Paper: Channel Vision Transformers: An Image Is Worth 1 x 16 x 16 Words (ICLR-2024)

Reviewer comment (Novelty):
The novelty of the work is limited, as it seems that the channel splitting proposed in this paper is similar to a multi-modal approach to multi-channel data that has been explored earlier (albeit not with images). Also, HCS can be viewed as a modification of input channel dropout that has also been known before.

Author response:
+ **Novelty:** We wish to emphasize the novel aspects of our work in comparison to the existing literature:
  + **Robustness of ViT to Missing Channels:** Prior research has explored various robustness measures for ViT models, such as resilience to spurious correlations and adversarial attacks. Our work pioneers the investigation into the channel robustness of ViTs, addressing realistic scenarios in multi-channel imaging applications where sensor discrepancies between training and testing are common.
  + **ChannelViT for modeling multi-channel images:** ChannelViT is designed to create patch tokens from each channel, enabling effective cross-channel and positional reasoning. Unlike the main literature, we employ weight sharing across channels and leverage learnable channel embeddings to encapsulate channel-specific information. In Appendix B, we present additional comparisons with recent ViT variants for multi-channel imaging, where our simple ChannelViT demonstrates significant performance enhancements.
  + **HCS as a Training Regularizer:** HCS not only improves training efficiency but also substantially bolsters model robustness when evaluated on varying channel combinations. It is true that it is largely inspired by channel dropout, and we have delineated the similarities and distinctions between HCS and channel dropout within the paper. Figure 3 showcases its superior efficacy, even when combined with a standard ViT.

Reviewer comment (Evaluation):
The gains from the proposed approach are limited to the data with many channels (e.g., some microscopy images) and seem less reasonable for other types. At the same time, the processing with this new approach takes significantly more time.

Author response:
+ **Limited to Data with Multiple Channels:** ChannelViT is indeed tailored for modeling cross-channel interactions, a critical yet previously neglected issue in multi-channel imaging. As shown in Table 2, the advantages of ChannelViT amplify with the diversity of input sources. In the paper we have also conducted an exhaustive evaluation of ChannelViT on conventional imaging datasets:
  + On ImageNet, ChannelViT outperforms a standard ViT even when both are trained and evaluated on all channels. ChannelViT's robustness is evident when tested with missing channels.
  + On Camelyon17-WILDS, ChannelViT's parameter sharing across channels results in enhanced generalization to new hospitals compared to regular ViT.
+ **Computational Cost:**
  + A new section (Section 4.2) has been added to the manuscript to address computational efficiency, with an extensive runtime analysis in Table 8. Although training ChannelViT requires approximately 3.64 times more resources, the inference time is merely 1.6 times longer than that of ViT. We anticipate future integration of ChannelViT with more efficient attention mechanisms, such as Linformer or LongNet, will lead to further efficiency gains.
  + It is also noteworthy that the additional training time is counterbalanced by eliminating the need to train separate expert models for each channel combination. ChannelViT's performance at processing inputs with varying channels translates to significant practical savings.

Reviewer comment (Writing):
I suggest revisiting the title. The inspiration for the title used in this paper has clearly come from the ViT’s “An image is worth 16x16 words”. But in the case of ViT, it was about patches of size 16x16 across all channels, i.e., "Cx16x16", while the proposed approach uses "1x16x16" "words", as the image is split into channels as well.

Author response:
+ **Title Revision:** We really appreciate your careful consideration of the title's interpretation. The original ViT paper examined patch sizes of both 16x16 and 14x14, with the latter yielding superior performance. Given their use of a 224x224 training resolution, this equates to 16x16 patch tokens (224/14=16) for each input image. In our work, as we create image patches for each input channel, this results in Cx more patch tokens (words). We acknowledge the potential for confusion and are considering updating the title for better clarity.

Reviewer comment (Writing):
Please clarify why the proposed channel sampling is “hierarchical.”

Author response:
+ **Hierarchical Channel Sampling:** In HCS, we first determine the number of channels to utilize (m). Subsequently, based on m, we select the specific channel combination. The term "hierarchical" is derived from the two-stage nature of the sampling process.

Reviewer comment (Writing):
It would be beneficial to review the notation used in the formulae, e.g. use AB instead of A\cdotB for matrix multiplication.

Author response:
+ We have amended the notation in the formula as per your suggestion—thank you for bringing this to our attention.

