Faithful Vision-Language Interpretation via Concept Bottleneck Models

Dear Reviewer W5Db,

We would like to express our sincere gratitude for taking the time to review our paper and providing valuable feedback. We have carefully considered your comments and have made revisions to address each of the issues raised. Please find our responses to your specific points below:

Response to W1:

Unlike the original concept model, there is no ground truth concept annotated by experts. So it is hard to evaluate the explainability. The same issue also appears in Label-free CBM so the metric of explainability is out of the scope of this paper. In our paper, we verify the effectiveness of the output explanatory results by outputting a large number of visual samples.

Response to W2:

We kindly disagree with your point. Actually, our objective function (2) heavily depends on the Label-Free CBM: (1) We can easily see that $y(x, \tilde{c})$ and $y(x, c)$ depend on the weight matrix $W_F$ of the fully connected layer of a trained Label-Free CBM. (2) Moreover, $\mathcal{L}_{k} (\tilde{g}(x), g(x))$, which is a surrogate loss of $V_k$, depends on $W_c$, which is the weight matrix of the concept layer in Label-Free CBM. We can also see these from Definition 2. Thus, FVLC heavily relies on the performance of its corresponding Label-Free CBM.

Response to W3:

In terms of accuracy on image classification tasks, we have compared with PCBM. However, in the task of evaluating interpretability, although these are concept-based models, their concept outputs are different, so it is difficult to make a comparison. In addition, for recently developed unsupervised CBM models (LCBM and PCBM), it is difficult to quantify the effectiveness of their interpretability and the "accuracy" of the output concept. The goal of our work is to make unsupervised CBM models more faithful.

Response to W4:

Sorry for the confusion, yes, you are right all the extracted concepts are input-dependent. To address your concern, in the revised version, we rewrote Definition 2 and our optimization procedure in the revised version. Moreover, we give more details on the optimization procedure in Appendix B. About intuitive properties, in the revised version, we add one additional section Appendix A on more intuition of our Definition 2 and its four properties.

About notation $\tilde{c}$, we have modified it in the revised version.

Response to Remark:

Sorry for the confusion, in fact, $D$ should be a divergence or probability distance. In this case, our claim will be correct. We have changed it in the revised version. Yes, different losses may lead to different performances. In fact, in our experiments, we consider $D$ as the KL divergence for ease of optimization.

I thank the authors for going through my review and for the effort in improving the paper.

Regarding my review, I want to comment on some points:

1. Interpretability of Language-based CBMs As I understand from your reply, measures of concept interpretability are not adopted in Language-based CBMs. This can be a serious limitation of these CBMs, I think guaranteeing faithfulness cannot be enough without interpretability. This should be discussed in a limitations section

2. Using the LFCBM as a reference Thank you for the clarification and I do not want to depreciate the method you proposed. I understand your point but still, if the FVLC improves the existing LFCBM but takes it as a reference, would it inherit limitations of LFCBM (e.g. if some predictions are wrong for the LFCBM they will be wrong also in the FVLC)?

3. Comparison with PCBMs Thank you for pointing to the comparison, I will adjust my confidence score.

4. I would not call PCBMs, LABO, and LFCBs unsupervised methods (like Self-explainable Neural Networks which are unsupervised), rather weakly supervised or multimodal.

Remark If you use the KL divergence you can miss the scale due to the softmax operation for obtaining $p(y \mid c)$. MSE or l1 would be better, maybe.

(1/2)

Dear Reviewer UywT,

We would like to express our sincere gratitude for taking the time to review our paper and providing valuable feedback. We have carefully considered your comments and have made revisions to address each of the issues raised. Please find our responses to your specific points below:

Response to W1:

In the revised versions, to make the paper more readable, first, we added more details to each figure to provide better illustration (such as Figure 2); secondly, we highlighted the results of our method in all tables; third, we added more details on the baseline methods (Section D in Appendix); finally, we also add more intuition of our definition of FVLC, and more details on the definition of FVLC (Section A in Appendix). You can also see our response to all reviewers.

We hope these changes will make you satisfied. If not, please feel free to reply to us.

Response to W2:

Thanks, we have added these references to the related work section in the revised version.

