STBLLM: Breaking the 1-Bit Barrier with Structured Binary LLMs

We sincerely thank the reviewer for their time and insightful comments. We appreciate the recognition of the strengths of our paper, including the integration of sparsity with quantization, the reduction in storage needs, and the development of a dedicated CUDA kernel for optimized GPU performance. Below is our answers to the reviewer's concerns, and we hope that these responses address your concerns.

Q1. About performance gain.

While the proposed quantization methodology shows promise, the performance improvements over the baseline BiLLM implementation appear to be incremental. I would encourage the authors to further highlight the distinctive advantages of their approach and potentially explore additional optimization strategies to achieve more substantial gains.

Ans for Q1: We respectfully disagree that our improvements are merely incremental. Our approach offers several substantial advantages over BiLLM:

(1) Significant Performance Gains: Our method achieves dramatically better perplexity scores while maintaining a sub-1-bit regime:

• For LLaMA-1-7B: 31.72 perplexity vs BiLLM's 207.32 (6.5x improvement)
• For LLaMA-2-7B: 27.93 perplexity vs BiLLM's 97.54 (3.5x improvement)

(2) Novel Technical Contributions:

• Our Standardized Importance (SI) method introduces sophisticated statistical normalization that provides theoretical guarantees for weight importance scores.
• Our trisection-based partitioning of non-salient weights offers more nuanced handling compared to BiLLM's binary approach.
• We uniquely combine N:M structured pruning with binarization, enabling hardware-friendly implementations.

(3) Practical Efficiency:

• Our specialized CUDA kernel achieves a 17.85x speedup over ABQ-LLM's 2-bit implementation
• Support for arbitrary N:M ratios through Vectorized N:M format, enabling flexible deployment on NVIDIA Sparse Tensor Cores

These improvements represent fundamental advancements in LLM compression, not just incremental gains. We are actively exploring additional optimization strategies to push these boundaries even further.

Q2. About average bit count calculation theoretically.

The manuscript would benefit from enhanced clarity in several sections. Of particular importance is the need for a more comprehensive explanation of the average bit count calculation methodology. I suggest:Including a detailed step-by-step breakdown of the calculation process; Providing specific examples to illustrate the computational procedure at inference time; Clarifying how this calculation relates to the overall system performance on speedup or memory reduction Regarding the calculation of average bit count: Could you clarify whether the overhead from indices associated with sparsity has been factored into the calculation? It would be helpful if you could provide a concrete example illustrating the calculation methodology, including both the weight bits and any additional storage requirements.

Ans for Q2: Thank you for suggesting we enhance clarity regarding the average bit count calculation. Our bits calculation is the same as BiLLM, based on which we just add analysis over the N:M structured pruning. Let me provide a detailed breakdown of how we calculate the average bit count in STBLLM ($N_{param}$):

$$N_{param} = 2 × r_{salient} + 1 × (1 - r_{salient})$$

where $r_{salient}$ is the proportion of salient weights

where 2 bits are allocated for marking the division of non-salient weights and bsize is the block size used in OBC compensation

(3) N:M Structured Sparsity Impact: Under N:M settings (where N < M), we retain only N/M fraction of weights theoretically following the calculation of [1][2][3]. These methods calculate the average bit just theoretically using the N:M sparsity ratio. We make sure that our calculation of average bit count is fair across different methods.

Final number of parameters:

$$N_{stbllm} = N_{param} × (N/M)$$

(4) Concrete Example (for 4:8 sparsity):

• Under blocksize of 128, the averaged proportion of salient weights is around 10%, which is also aligned with the result in BiLLM. For example, with $r_{salient} = 0.1$ (10% salient weights), we first calculate $N_{param} = (2 × 0.1) + (1 × 0.9) = 1.1$ bits. Then applying 4:8 sparsity gives us $N_{stbllm} = 1.1 × (4/8) = 0.55$ bits.

def semi_structured_pruning(W_metric, subset, name, prune_n, prune_m):
    """
    Applies N:M structured pruning based on standardized importance scores