Reviewer comment (Experiments):
Limited baselines reported. The paper only considers ViTs as a baseline, which is a natural comparison given that the proposed method is an extension of this architecture. However, comparison to other architectures, especially CNNs to solve the multi-channel problems should be reported. This is specially important to appreciate the relative performance compared to other solutions tested before in multi-channel images.

Author response:
+ **Baselines:** We are grateful for the recommendation to include additional baselines. In response, we have expanded our paper to incorporate the following new results, detailed in Appendix B:
  + **CNNs (Appendix B.3):** We conducted experiments with ResNet-50 and ResNet-152 on the JUMP-CP dataset. The outcomes are presented in Table 7. Our analysis reveals that both ResNet models exhibit performance comparable to ViT-S/8, with ResNet-152 slightly outperforming ResNet-50. However, when testing on different channel combinations, the ResNets' performance diminishes. Attempts to integrate ResNet with HCS during training resulted in instability, culminating in a final 8-channel accuracy of approximately 5%. Finally, the performance disparity between the new ResNet baselines and ChannelViT is consistent and substantial.
  + **MultiViT (Appendix B.1):** Hussein et al. recently proposed the Multi-Channel ViT architecture for multi-channel EEG data analysis (https://pubmed.ncbi.nlm.nih.gov/35884859/). Their approach involves learning individual ViTs for each channel and fusing the outputs of their final layers for classification. Unlike MultiViTs, ChannelViT models cross-channel dependencies directly from the very first layer. Our comparative analysis of MultiViT, ViT, and ChannelViT, presented in Table 5, demonstrates that MultiViT, when trained without HCS, is more robust than ViT. Nonetheless, it consistently underperforms compared to ChannelViT. Incorporating HCS with MultiViT adversely affects its performance.
  + **Fully Attentional Networks (Appendix B.2):** Zhou et al. introduced Fully Attentional Networks (FANs) that enhance a standard transformer encoder with channel-wise attention (arxiv.org/abs/2204.12451). Contrary to FANs, ChannelViT executes cross-channel and cross-location attention jointly, allowing each patch token to attend to different channels at distinct locations. FANs restrict attention to different channels within the same location. Utilizing the official implementation, we reported FANs' performance in Table 6. Training FANs without HCS significantly improves performance over a standard ViT (52.06 vs. 65.42). However, ChannelViT still slightly outperforms FANs (66.22 vs. 65.42). When trained with HCS, ChannelViT's performance markedly increases to 68.09, while FANs experience a significant performance decline (from 65.42 to 20.31).

Reviewer comment (Evaluation):
Computational cost increases quadratically with the number of channels. This problem is not addressed or commented in the main manuscript. According to the reported times in the appendix, the training cost increases linearly with the number of channels. The computational cost should be analyzed and discussed in more detail. While the solution seems effective, it can be prohibitive in practice.

Author response:
+ **Computational Cost:**
  + We have incorporated a new section (Section 4.2) to discuss computational efficiency, including a more comprehensive runtime analysis in Table 8. While training ChannelViT is approximately 3.64 times more resource-intensive, the inference time is only 1.6 times longer than that of ViT. We anticipate that integrating ChannelViT with more efficient attention mechanisms, such as Linformer or LongNet, could yield further improvements in efficiency.
  + It is also noteworthy that the additional training time is counterbalanced by eliminating the need to train separate expert models for each channel combination. ChannelViT's performance at processing inputs with varying channels translates to significant practical savings.

Reviewer comment (Novelty):
In a similar note as the first point, other adaptations of ViTs have been reported for video analysis and 3D imaging, which also increase the image dimensions in a new axis (different than channels). Do any of these existing adaptations apply for channels?

Author response:
+ **Baselines:** We are grateful for the recommendation to include additional baselines. In response, we have expanded our paper to incorporate the following new results, detailed in Appendix B:
  + **Other baselines:** We acknowledge the reviewer's suggestions regarding other ViT variants for video analysis and 3D imaging. We argue that the data distribution in multi-channel imaging applications is fundamentally distinct from that of video or 3D data. Specifically, the images we considered are centered around the same object but captured with different sensors. We believe that while ChannelViT could potentially be adapted for sensor fusion beyond multi-channel imaging, such applications are beyond the scope of our current work.

