reflect this in your evaluation if your concerns have been addressed. If there are any remaining concerns preventing this, we would appreciate further clarification and are happy to continue addressing them.

Best,
Authors

Dear Reviewer KdDJ,

Thank you for your valuable contributions during this review process. We wish to kindly remind you that the extended discussion period will end in a few days.

Since we have addressed your remaining concerns about Figure 5 and notations above and included additional explanations in the appendix, we would be happy if you could read them and update your score or leave additional comments. We trust that you will re-evaluate our paper based on our additional clarifications.

Finally, we deeply appreciate your participation in this thorough discussion and look forward to hearing your final decision.

Best,
Authors

Dear Reviewer KdDJ,

We hope you had a wonderful Thanksgiving. Once again, we sincerely thank you for your valuable time and effort, and we fully understand your busy schedule. We noticed that we haven’t received feedback from you following our latest revision updates in which we added explanations for figure 5 and notations. In the meantime, we have addressed the concerns of Reviewer oeij, who has expressed a positive attitude and increased the score.

We would be truly grateful if you could let us know whether there are any additional questions or concerns we can address before the rebuttal deadline. Your feedback is invaluable and plays a crucial role in strengthening our work.

Thank you once again for your contribution to ICLR! Wishing you all the best with your current and future submissions.

Sincerely,
Authors

Weakness

W1: ...think it needs to be proof-read carefully and if possible use simpler notations. The loss functions should be defined so that the method can be understood better ...In multiple places, it is not clear how the gradient and Hessian are defined with respect to a function, e.g., is $H_{\hat{g}}$ (last line of page 4) the Hessian of the function w.r.t the parameters of $\hat{g}$ ?

The detailed loss function is shown in lines 106-107. Here, both $L_C$ and $L_Y$ are chosen as cross-entropy loss, which is commonly used in classification tasks.

The loss function may initially be non-convex. while the classical influence function is most straightforwardly applied to convex functions, its principles can be adapted to non-convex functions through regularization techniques. Moreover, the influence function has been successfully applied to modern neural networks including large language models (LLMs) and diffusion models [1-3].

$g$ and $f$ refer to model parameters, rather than functions. $\nabla_{\hat{g}}$ represents the derivative of the loss function with respect to the parameter of the concept predictor, denoted by $g$. Therefore, $\nabla_{\hat{g}}$ shares the same shape as $g$. The Hessian $H_{\hat{g}}$ is defined similarly.

[1]. Grosse, R., Bae, J., Anil, C., Elhage, N., Tamkin, A., Tajdini, A., ... & Bowman, S. R. (2023). Studying large language model generalization with influence functions. arXiv preprint arXiv:2308.03296.
[2]. Choe, S. K., Ahn, H., Bae, J., Zhao, K., Kang, M., Chung, Y., ... & Xing, E. (2024). What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions. arXiv preprint arXiv:2405.13954.
[3]. Kwon, Y., Wu, E., Wu, K., & Zou, J. (2023). Datainf: Efficiently estimating data influence in lora-tuned llms and diffusion models. arXiv preprint arXiv:2310.00902.

W2: The theorems need some explanations to convey the implications. The paper is currently like theorem after theorem and it may be hard for readers to see the connection. In general, the presentation of ideas could be improved.

While the paper includes 6 theorems, these theorems are systematically categorized into three distinct parts—data-level, concept-level, and concept-label-level, each representing a specific aspect of our model editing framework. In each part, two theorems are presented, with one focusing on the editing of the concept predictor and the other on the label predictor within that level.

This is also one of the advantages of our paper. We comprehensively consider all potential editing needs that CBM may face in practical applications, modeling them and deriving theorems to provide corresponding methods for editing models. The challenge of this paper lies in the fact that the model editing methods differ significantly at each level, requiring the use of different technical means to derive the model editing theorems. Therefore, although our paper contains many theorems and may appear complex, this is necessary to comprehensively cover the scenarios of CBM editing.

W3: In the experiments, it is not clear what is the CBM architecture and the number of model parameters? How well does the proposed method scale to a large number of parameters, given that Hessian matrices or their approximations are involved?

In the experiments, the CBM architecture is the same as [1]. And for the concept predictor, we use ResNet-18.

Our method has been designed to accommodate the majority of current CBMs, which typically do not involve very large-scale models, such as VLMs with millions of parameters. By utilizing EK-FAC to accelerate, our approach can effectively manage the computational requirements associated with these CBMs.

In [2-4], influence function has been scaled to LLM with billions of parameters, which fully validates the efficiency of EK-FAC in the inverse Hessian-vector product. As a result, CBMs, which usually have millions of parameters, are computationally feasible for EK-FAC.

[1]. Koh, P. W., Nguyen, T., Tang, Y. S., Mussmann, S., Pierson, E., Kim, B., & Liang, P. (2020, November). Concept bottleneck models. In International conference on machine learning (pp. 5338-5348). PMLR.
[2]. Choe, S. K., Ahn, H., Bae, J., Zhao, K., Kang, M., Chung, Y., ... & Xing, E. (2024). What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions. arXiv preprint arXiv:2405.13954.
[3]. Kwon, Y., Wu, E., Wu, K., & Zou, J. (2023). Datainf: Efficiently estimating data influence in lora-tuned llms and diffusion models. arXiv preprint arXiv:2310.00902.
[4]. Grosse, R., Bae, J., Anil, C., Elhage, N., Tamkin, A., Tajdini, A., ... & Bowman, S. R. (2023). Studying large language model generalization with influence functions. arXiv preprint arXiv:2308.03296.