    Args:
        W_metric: Standardized importance scores (SI)
        subset: Model weights dictionary
        name: Name of weight tensor
        prune_n: N in N:M pruning (number of weights to keep)
        prune_m: M in N:M pruning (block size)
    """
    # Initialize pruning mask
    W_mask = torch.zeros_like(W_metric) == 1

    # For each block of M weights
    for ii in range(W_metric.shape[1]):
        if ii % prune_m == 0:
            # Get importance scores for current block
            tmp = W_metric[:, ii:(ii + prune_m)].float()

            # Keep top N weights based on importance scores
            # Note: largest=False because we want to keep highest importance
            W_mask.scatter_(
                1,
                ii + torch.topk(tmp, prune_n, dim=1, largest=False)[1],
                True
            )

    # Apply mask by zeroing out pruned weights
    subset[name].weight.data[W_mask] = 0

Dear Respected Reviewer yy1T,

We sincerely appreciate your thoughtful comments and the time you dedicated to reviewing our work. Your feedback has been instrumental in improving the quality and clarity of our paper. In response to your concerns, we have undertaken a number of revisions and clarifications:

• We have clarified the contributions of our work and detailed the differences between our approach and BiLLM to highlight our unique contributions.
• We have extended the explanation of how the bit calculation is performed, including a concrete example for better clarity.
• We have introduced a detailed explanation of how semi-structured pruning is conducted, including the methodology and rationale.
• We have clarified the process behind achieving the 17× speedup over ABQ-LLM, providing additional details to substantiate this result.
• We have provided clearer explanations for the results presented in Table 5 and Table 7, addressing your concerns and ensuring the data's interpretability.

Given that we have not received further questions or feedback from you in the past few days, we are hopeful that these revisions and clarifications have effectively resolved your concerns. However, if there are any remaining uncertainties or areas requiring further discussion, we would be most grateful for the opportunity to address them.

Alternatively, if you feel that our responses have sufficiently addressed your concerns, we kindly request you to consider updating your evaluation to better reflect the contributions and impact of our work.

Thank you once again for your valuable feedback and careful consideration.

Best regards, Authors of Paper #66

Dear Reviewer yy1T,

I hope this message finds you well.

I am writing to kindly follow up regarding our manuscript (#66) that is currently under review. We truly understand that you have many commitments, and we greatly appreciate the time and effort you’ve already dedicated to evaluating our work.

As it has been over eight days since the submission, and with the deadline approaching in about four days, we would be incredibly grateful if you could find a moment to provide your feedback. Your insights are invaluable to us, and we deeply appreciate your contribution to the review process.

Thank you so much for your time and consideration. We fully understand how busy you must be and truly appreciate any attention you can give to our manuscript.

With sincere thanks,

Authors of #66

Dear Reviewer yy1T,

Thank you for your thorough and comprehensive feedback on our paper. We have made significant efforts to address the many questions you raised, and we truly appreciate the prompt communication you had with the Area Chair on the first day of our rebuttal submission.

However, we noticed that, despite your quick response to our letter to the AC, we have not yet received any comments or feedback on our rebuttal itself. As today is the final day of discussion, we kindly ask if you could take a moment to review and provide your thoughts on our responses.

Your feedback is invaluable to us, and we deeply appreciate your time and effort in helping improve the paper.

Best regards,

Authors of #66

We are deeply honored and extremely grateful to receive such a positive evaluation from the reviewer. We sincerely appreciate your thorough review and the recognition of multiple strengths in our work, including the well-organized structure, clear problem formulation, novel and computationally efficient weight importance metric, and our innovative approach to non-salient weight binarization. I hope we can address your concerns in the below responses.

Q1. About zero-shot evaluation.

In the zero-shot experiment, the paper mentions seven zero-shot tasks. It would be helpful to include a brief description of each task to provide readers with a clearer understanding of the evaluation scope.