Reviewer comment (Evaluation):
The prediction of treatment in the JUMP-CP dataset is not necessarily a biologically relevant task. Prior literature makes the distinction that this is a pretext task for learning representations (weakly supervised learning), and not the main goal of analyzing these images. This clarification should be mentioned and prior work should be cited. Ideally, a biologically relevant task should be reported to ensure that classification performance in this pretext task is not dominated by confounders or spurious correlations. If this is not possible, an alternative test or explanation should be provided.

Author response:
+ **Task of Treatment Classification:** In line with the initial release of the JUMP-CP benchmark (https://www.biorxiv.org/content/10.1101/2022.01.05.475090v3), we have framed the task of perturbation detection (or treatment classification) as a means to assess representation models for cell imaging. We concur that the primary objective of cell image analysis extends beyond perturbation prediction to encompass other biologically pertinent tasks. We have clarified this point in our manuscript (Page 5, JUMP-CP section) and welcome the opportunity to reference any relevant prior work that you may suggest.

Reviewer comment (Evaluation):
Does figure 6 include error bars? Can you clarify how these were obtained?

Author response:
+ **Standard Deviation and Error Bars:**
  + The results presented in Table 3 and Figure 5 were derived from multiple runs using different random seeds for both the partitions and the model initializations. We have now included a descriptive text to clarify these results.
  + Table 14 details the standard deviations across different channel combinations. Additionally, Table 15 provides the mean and standard deviation of the improvements observed for each channel combination with ChannelViT over ViT.

Reviewer comment (Experiments):
Can the authors report additional baselines and compare to other state-of-the-art methods in the same datasets that they evaluate? This could clarify the achievements of the method in context to prior art in these domains.

Author response:
+ **Baselines:** We are grateful for the recommendation to include additional baselines. In response, we have expanded our paper to incorporate the following new results, detailed in Appendix B:
  + **CNNs (Appendix B.3):** We conducted experiments with ResNet-50 and ResNet-152 on the JUMP-CP dataset. The outcomes are presented in Table 7. Our analysis reveals that both ResNet models exhibit performance comparable to ViT-S/8, with ResNet-152 slightly outperforming ResNet-50. However, when testing on different channel combinations, the ResNets' performance diminishes. Attempts to integrate ResNet with HCS during training resulted in instability, culminating in a final 8-channel accuracy of approximately 5%. Finally, the performance disparity between the new ResNet baselines and ChannelViT is consistent and substantial.
  + **MultiViT (Appendix B.1):** Hussein et al. recently proposed the Multi-Channel ViT architecture for multi-channel EEG data analysis (https://pubmed.ncbi.nlm.nih.gov/35884859/). Their approach involves learning individual ViTs for each channel and fusing the outputs of their final layers for classification. Unlike MultiViTs, ChannelViT models cross-channel dependencies directly from the very first layer. Our comparative analysis of MultiViT, ViT, and ChannelViT, presented in Table 5, demonstrates that MultiViT, when trained without HCS, is more robust than ViT. Nonetheless, it consistently underperforms compared to ChannelViT. Incorporating HCS with MultiViT adversely affects its performance.
  + **Fully Attentional Networks (Appendix B.2):** Zhou et al. introduced Fully Attentional Networks (FANs) that enhance a standard transformer encoder with channel-wise attention (arxiv.org/abs/2204.12451). Contrary to FANs, ChannelViT executes cross-channel and cross-location attention jointly, allowing each patch token to attend to different channels at distinct locations. FANs restrict attention to different channels within the same location. Utilizing the official implementation, we reported FANs' performance in Table 6. Training FANs without HCS significantly improves performance over a standard ViT (52.06 vs. 65.42). However, ChannelViT still slightly outperforms FANs (66.22 vs. 65.42). When trained with HCS, ChannelViT's performance markedly increases to 68.09, while FANs experience a significant performance decline (from 65.42 to 20.31).

Reviewer comment (Evaluation):
Can the authors add computational analysis and comparisons to other methods for training / testing time of the methods? Even if the cost is a limitation, reporting and evaluating this aspect transparently can enhance the understanding of how useful this method can be in practice.