Response to W3:

Generally speaking, our faithful concept is more stable on prediction and interpretability against different perturbations than the original concept in Label-free CBM, while it also keeps the prediction performance and interpretability of the original concept. To give a better illustration, in Appendix A of the revised version, we provided more details on the intuition of our definition 2. Next, we will show more of the difference between faithful and original concepts in definition 1.

(1) The first condition ensures that the faithful concept keeps almost the same interpretability as in the original concept for each input. This is modeled via the top-k indices overlap between these two vectors is large.

(2) The second condition ensures that our faithful concept is stable for explainability w.r.t. different perturbations, especially input perturbation and word perturbation. This is significantly different from the original concept. As illustrated in Figure 1, the interpretability of the original concept is very unstable.

(3) The third condition ensures that the faithful concept keeps almost the same prediction output as in the original concept for each input. This is modeled via the distance or divergence between the prediction distributions of the faithful concept and the original concept.

(4) The last condition guarantees that our faithful concept is stable for the prediction w.r.t. different perturbations. This is also motivated by the fact that the original concept may have wrong predictions with perturbations.

Response to W4:

We have corrected it in section 3.

Response to W5:

In the revised version, we have added more details on all Figures including Figure 2.

Response to W6:

$D$ should be a divergence distance, which is defined in Definition 2. In our experiments, we use KL divergence. For the role of two constraints on $\delta$ and $\rho$, please refer to Stability and Prediction on Page 5. In the revised version, we have added more details for our optimization loss. Moreover, we polished Appendix Section B with details on the optimization procedure for the relaxed problem.

Response to W7:

We have added some experiments on the HAM10000 dataset to improve the reliability of our model, as detailed in Appendix G, Table 12 and Figure 9 in the revised version. We hope these changes will make you satisfied. If not, please feel free to reply to us.

Response to W8:

(1) For more details of the experiment, such as baseline, etc., we have made additional supplements, which are detailed in Table 5 of Appendix D. We hope these changes will make you satisfied. If not, please feel free to reply to us.

(2) We conducted a set of ablation experiments to compare the performance, and we did not seem to find that our optimization had a significant impact on the experimental image classification performance, but it could effectively improve the stability of the output concept (see in Table 2 and Table 3). Due to time constraints, we only conducted supplementary ablation experiments on the CIFAR10 dataset (WP1(10%)+WP2+IP - FVLC).

(3) Although they are both concept based models, their frameworks are very different, as are the output concepts and the forms of concept weights. It is meaningless to discuss the anti-interference ability of the concept that interpretability outputs differ between models. So we only compared the performance of the model, and we also compared the performance of P-CBM, LCBM and our model.

(2/2)

(3) It is notable that it is impossible to compare our method with previous methods with annotated concepts: (1) Our concept set is generated by LLM with previous work needs to use concept sets given by experts. Since the concept sets are different, they are incomparable. (2) It is notable that the main motivation of our methods is label-free CBM so there is no ground truth of concepts. And it is meaningless to compare with previous methods.

(4) We repeated the last group of experiments in Table 1 for 5 times, and calculated the mean and variance of the output data in this group as shown below. The experimental results show that the variances of our experimental data is very small. Because of time, we did not repeat all the experiments to calculate the variances. We hope these changes will be satisfactory to you. If not, please feel free to reply us with more experiments and explanations.

Response to W9:

In the revised version, we have highlighted all the results of our method in grey color in all tables. Please check the revision.

Dear Reviewer UywT,

We would like to express our gratitude for your thorough review and the insightful comments you provided.

We have carefully addressed each of your comments and suggestions in response and revised version we submitted earlier. We believe that the revisions we made have significantly strengthened the paper and addressed the concerns you raised. If there are any remaining questions or concerns, we would be more than happy to response.

Additionally, we would like to take this opportunity to request your consideration for a potential increase in the score of our paper. We believe that the revisions we made, as outlined in the rebuttal, have substantially improved the quality and contribution of our work. We hope that you will take these revisions into account and consider adjusting the score accordingly. We are looking forward to your timely feedback and would greatly appreciate you consider raising the scores.