Ans for Q1: We appreciate the reviewer's suggestion to include a brief description of each zero-shot task to provide readers with a clearer understanding of the evaluation scope. In our experiments, we carefully selected seven zero-shot tasks that are widely recognized benchmarks in the NLP community for evaluating language models' generalization capabilities. These tasks were chosen because they cover diverse aspects of language understanding and reasoning, making them particularly effective for assessing LLM performance. The tasks include:

(1) Winogrande, which evaluates commonsense reasoning through pronoun resolution in challenging contexts - this is crucial for testing the model's understanding of contextual relationships;

(2) OBQA (OpenBook Question Answering), testing the model's ability to answer science questions using common knowledge, which assesses both factual recall and reasoning;

(3) Hellaswag, assessing the model's ability to complete situations with common sense - a key metric for evaluating real-world understanding;

(4) BoolQ, which presents yes/no questions requiring passage comprehension, testing the model's reading comprehension abilities;

(5) ARC-easy, containing natural grade-school science questions with straightforward reasoning, providing a baseline for scientific knowledge;

(6) ARC-challenge, featuring more complex science questions requiring deeper reasoning, which tests advanced problem-solving capabilities;

(7) RTE (Recognizing Textual Entailment), evaluating whether one text logically follows from another - a fundamental task for natural language inference.

These tasks are standard benchmarks used by previous research to evaluate LLM performance.

Q2. About structured pruning.

Regarding Figure 3, part (b), after structured pruning, the empty parts should have no values. Why are zeros assigned to these parts? Additionally, structured pruning usually doesn't achieve weight-wise pruning, so what does 'structured' mean in this context?

Ans for Q2: Thank you for pointing out the need for clarification regarding Figure 3 (b). In fact, we want to present this figure to show the same thing as Algorithm 1 and 2. However, due to the space limitation, it is hard to present it well, making it confusing to understand. To make it clear, we remove the original salient weight illustration and only keep the non-salient weight in figure 3(b).

Based on your advice, we further add a Figure5 in Appendix A to show the detailed illustration of how to partition the non-salient and salient weights. We hope this new figure and modification (highlighted in yellow) can address your concerns and make our paper more clear.

Finally, we hope these responses address the concerns and appreciate the constructive feedback. We are committed to improving our manuscript and believe the insights will significantly contribute to this goal. We are glad to discuss further comments and suggestions.

Q4: About trisection search.

The motivation behind using a trisection-based partition for non-salient weights is confusing. It seems the authors aim to balance bits and performance (Section 3.4). However, the evaluation results show that the improved compression ratio and performance are due to n:m pruning, rather than the processing of non-salient weights. So, why should we partition the non-salient weights into three parts? Why not four or five? What do the terms dense, intermediate, and sparse mean?

Ans for Q4: We appreciate your feedback on the clarity of our evaluations. Let me break down this question into two parts.

Q4.1: It seems the authors aim to balance bits and performance (Section 3.4). However, the evaluation results show that the improved compression ratio and performance are due to N:M pruning, rather than the processing of non-salient weights.

Let me clarify two points.

• First, both quantization and pruning can degrade model performance. So "the improved compression ratio and performance are due to n:m pruning" is not a correct statement. Instead, we mitigate it through several techniques:

(1) Non-salient Aware Quantization: a fine-grained weight quantization using trisection partitioning that can improve the performance of binarized LLMs ($\uparrow$ Quantization).

(2) Adaptive Layer-wise Binarization: to further reduce the performance degradation by adaptively addressing different layer with different ratios ($\uparrow$ Pruning).

(3) Better Pruning Metric: better pruning metric (SI) that can reduce the performance degradation from N:M pruning ($\uparrow$ Pruning).

• Second, to clarify the function of N:M structured pruning, as presented in Q2 of reviewer jQJp, N:M pruning is a compromising and suitable strategy to address the redundancy in binarized LLM as well as save the computation resource. Meanwhile, trisection partition can elevate the binarized LLM with acceptable overhead, a.k.a. a scaling vector. You can refer to the answer to Q2 of reviewer KgJf for more details over the complexity computation and how our trisection partitioning works.