Author response:
+ **Computational Cost:**
  + We have incorporated a new section (Section 4.2) to discuss computational efficiency, including a more comprehensive runtime analysis in Table 8. While training ChannelViT is approximately 3.64 times more resource-intensive, the inference time is only 1.6 times longer than that of ViT. We anticipate that integrating ChannelViT with more efficient attention mechanisms, such as Linformer or LongNet, could yield further improvements in efficiency.
  + It is also noteworthy that the additional training time is counterbalanced by eliminating the need to train separate expert models for each channel combination. ChannelViT's performance at processing inputs with varying channels translates to significant practical savings.

Reviewer comment (Experiments):
While the main application of ChannelViT is in targeting problems such as those in multiplexed imaging due to the challenge of generalizing encoders across datasets that would have the same set of probes, only one dataset explored in this work is related to multiplexed imaging. Experimentation on ImageNet, C17-WILDS, and others are informative and appreciated, are not as relevant to the ultimate application that ChannelViT serves. Though C17-WILDS is microscopy, hematoxylin and eosin (H&E) pathology is not a domain where only the hematoxylin or eosin stains are performed. Rather, it would be more interesting to explore this problem on other relevant multiplexed imaging benchmarks such as RXRX1 [1], RXRX1-WILDS [2], TissueNet [3], and others [4-6]. To this end, it would also be useful to discuss and compare ChannelViT in context with label-free approaches, which suggest channel synthesis as a paradigm for addressing missing channels.

Author response:
Thank you for the detailed review and the constructive suggestions, which we have found to be very helpful.
+ **Scope of ChannelViT:** We acknowledge the references you provided, which pertain to cell imaging. It is important to clarify that ChannelViT is designed as a versatile image representation backbone suitable for a broad range of multi-channel imaging applications, not exclusively for cell imaging. To demonstrate this, we have selected four diverse datasets for a thorough evaluation of ChannelViT:
  + **ImageNet:** As a foundational image representation benchmark, ImageNet is critical for assessing ChannelViT's performance in standard computer vision tasks. Our results on ImageNet demonstrate that ChannelViT not only surpasses the standard ViT in full-channel scenarios by enabling cross-channel reasoning but also exhibits superior robustness when channels are missing.
  + **JUMP-CP:** The JUMP-CP benchmark, released by the Broad Institute, represents the largest public cell imaging dataset available at the time of our submission. While the mentioned Rxrx datasets and TissueNet are interesting, our comprehensive analysis on JUMP-CP covers similar ground. Also we were unable to access TissueNet via their link in the paper (https://netbio.bgu.ac.il/tissuenet3).
  + **So2Sat:** Satellite imaging, with its multi-channel, multi-resolution data, is an ideal application for ChannelViT. Our empirical results confirm that ChannelViT outperforms ViT across various data splits and channel availability.
  + **Camelyon17-WILDS:** Although Camelyon17 features fewer channels compared to JUMP-CP and So2Sat, the challenge of cross-hospital generalization remains compelling. ChannelViT's robust performance across varying staining color distributions from different hospitals is noteworthy. Due to space constraints, we have included this application in our appendix.
  + Finally, we again appreciate the cell imaging references and will consider them for future work for life science journals. We hope this clarification addresses your concern regarding the scope of our paper.

Reviewer comment (Experiments):
As a drop-in replacement for ViT in conventional natural image classification or medical imaging tasks, one concern I have (raised in the work) is lack of experimentation on model scale. The title of this work, "Channel Vision Transformers: An Image Is Worth C x 16 x 16 Words", is similar to a title of a related seminal work in ViTs [7], but does not evaluate and demonstrates the scale of Channel ViTs in the same manner in demonstrating its universality of overtaking current state-of-the-art architectures. As ViT-Small architectures are not the most commonly-used model size for ViT, it would be informative to explore Channel ViTs at greater scale (such as ViT-B and ViT-L). An additional limitation connected to this is the efficiency of learning channel embedings, which may have been the reason for not developing larger ViT models. As shown in the DINO experimentation, even with HCS, training is approximately 3.64x more expensive than its baseline comparison, which may limit its usability.

