Enhanced Face Recognition using Intra-class Incoherence Constraint

Thank you for expressing your appreciation for our work and providing your insightful suggestions.

Regarding Q.1, we acknowledge the limitation mentioned in our paper that our method has only been implemented on face recognition tasks. We are actively conducting further experiments in more challenging classification tasks to explore the potential application of our method beyond face recognition.

Regarding Q2, we decompose the learned features into original features and innovation. We have compared the performance of the learned innovation across different models, as shown in Table 9 in the appendix of our paper.

As for the weakness you mentioned, it is challenging to achieve significant accuracy improvements in face recognition, given the already high accuracy of existing benchmarks. As pointed out by Reviewer V2zT, “Existing face recognition benchmarks already have high accuracy, so the improvement doesn't look too significant.” We are actively exploring how to apply our approach in other domains.

Thank you for your valuable insights.

For Weakness 1, we specify the computation as follows:

$L_{dissim}= \frac{<emb,ref\\_emb>}{||emb||_2\cdot||ref\\_emb||_2}$

Here, $<a,b>$ represents the inner product of vectors a and b, and $||\cdot||2$ denotes the L2 norm. The reason for this design is that as the cosine similarity of the vectors decreases, $L_{dissim}$ becomes smaller. This term is to make the two embeddings as dissimilar as possible, which intends to introduce innovation. In reality, the exact method for achieving the optimal solution is unknown. We aim to utilize the aforementioned dissimilarity measure between $emb$ and $ref\\_emb$ to promote learning better features. However, we acknowledge that there may be alternative approaches to describe this relationship more effectively.

For Weakness 2, thank you for sharing your novel idea and we conduct some experiments following your idea（denoted as "ArcFace+IIC+IIC"）. The table shows the performance of different methods on various datasets.

Based on the results, it seems that the proposed method does not provide significant improvements. One possible reason for this could be that the optimal direction may be the unknown global optimum but our optimization is for an existing known feature. The proposed IIC method can improve the existing feature directions so that they become closer to local optima only. The use of this method multiple times may cause the feature direction to zigzag around the local optimal direction. As a result, the improvement could be limited.

For Weakness 3, we appreciate your perspective on analyzing face recognition from the view of feature distillation and representation learning. However, most of the settings in state-of-the-art (SOTA) methods for distillation are different from ours. While our teacher model and student model share the same structure, this setting differs from the typical approach employed in the SOTA methods. Most SOTA methods aim to approximate the performance of the original model by reducing the model parameters, which often leads to a loss in accuracy.

In contrast, our initial intention in designing the loss function was not solely focused on achieving distillation (i.e., reducing model parameters to closely match the performance of the original model). Instead, our goal is to learn new information and enhance model accuracy by leveraging the dissimilarity of features. Furthermore, we have compared our method with SOTA FR approaches and achieved better performance.

Thank you very much for providing valuable feedback. For your questions, we shall address each of them separately.

For Q.1, the feature vectors in Fig.1 and Fig.2 are used to illustrate the differences between the innovation and other feature vectors, as well as to demonstrate the possibility of synthesizing better features. As you mentioned, the high-dimensional space is more complex and difficult for visualization. Figs.1 and 2 are included to assist in showing the potential relationships among the features, which subsequently motivates the development of a new adaptive learning method based on IIC in this work to learn better features in high-dimensional space.

For Q.2, our intention here is to state that innovation contains useful information for improving face recognition accuracy that was not yet captured by the inferior model. Innovation being orthogonal to the feature vector from the inferior model is consistent with this statement. We are going to use the term orthogonality, instead of independence, in the revised manuscript for clarity.

For Q.3, thank you for your careful reading. We will make further improvements, particularly in the choice of terminology, and revise the manuscript carefully.

For Q.4, we acknowledge that a and b being on different sides of d in fact implies the more general case where a and b are on different sides of the projection of d on the hyperplane specified by a and b. Under this scenario, the arguments presented in the manuscript remain valid. In other words, changing the modulus of the innovation may still be necessary to synthesize feature vectors close to the projection of the optimal feature vector d. We are going to point this out in the revised manuscript.

For Q.5, Eq. 3 and Eq. 4 are both total loss functions but they represent two different formulations. On the right hand side of Eq. 3, $L_{{dissim}_i}$ represents the dissimilarity between the outputs of the $i$-th layer of the teacher and student networks, where $i$ takes a value within [1, N]. In Eq. 4, we utilize all the available N+1 dissimilarities (N hidden layers + final output layer). As such, Eq. 3 can be considered as a special case of Eq. 4. We compare the performance under different loss functions in Table 8 in the appendix of our paper. In the experiments, we chose to include the dissimilarity between the features in the final layer only.

Furthermore, we would like to supplement some explanations regarding the concerns raised in your Weaknesses.

For Weakness 1, we use the 2D space to describe the feature space solely for the purpose of convenience in analysis and visualization. Analyzing and synthesizing features in a high-dimensional space is a non-trivial task. It is precisely because we conduct thorough experiments and analysis in 2-D space that we come up with the idea of using innovation to improve model accuracy. Finally, we propose an adaptive learning method (i.e., IIC) in a high-dimensional space.

For Weakness 2, we are trying to explore the theoretical proof for the suggested improvements. However, the fact that a superior model can be improved does not necessarily imply insufficient training but could also be due to the corresponding algorithm not effectively capturing more informative features. The idea of combining multiple inferior models is interesting, but how to properly integrate these features is a challenging task. This is because multiple models have different feature vectors, while the optimal vector is unknown. Nevertheless, we have made some attempts, and the experimental results are shown in the table below.

It seems that the method did not achieve significant improvements. One possible reason for this could be that the optimal direction is unknown and may represent a global optimum. However, our optimization is based on an existing known feature. Compared to the global optimal direction, the existing feature direction may be near the local optimal. The proposed IIC method can improve the existing feature directions to be closer to local optima. The use of multiple models may cause the feature direction to oscillate back and forth in the local optimal direction. As a result, the improvement is limited.

Authors, thank you for your careful responses to my review comments and questions and proposed revisions to your manuscript. Based on your response and other reviews, I have slightly increased my rating of your manuscript.

Thank you very much for your recognition of our work and for providing us with promising suggestions. As stated in the limitations section in the paper, our method only proves to be effective in face recognition tasks, and its improvements for other classification tasks remain unknown. We are investigating its effectiveness in more challenging classification tasks to explore the potential application of our method beyond face recognition. We appreciate your valuable feedback and will continue to explore and expand the scope of our work.