Q4.2 So, why should we partition the non-salient weights into three parts? Why not four or five? What do the terms dense, intermediate, and sparse mean?

• The choice of three partitions is driven by computational feasibility considerations. The complexity of our search algorithm scales exponentially with the number of partitions T as $O(N^T)$, where N is the number of weights. To empirically validate this, we conducted an ablation study on the number of partitions under the same setting (LLaMA-2-7B, 6:8 sparsity):

We presented Bell-shaped as proposed in BiLLM, Non-salient in STBLLM and Naive Implementation as raise in Q2 of reviewer KgJf. Although the naive implementation can achieve slightly better performance, it requires 12x longer search time.

Given these practical constraints, we determined that three partitions (T=2) provides the optimal balance between granularity of weight segmentation and computational feasibility. This allows us to meaningfully differentiate between weight importance levels while keeping the search time reasonable. We will include detailed analysis in Table 15 of Appendix E.5 of the revised manuscript.

Thank you for your time and valuable feedback on our paper. We appreciate your recognition of the importance of our work in accelerating LLM inference through 1-bit weight quantization. Please see our responses to your questions and concerns below. We hope that these responses can resolve your concerns and enhance the quality of our paper.

Q1: About SI.

its novelty is limited: The proposed SI method is very similar to Wanda, with the main difference being the introduction of additional data normalization.

Ans for Q1: Thank you for raising this important point about SI. We respectfully disagree and would like to highlight several key innovations in our SI method that differentiate it substantially from Wanda:

(1) Novel Statistical Normalization: While Wanda uses simple magnitude-based importance, our SI method introduces a fine-grained statistical normalization approach ($\sigma(\mu(|W_{i,j}|))$) that captures the relative importance of weights. This is fundamentally different from Wanda's direct magnitude measurement.

(2) Empirical Superiority: The substantial performance gap demonstrated in our ablation studies validates the significance of our innovations:

The dramatic improvement in perplexity (6.5x better for LLaMA-1 and 3.5x better for LLaMA-2) demonstrates that our method represents a fundamental advancement, not just an incremental improvement.

(3) Synergistic Integration: Our SI method was specifically designed to work in concert with our binarization approach, enabling more effective pruning decisions that account for the unique challenges of binary quantization - an aspect entirely absent from Wanda's design.

Q2: About trisection search.

The binary quantization method is quite similar to BiLLM, where the hessian matrix is used to divide weights into salient and non-salient parts, and residual approximation is employed to handle the salient part. The only difference is that STBLLM processes the non-salient weights into three parts instead of two as in BiLLM.

Ans for Q2: Thank you for this observation. While BiLLM serves as an important baseline for our work, STBLLM introduces several fundamental innovations that go well beyond a simple extension of partitioning:

(1) Efficient Three-Part Optimization: While BiLLM uses a simple two-part split requiring $O(N)$ complexity, naively extending to three parts would result in $O(N^2)$ complexity. Our key innovation is a novel fixed-ratio approach between partitions that maintains $O(N)$ complexity while achieving better quantization granularity. It significantly improves the performance of STBLLM while achieve the better efficiency.

(2) Statistical Threshold Selection: Unlike BiLLM's direct threshold approach, we introduce a statistically-driven method for determining partition boundaries that better preserves the weight distribution characteristics as shown in Algorithm 2. This results in more fine-grained quantization.