Author response:
+ **Model Scale:** We have expanded our results to include larger models: ViT-Base, ViT-Large, ChannelViT-Base, and ChannelViT-Large, detailed in Appendix C.7. Unsurprisingly, larger backbones result in superior performance. Our findings also reveal that despite the increased parameter count in ViT-Base and ViT-Large, ChannelViT maintains a significant performance lead. For instance, ViT-Large/16, with 13.9x more parameters, still lags behind ChannelViT-Small/16 (57.96 vs. 68.09), underscoring the importance of explicitly modeling cross channel interactions. We believe this addition should also address your concern regarding the efficiency of learning channel embeddings in larger ViT models.
+ **Time Efficiency:**
  + We have added a new paragraph in Section 4.2 to discuss time efficiency, with a comprehensive runtime analysis presented in Table 8. Training ChannelViT is indeed 3.64x more resource-intensive, but the inference time is only 1.6x longer than ViT. We anticipate further efficiency gains by integrating ChannelViT with more efficient attention mechanisms like Linformer or LongNet.
  + It is also important to highlight that the additional training time is offset by the avoidance of training separate expert models for each channel combination. ChannelViT's performance in handling inputs with varying channels results in considerable savings in practical applications.

Reviewer comment (Experiments):
Discussion and benchmark evaluation against label-free approaches in multiplex imaging.

Author response:
Thank you for the detailed review and the constructive suggestions, which we have found to be very helpful.
+ **Scope of ChannelViT:** We acknowledge the references you provided, which pertain to cell imaging. It is important to clarify that ChannelViT is designed as a versatile image representation backbone suitable for a broad range of multi-channel imaging applications, not exclusively for cell imaging. To demonstrate this, we have selected four diverse datasets for a thorough evaluation of ChannelViT:
  + **ImageNet:** As a foundational image representation benchmark, ImageNet is critical for assessing ChannelViT's performance in standard computer vision tasks. Our results on ImageNet demonstrate that ChannelViT not only surpasses the standard ViT in full-channel scenarios by enabling cross-channel reasoning but also exhibits superior robustness when channels are missing.
  + **JUMP-CP:** The JUMP-CP benchmark, released by the Broad Institute, represents the largest public cell imaging dataset available at the time of our submission. While the mentioned Rxrx datasets and TissueNet are interesting, our comprehensive analysis on JUMP-CP covers similar ground. Also we were unable to access TissueNet via their link in the paper (https://netbio.bgu.ac.il/tissuenet3).
  + **So2Sat:** Satellite imaging, with its multi-channel, multi-resolution data, is an ideal application for ChannelViT. Our empirical results confirm that ChannelViT outperforms ViT across various data splits and channel availability.
  + **Camelyon17-WILDS:** Although Camelyon17 features fewer channels compared to JUMP-CP and So2Sat, the challenge of cross-hospital generalization remains compelling. ChannelViT's robust performance across varying staining color distributions from different hospitals is noteworthy. Due to space constraints, we have included this application in our appendix.
  + Finally, we again appreciate the cell imaging references and will consider them for future work for life science journals. We hope this clarification addresses your concern regarding the scope of our paper.

Reviewer comment (Experiments):
Ablation experiments with ViT-B and ViT-L, with expanded discussion on the intended usage of ChannelViT with respect to efficiency.

Author response:
+ **Model Scale:** We have expanded our results to include larger models: ViT-Base, ViT-Large, ChannelViT-Base, and ChannelViT-Large, detailed in Appendix C.7. Unsurprisingly, larger backbones result in superior performance. Our findings also reveal that despite the increased parameter count in ViT-Base and ViT-Large, ChannelViT maintains a significant performance lead. For instance, ViT-Large/16, with 13.9x more parameters, still lags behind ChannelViT-Small/16 (57.96 vs. 68.09), underscoring the importance of explicitly modeling cross channel interactions. We believe this addition should also address your concern regarding the efficiency of learning channel embeddings in larger ViT models.
+ **Time Efficiency:**
  + We have added a new paragraph in Section 4.2 to discuss time efficiency, with a comprehensive runtime analysis presented in Table 8. Training ChannelViT is indeed 3.64x more resource-intensive, but the inference time is only 1.6x longer than ViT. We anticipate further efficiency gains by integrating ChannelViT with more efficient attention mechanisms like Linformer or LongNet.
  + It is also important to highlight that the additional training time is offset by the avoidance of training separate expert models for each channel combination. ChannelViT's performance in handling inputs with varying channels results in considerable savings in practical applications.

Reviewer comment (Theory):
The patch embedding technique described in Section 3.1 overlooks the issue of channel alignment when deconstructing images into separate channels.

