Q1: Comparison with the Baseline

We have included comparisons with the Logit Adjustment baseline for your reference. Thank you for your suggestion. As a method that considers long-tailed distributions, Logit Adjustment exhibits more balanced performance and higher tail-class accuracy. In this setting, our method still achieves the highest C/F while retaining superior tail-class performance compared to other pruning baselines. This strongly demonstrates the applicability of our method.

Thank you for your question, which helped clarify our contributions. Additionally, we have incorporated more details to facilitate reproducibility in the shared link.

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IR = 50

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IR = 100

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Q2: Over-parameterization for Tail Classes

Thank you for acknowledging our proof. The additional experiments we conducted further illustrate this point. Using the static pruning method ReGG (where a sparser network is pruned only at initialization), we ensured the model’s C/F remains 1 (this can be seen as reducing the model’s over-parameterization). Under the standard cross-entropy (CE) loss (as requested by Reviewer hf3A, which applies no corrections for long-tailed distributions), tail-class performance suffered catastrophic declines.

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Q3: Additional Overhead

In fact, our method introduces minimal additional overhead. The time complexity of our pruning method is O(d) , where d is the number of model parameters. This is significantly lower than ATO’s O(Dd) , where D is the size of the supernet used in that method. The additional complexity of the dynamic scoring and balancing mechanism is O(nk) , where n is the number of classes and k is the number of criteria. Even for datasets with long-tailed distributions, this remains much smaller than O(d) , as our total complexity is O(d) .

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Q4: Negative Impact on Head Classes

In practice, our method does not cause significant negative impacts on head classes.

The core of our method lies in considering the impact of pruning on class distributions when selecting pruning locations and dynamically incorporating feedback. Under this approach, compared to methods that use average model performance as the sole criterion, our method continuously adjusts to achieve distribution-adaptive pruning.

Our method implicitly assumes that performance changes on each class (whether head or tail) are equally important, which partially offsets some of the negative effects caused by sample size differences. However, our method remains fair: when a pruning criterion harms head classes, our method reduces its weight and attempts to find alternative pruning criteria to avoid such harm.

The experiments in the main text, as well as the supplementary experiments, have demonstrated this. Our method achieves performance improvements across classes with varying frequencies.

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Q5: How Many Iterations Are Needed to Determine Parameter Weights?

The weights are computed once per epoch until pruning ends. Thus, the number of iterations is generally fewer than the total number of training epochs.

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Q6: How Are Pruning Stopping Points Determined?

In our experiments, we followed standard pruning settings, stopping once pruning reached a certain proportion.

Beyond this, since our method is sensitive to class-level performance changes, it can be adapted to additional stopping criteria as needed. For instance, pruning can stop when excessive performance drops are observed in too many classes (a certain number of classes), or when head-class/tail-class performance declines sharply over consecutive rounds. This flexibility allows the method to meet more realistic deployment requirements.

Q1: Writing Issues

We sincerely appreciate your feedback. Here, we clarify our writing structure to address your concerns:

1. Introduce the background of long-tailed learning and its importance in addressing the challenges of imbalanced class distributions, particularly highlighting the difficulty posed by the scarcity of tail-class data.
2. Analyze the limitations of existing methods in terms of computational resource consumption and dynamic adaptability, emphasizing the necessity of pruning techniques for optimizing model efficiency.
3. Explain the unique challenges traditional pruning methods face in long-tailed learning, such as exacerbated class imbalance, lack of dynamic adjustment capabilities, and overly simplistic pruning criteria.
4. Propose our Long-tailed Adaptive Pruning (LTAP) method, which achieves dual optimization of model performance and efficiency through dynamic weight adjustment and tail-class protection mechanisms.

Additionally, we have supplemented and rewritten the methodology section to reduce potential misunderstandings caused by our previous oversights. Thank you for your valuable suggestions.

If you have other suggestions for improving the writing of the introduction or methodology, please feel free to share them, and we will address them promptly.

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Q2: Definition of p provided, but not θ

The definition of p is at line 166, where P is described as the number of pruning stages. Additionally, we have supplemented the definition of θ (referring to model parameters). Thank you for pointing this out.