In fact, we introduce a more nuanced handling of non-salient weights by dividing them into three distinct parts. There is only a little burden extend from 2 parts to 3 parts for scaling parameters. But it brings high complexity over searching for the best parameter $p^*_1$ and $p^*_2$. Here is the pesudo code:

# BiLLM's implementation: Two Parts
## Complexity: O(N)

// BiLLM's implementation: Two Parts
// Complexity: O(N)
running_error ← ∞
best_p ← 0
for i from 0.1 to 0.9 step (0.8/160) do
    p1 ← i × max(|W|)
    (B1, B2) ← Split_by_Alpha(p1)
    error ← ||W - (B1 + B2)||^2
    if error < running_error then
        running_error ← error
        best_alpha ← alpha_1
    end if
end for

// NAIVE implementation Three Parts
// Complexity: O(N²)
running_error ← ∞
best_alpha_1 ← 0
best_alpha_2 ← 0
for i from 0.1 to 0.9 step (0.8/160) do
    for j from 0.1 to 0.9 step (0.8/160) do
        p1 ← i × max(|W|)
        p2 ← j × max(|W|)
        (B1, B2, B3) ← Split_by_Alpha(p1, p2)
        error ← ||W - (B1 + B2 + B3)||^2
        if error < running_error then
            running_error ← error
            best_p1 ← p1
            best_p2 ← p2
        end if
    end for
end for

// STBLLM's implementation Three Parts
// Complexity: O(N)
running_error ← ∞
best_p1 ← 0
best_p2 ← 0
for i from 0.1 to 0.9 step (0.8/160) do
    p1 ← i × max(|W|)
    p2 ← alpha × p1  // Fixed ratio between p1 and p2

    B1 ← Binary(W[|W| > p2])
    B2 ← Binary(W[p1 < |W| ≤ p2])
    B3 ← Binary(W[|W| ≤ p1])

    error ← ||W - (B1 + B2 + B3)||^2
    if error < running_error then
        running_error ← error
        best_p1 ← p1
        best_p2 ← p2
    end if
end for

Dear Reviewer KgJf,

I hope this message finds you well.

I am writing to kindly follow up regarding our manuscript (#66) that is currently under review. We truly understand that you have many commitments, and we greatly appreciate the time and effort you’ve already dedicated to evaluating our work.

As it has been over eight days since the submission, and with the deadline approaching in about four days, we would be incredibly grateful if you could find a moment to provide your feedback. Your insights are invaluable to us, and we deeply appreciate your contribution to the review process.

Thank you so much for your time and consideration. We fully understand how busy you must be and truly appreciate any attention you can give to our manuscript.

With sincere thanks,

Authors of #66

We sincerely thank the reviewer for their time and insightful comments. We appreciate the recognition of the strengths of our paper, including the intriguing analysis on flipping non-salient binarized weights, the achievement of the lowest perplexity in the sub-1-bit regime, and the development of a specialized CUDA kernel for structural binarization that achieves a significant speedup.

Q1: About higher ratio.

what would happen if we increase the ratio from 0.15 to 0.5?

Ans for Q1: Our initial experiments focused on a conservative ratio of 0.15 to ensure minimal performance degradation while maximizing compression. We perform extended experiments from 0.2 to 0.5 as the following table shows:

We find that as the ratio increases, the performance fluctuates but still does not deteriorate drastically. This suggests a degree of robustness in our approach to varying ratios of flipped non-salient weights. We also add an additional Figure6 with variance in Appendix B to show the performance (Highlight by yellow).

Q2: About residual approximation and trisection search.

The proposed method is a combination of several existing techniques including N:M sparsity, residual approximation, block-wise error compensation, and Trisection search (for the non-salient part). This raises some novelty concerns. I suggest the authors to 1) highlight the main novelty and contribution of the current submission; 2) provide ablation studies on a. how important the residual approximation is, b. the impact of Trisection search for grouping and why there are two groups.

Ans for Q2: We want to clarify that “residual approximation” and “block-wise error compensation” are not our contribution.

(1) For residual approximation, this technique is a well addressed techique, which has been adopted by BiLLM[1] and QBB[2]. We cited this technique in lines 52, 102 and 169, and do not claim it as our contribution.

(2) For block-wise error compensation, it is also a well-established technique as shown in GPTQ[3], SparseGPT[5], Wanda[4] etc, which already becomes a routine or commonsense. We cited this technique in lines 161 and 215, and did not claim that this is our contribution.