Author response:
+ **Information Loss & Channel Alignment:** ChannelViT employs learnable positional and channel embeddings to align image patches effectively. The shared positional embeddings across channels enable ChannelViT to easily identify patch tokens from different channels at identical positions.
  + **Empirical Evidence 1:** Figure 7 illustrates ChannelViT's ability to concentrate on the same region across RGB channels when identifying a zebra.
  + **Empirical Evidence 2:** We conducted a sanity check to validate the alignment. By using ChannelViT's last layer output for each patch token to predict the original position and channel identity for each patch, we observed that ChannelViT achieves 100% accuracy on both ImageNet and JUMP-CP datasets within a single epoch of training. This underscores the effectiveness of the positional and channel embeddings.

Reviewer comment (Novelty):
The innovation of the proposed method warrants further scrutiny. Elements such as patch embedding, positional embedding, and Transformer Encoders, as discussed in Section 3.1, do not significantly diverge from the traditional Vision Transformer framework. These aspects should be acknowledged in the Related Work section, with a stronger emphasis on the unique contributions of this research.

Author response:
+ **Distinguishing ChannelViT from Traditional ViT:** We appreciate your suggestion to delineate the differences between ChannelViT and the conventional ViT. We had initially discussed these distinctions in the second paragraph of our introduction. Following your advice, we have now included a comparative analysis in the related work and methodology sections of our revised manuscript.
  + We would also like to emphasize that, although ChannelViT's patch and positional embeddings are conceptually similar to those in traditional ViT, several nuanced yet critical modifications have been made to enhance performance significantly.
    + **Patch Embedding:** Traditional ViT acquires patch embeddings through a linear transformation of 3-channel image patches, with distinct weights for each channel. Conversely, ChannelViT processes each channel's image patches separately, employing shared weights across channels, which we demonstrate leads to improved performance (see Appendix C.3).
    + **Positional Embedding:** Given that ChannelViT generates individual image patches for each channel, we opted to share positional embeddings, thereby equipping the model with cross-channel reasoning capabilities based on identical positions.

Reviewer comment (Theory):
The assertion in Section 3.2 that 'HCS guarantees equitable sampling across each m' lacks intuitive justification. While empirical results support this claim, a theoretical rationale would be beneficial.

Author response:
+ **Clarification of HCS in Section 3.2:**
  + The variable m is uniformly sampled from the total number of channels (as described in step 1 of HCS), ensuring that the number of channels of the images processed by HCS are uniformly distributed over {1, 2, … C}. We have appended this clarification to the relevant paragraph to alleviate any confusion.

Reviewer comment (Reproducibility):
Is HCS also employed during the testing phase? It was mentioned that HCS simulates a test-time distribution during training.

Author response:
+ **Clarification of HCS in Section 3.2:**
  + We have clarified in Section 3.2 that HCS is utilized solely during the training phase.

Reviewer comment (Experiments):
Regarding Table 2, when selecting channels for testing, are these chosen at random, or were all possible combinations tested? If it's the latter, could you provide the mean and standard deviation of the results?

Author response:
+ **Evaluation in Table 2:** For an 8-channel image, we have considered all 255 possible channel combinations. The exhaustive results, including mean and standard deviation, are presented in Appendix C.8. Notably, despite each row having a consistent number of channels, the informational content across different channel combinations can vary markedly. This variation is reflected in the substantial standard deviation observed in Table 14. To further investigate this variance, we analyzed ChannelViT's performance gains over ViT for each channel combination, reporting both the mean improvement and standard deviation in Table 15. These findings affirm that ChannelViT's performance enhancements are not only uniform but also substantial.

Reviewer comment (Experiments):
Has the model's performance been evaluated on datasets with varying channel availability, where some data might have only partial channels while other portions are fully channeled?

Author response:
+ **Evaluation on Datasets with Varying Channel Availability:**
  + In Tables 3 and Figure 5, we have trained ViT and ChannelViT on datasets with diverse channel combinations, reporting their accuracy on both full and partial channels.
  + In Tables 2 and 4, we trained ViT and ChannelViT on full channels and assessed their performance under various channel availability. We did not test them on datasets with a mix of partial and full channels. Since the models are fixed post-training, the evaluation scenario you described can be viewed as a blend of different channel combinations. Consequently, we can interpolate performance metrics from Table 2, which already encompasses all potential channel combinations.