Thanks,

Authors

Dear Reviewer 6N2M,

We sincerely appreciate the time you took to review our paper and provide valuable feedback. We have carefully considered your comments and made revisions to address each issue raised. Please find our responses to your specific points below:

Response to W1: Briefly speaking, the main idea and our faithful concept can be directly extended to other forms of data such as text since they do not rely on the specific form of images. However, we are not sure about the performance of other data and this could left for future work. In fact, we think this should not be a reason that our paper will be rejected as to the best of our knowledge, most of the previous work on concept bottleneck models only considers image data and there is less study on other data types [1,2,3]. But it is certain that our method can migrate data to the remaining modes. Because we are based on the output of the feature layer for subsequent operations. [1] Yang, Yue, et al. "Language in a bottle: Language model guided concept bottlenecks for interpretable image classification." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023. [2] Chauhan, Kushal, et al. "Interactive concept bottleneck models." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 5. 2023. [3] Yuksekgonul, Mert, Maggie Wang, and James Zou. "Post-hoc concept bottleneck models." arXiv preprint arXiv:2205.15480 (2022).

Response to W2: Thanks for your question. There are mainly two reasons we do not use invariant metrics: (1) Note that unlike the previous paper (such as the one you mentioned) which only considers adding noises to image inputs as the perturbation, in our experiments, we consider (a combination of) three different perturbations. It is hard to normalize these three perturbations on the same scale, such as the word perturbation. (2) Note that in our experiments, due to different combinations of perturbations, we do not intend to discuss the change of stability w.r.t. perturbation scale. Our main goal is to show that under the same scale of perturbation, our FVLC is more stable than baselines (Table 2). Thus, there is no need to consider the invariant metrics.

Response to W3: Thanks for your suggestion. We will make the text in Figure 3 larger in the final version if additional pages are allowed. Moreover, in the revised version, we enlarge the fonts in Figure 3, see Figure 5-8 in Appendix for details. In the revised version, we also added more details to all figures (including Figure 2) in our paper.

Dear Reviewer Ak8W,

We would like to express our sincere gratitude for taking the time to review our paper and providing valuable feedback. We have carefully considered your comments and have made revisions to address each of the issues raised. Please find our responses to your specific points below:

Response to W1:

In the revised version, we have added more details to all figures (including Figure 2) in our paper.

Response to W2:

In the revised version, we have added a notation Table 4 in Appendix (page 13). We will move it to the main context if additional pages are allowed.

Response to Q1:

Our text encoder and image encoder make up CLIP. The text encoder of CLIP is used to convert natural language text into vector representations. It is based on the Transformer model architecture, which learns to embed text into a high-dimensional vector space, where text with similar semantics are closer in the vector space. The text encoder transforms input text sequences into fixed-dimensional vector representations, capturing the semantic and contextual information of the text. The image encoder of CLIP is used to convert images into vector representations. It employs a convolutional neural network (CNN) as the backbone model to extract image feature representations. These feature representations are mapped to a fixed-dimensional vector space for comparison with the vectors from the text encoder. By using the pre-trained CLIP text encoder and image encoder, our model is capable of understanding both images and text (concepts). By encoding images and text into the same vector space, CLIP quantifies the semantic similarity between images and text, enabling joint encoding and understanding across modalities. CLIP leverages large-scale pre-training datasets, allowing it to learn rich semantic representations. The advantage of pre-training is the ability to learn general-purpose feature representations from large-scale data. It is important to emphasize that we did not train the image encoder and text encoder ourselves. We use the encoder to obtain the image-concept matrix to complete the concept-neuron (feature) mapping. In fact, this is the process that affects the interpretability of the model, and whether the choice of encoder affects accuracy is something we have not discussed. Because we couldn't find another image-text encoder model that was pre-trained on large-scale datasets for comparison.

Response to Q2:

The standard model represents an image classification model, which extracts image features through the same backbone as our FVLC model and then connects a fully connected layer to complete the image classification task. In fact, this is a common practice in the field of CBM. After adding the bottleneck layer, the accuracy of the image classification task will be affected due to the intervention of the concept task. We have added all baseline settings in the revised version (Section D.3 in Appendix - page 16).