Our work STBLLM stems from a crucial observation: there exists significant redundancy in binarized LLMs (Figure1), making it possible to further compress binarized LLMs. Our motivation experiments show that randomly flipping binary weights does not substantially degrade performance on downstream tasks. Motivated by this finding, we aim to advance the frontier of extreme model compression. To achieve it, we have the following choices:

(1) For unstructured pruning, it can not be accelerated by the existing hardware.

(2) For structured pruning, it will damage the performance of binarized LLM without retraining. For example, ShortGPT[6] conducted a series of experiments on LLaMA-2-7B, finding that when pruning ratio is larger than 30%, the perplexity exceed $10^4$.

(3) N:M semi-structured pruning emerges as a promising approach, as it effectively addresses the memory-intensive computational requirements while enabling efficient hardware acceleration through specialized architectures.

These insights led us to adopt N:M semi-structured pruning, the most suitable approach for our scenario. While N:M structured pruning and binarization are established individually, our novel approach uniquely combines and extends them to address this challenging problem. Our framework introduces three key components that work synergistically:

(1) To improve the accuracy of pruning, we introduce Standardized Importance (SI) to enable more precise and effective pruning.

(2) To improve the performance of binarization, we introduce Adaptive Layer-wise Binarization to dynamically adjust bitwidth allocations across layers.

(3) To further improve the accuracy of quantization, we introduce Non-Salient Aware Quantization to specifically address and mitigate the inherent limitations of binary quantization.

# BiLLM's implementation: Two Parts
## Complexity: O(N)

// BiLLM's implementation: Two Parts
// Complexity: O(N)
running_error ← ∞
best_p ← 0
for i from 0.1 to 0.9 step (0.8/160) do
    p1 ← i × max(|W|)
    (B1, B2) ← Split_by_Alpha(p1)
    error ← ||W - (B1 + B2)||^2
    if error < running_error then
        running_error ← error
        best_alpha ← alpha_1
    end if
end for

// NAIVE implementation Three Parts
// Complexity: O(N²)
running_error ← ∞
best_alpha_1 ← 0
best_alpha_2 ← 0
for i from 0.1 to 0.9 step (0.8/160) do
    for j from 0.1 to 0.9 step (0.8/160) do
        p1 ← i × max(|W|)
        p2 ← j × max(|W|)
        (B1, B2, B3) ← Split_by_Alpha(p1, p2)
        error ← ||W - (B1 + B2 + B3)||^2
        if error < running_error then
            running_error ← error
            best_p1 ← p1
            best_p2 ← p2
        end if
    end for
end for

// STBLLM's implementation Three Parts
// Complexity: O(N)
running_error ← ∞
best_p1 ← 0
best_p2 ← 0
for i from 0.1 to 0.9 step (0.8/160) do
    p1 ← i × max(|W|)
    p2 ← alpha × p1  // Fixed ratio between p1 and p2

    B1 ← Binary(W[|W| > p2])
    B2 ← Binary(W[p1 < |W| ≤ p2])
    B3 ← Binary(W[|W| ≤ p1])

    error ← ||W - (B1 + B2 + B3)||^2
    if error < running_error then
        running_error ← error
        best_p1 ← p1
        best_p2 ← p2
    end if
end for

Dear Respected Reviewer jQJp,

We sincerely appreciate your thoughtful comments and suggestions, which have greatly helped us improve our work. In response, we have conducted extensive experiments and analyses to thoroughly address all the points you raised. We hope our detailed revisions effectively resolve your concerns. Specifically:

• We have conducted extended experiments over a larger ratio to provide a more comprehensive evaluation of our method.
• We have clarified our contributions, emphasizing that the residual approximation and trisection search are not part of our primary contributions but are supportive techniques.
• We have added an additional ablation study to thoroughly analyze the effects of the residual approximation and trisection search, providing more insights into their roles in the overall framework.
• We have addressed your question regarding how our proposed method can be effectively applied to NVIDIA GPUs, ensuring its practical applicability.