W4: Limitations of the proposed work are not addressed.

Due to the space limitation, this part is included in the Appendix I in the revision.

Questions

Q1: How frequently are such editing updates expected to be made in a practical setting? After training the CBM, one may find some concept labeling errors and/or the need to remove some training samples or concepts. So applying the ECBM method once after training makes sense, but are there scenarios where the editing is done periodically? In situations where the distribution of the test data can change over time, it makes sense to adapt the CBM efficiently, instead of retraining.

Our method can perform periodic editing. However, as the number of edits is very large, our method becomes less accurate. Actually, this is unavoidable for all IF methods. However, our method's ability to handle multiple edits, when the edit number is relatively large, we conducted multiple editing experiments.

Firsly, we introduce noises under three levels. In concept level, we choose 10% of the concepts and flip these concept labels for a portion of the data. In data level, we choose 10% of the data and flip their labels. In concept-label level, we choose 10% of the total concepts and flip them. Then we conduct the following experiments.

In the concept level, we firstly remove 1% of the concepts, then retrain or use ECBM to edit and repeat. In the data level, we firstly remove 1% of the data, then retrain or use ECBM to edit. In the concept label level, we firstly remove one concept label from 1% of the data, then retrain or use ECBM to edit. Note that when remove the next 1% of the concepts, ECBM edit the model based on the last editing result.

The results are listed in Table A, B and C, where the first column refers to the portion of mislabeled concept/data/concept label left to be removed.

Table A: Multiple Editing under Concept Level.

Table B: Multiple Editing under Data Level.

Table C: Multiple Editing under Concept-label Level.

From the above three levels, we can find that with the mislabeled information removed, the retrained model achieves better performance in both accuracy and F1 score than the initial model. Furthermore, the performance of the ECBM-edited model is similar to that of the retrained model, even after 10 rounds editing, which demonstrates the ability of our ECBM method to handle multiple edits.

Dear Reviewer nBLD,

We are truly grateful for the time and effort you have dedicated to reviewing our work. We would like to respectfully inform you that two reviewers have already increased their scores: Reviewer KdDJ raised the score from 5 to 6, and Reviewer Oeij raised it from 3 to 5.

We would highly appreciate your review and feedback on the responses. Should you have any questions or concerns, we would be happy to discuss and address them.

Best,
Authors

Dear Reviewer nBLD,

Thank you again for your detailed and constructive review comments. We respectfully remind you that the discussion period will end in a few days. We have responded above to your concerns. We believe these address your concerns. We would appreciate it if you would take the time to read and comment on the responses.

Best, Authors

Dear Reviewer nBLD,

Thank you again for your constructive review comments. We have addressed your concern in the above. We respectfully request you to consider raising your rating score accordingly if your concerns are alleviated. Otherwise, we would be happy to hear the remaining concerns that prevent you from doing so and continue to discuss them.

Best,
Authors

Dear Reviewer nBLD

We hope you had a wonderful Thanksgiving. Once again, we sincerely thank you for your valuable time and effort, and we fully understand your busy schedule. We noticed that we haven’t received any feedback from you yet. In the meantime, we have addressed the concerns of the other two reviewers, who have expressed a positive attitude and increased their scores.

We would be truly grateful if you could let us know whether there are any additional questions or concerns we can address before the rebuttal deadline. Your feedback is invaluable and plays a crucial role in strengthening our work.

Thank you once again for your contribution to ICLR! Wishing you all the best with your current and future submissions.

Sincerely,
The Authors

Dear Reviewer nBLD,

Thank you for your valuable contributions to ICLR. We kindly remind you that the extended discussion period will end in a few days.

Since we have addressed the concerns you raised, we kindly request that you review our clarifications and consider providing additional comments or updating your score. We trust that you, as the reviewer, will re-evaluate our paper based on our clarifications.

Thank you for your valuable contributions, and we kindly await your thoughtful final decision.

Best,
Authors

Dear Reviewer nBLD,

I hope this message finds you well. I am writing to follow up as today marks the final day for providing feedback on our rebuttal discussions. Your insights are invaluable in addressing any remaining concerns and ensuring the best possible version of our submission.

If there are any points in the rebuttal that require further clarification or discussion, I would be more than happy to address them promptly. I truly appreciate the time and effort you dedicate to this review process. Otherwise, we respectfully request you to consider raising your rating score accordingly if your concerns are alleviated.

Thank you very much for your consideration, and I look forward to your feedback.

Best regards,
Authors

Thank you for your responses and for running additional experiments to address the reviews. I apologize for responding late in the process.

Most of my questions have been addressed, but I find that the revised paper is still lacking in clarity and I think a significant rewrite will help address this. Similar concerns have been raised by Reviewer oeij as well. Therefore, I will maintain my score of 5.

I also think that the contributions of the paper are valuable and it addresses and important problem. Therefore, I am not opposed to acceptance, if supported by the other reviewers.