Given that we have not received additional questions or feedback from you over the past few days, we are hopeful that our clarifications have been satisfactory. However, if there are any remaining uncertainties or aspects requiring further discussion, we would be most grateful for the opportunity to address them.

Alternatively, if our revisions have addressed your concerns, we kindly request you to consider updating your evaluation to better reflect the contributions and impact of our work.

Thank you once again for your time and thoughtful consideration.

Best regards, Authors of Paper #66

Q1

Thank you for providing the table showing accuracies under various flipping ratios of non-salient parameters. It is very intriguing that BoolQ results are even worse than random guessing (50%). Additionally, flipping non-salient parameters sometimes leads to even better performance than the baselines. I was wondering why we would still want to quantize these parameters instead of pruning them altogether.

Q2 I appreciate the authors' responses. Regarding the three key components, I respectively do not see the novelty in the first two. For example, the standardized importance score implies the idea of "importance of each weight by the product of its magnitude and the corresponding input feature norm," which was used on CNNs back in 2016 (e.g., [1]). Furthermore, there are more advanced ways to determine weight importance (e.g., [2,3]). In addition, the layer-wise quantization was also widely used in many quantization and pruning methods. Could the authors elaborate more their innovations?

[1] Hu, H., 2016. Network trimming: A data-driven neuron pruning approach towards efficient deep architectures. arXiv preprint arXiv:1607.03250.

[2] Dong, X., Chen, S. and Pan, S., 2017. Learning to prune deep neural networks via layer-wise optimal brain surgeon. Advances in neural information processing systems, 30.

[3] Frantar, E. and Alistarh, D., 2022. Optimal brain compression: A framework for accurate post-training quantization and pruning. Advances in Neural Information Processing Systems, 35, pp.4475-4488.

Dear Reviewer jQJp,

I hope this message finds you well.

I am writing to kindly follow up regarding our manuscript (#66) that is currently under review. We truly understand that you have many commitments, and we greatly appreciate the time and effort you’ve already dedicated to evaluating our work.

As it has been over eight days since the submission, and with the deadline approaching in about four days, we would be incredibly grateful if you could find a moment to provide your feedback. Your insights are invaluable to us, and we deeply appreciate your contribution to the review process.

Thank you so much for your time and consideration. We fully understand how busy you must be and truly appreciate any attention you can give to our manuscript.

With sincere thanks,

Authors of #66

Dear Reviewer jQJp,

Tomorrow is the final day for discussion regarding our paper. Over the past few weeks, we have not received any feedback from you, and we are unsure of the reason. As a reviewer, it is essential to provide feedback, even if it may be critical. We genuinely value your insights and believe that your comments will contribute greatly to improving the quality of our work.

We kindly request that you take a moment to share your thoughts with us before the deadline. Your efforts are instrumental in advancing the review process for ICLR.

Thank you for your time and consideration.

Best regards,

Authors of #66

From the perspective of an ICLR reader rather than an official reviewer, I find myself curious about the decision to focus solely on emphasizing the strengths of the paper in the section titled “Summary of Our Responses to All Official Reviews.” Are there truly no potential weaknesses that warrant mention in the summary? Considering that all reviewers’ feedback is publicly available, I wonder if re-summarizing the strengths serves to draw reviewers’ attention, or if it might inadvertently come across as misleading.

Please note that I have no intention to offend the authors. My comments are merely an attempt to better understand the rationale behind this strategy and to ensure the summary is as balanced and transparent as possible.

Dear Reviewer yy1T,

Thank you for your insightful suggestions and feedback on our paper. We greatly appreciate the time and effort you have dedicated to reviewing our work.

Over the past few days, we have made our best effort to address each reviewer's concerns individually, providing clarifications and conducting additional experiments. As we do not provide individual detailed responses to each reviewer's recognitions, we have collated and organized these comments in this section. As per your suggestion, we have revised the title of this section to avoid any potential confusion for the readers.

We look forward to you reviewing our response, and we will actively address any further questions or concerns you may have. Once again, thank you for your valuable input, which has helped us improve our work.

Best regards,

Authors of #66