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Q3: Added the fifth definition

Thank you for identifying this oversight. We have supplemented and rewritten this section to clarify the missing definition.

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Q4: Definition of wc

wc refers to the weighting mechanism for classes in long-tailed methods, similar to class weighting techniques in methods like balanced softmax. Thank you for your detailed observation. To avoid potential misunderstandings related to our method, we have removed this part.

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Q5: Clarification of w and wk

w is a 5×100 matrix that records the weight of each criterion for each class. wk is a 1×100 matrix representing the weights for one specific criterion. The initial value of wk is set to all ones. Thank you for pointing out this issue. To avoid confusion caused by continuing to use w to represent weights, we have replaced w with the symbol D in the manuscript and annotated its dimensions and update mechanism to prevent any potential misunderstanding.

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Q6: Clarification of αk

Thank you for your question. αk is shared across all classes. However, its calculation depends on the weights wk and γ, which are associated with each class. γ can be set as the weight for each class, and the transformation of wk fully considers the performance changes of each class. In other words, we evaluate performance changes class by class and ultimately derive the weight for the strategy accordingly.

Additionally, we have rewritten this section in the manuscript using more easily comprehensible language, split long formulas into shorter ones, and added the necessary textual explanations. Changes have been highlighted in red for your reference.

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Q7: Clarification of Ac and target

Ac and target refer to the performance change metrics under the selected criterion. We have avoided such ambiguous terms in the revised version. In the updated manuscript, we adopted multi-line short formulas and more intuitive symbols to ensure clarity.

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Q8: Clarification of the reference model

The "reference model" refers to using the current model gradient as a parameter to serve as a directional reference. This is indeed an uncommon approach, mentioned only in a few works on pruning design. We have clarified this concept in the manuscript.

Thank you for your rebuttal.

It appears that the revised version has overwritten the original submission. As many parts of the paper related to my initial review have been modified, I cannot fully assess the point-by-point clarifications in the rebuttal without access to the original version for reference. Would it be possible to include the original version, perhaps as an appendix?

I will take time to review the revised paper and provide feedback on it later.

For Q1: I maintain my concerns regarding the coherence of the first three paragraphs in the introduction.

For Q2: My question concerns the lowercase $p$, but the authors have only defined uppercase $P$ in both the main text and the rebuttal.

For Q6: The authors still have not directly clarified why the right-hand side of Equation 5 (in the original version) is a term that varies with class $c$, while the left-hand side is independent of $c$. This issue remains in the revised version of Equation 5 as well.

| 0.1 | 0.2 | 0.3 |
| 0.4 | 0.5 | 0.6 |
| 0.7 | 0.8 | 0.9 |
| 1.0 | 1.1 | 1.2 |
| 1.3 | 1.4 | 1.5 |

| 10 |
| 20 |
| 30 |

| 0.1 | 0.2 | 0.3 |   | 10 |   | 14.0 |
| 0.4 | 0.5 | 0.6 | · | 20 | = | 32.0 |
| 0.7 | 0.8 | 0.9 |   | 30 |   | 50.0 |
| 1.0 | 1.1 | 1.2 |            | 68.0 |
| 1.3 | 1.4 | 1.5 |            | 86.0 |

The revised version contains numerous fundamental formatting issues that should not appear in a qualified submission. For instance, lines 133, 136, 137, 148, 150, 163, 439, and 699 exhibit basic problems such as missing mathematical environments and incorrect use of subscript and superscript symbols.

Section 2 is poorly written and hard to follow. Each step and the introduction of formulas lack basic intuition and motivation, making it difficult for me to grasp the core contributions and innovations of the method.

The purpose of many formulas and variables is not clearly explained. For example:Why are both $S$ and $I$ referred to as the “comprehensive importance score,” and what is the distinction between them? Why is the right-hand side of Equation 5 a term that varies with class $c$, while the left-hand side is independent of $c$? What does p represent in Equation 7, and why is the left-hand side of Equation 7 a quantity determined by $p$, while the right-hand side appears to be a constant?

For Section 2: To help you better understand the motivation and contributions of this paper directly, we have made simple modifications to Section 2:

LTAP: Adaptive Pruner for Long-tailed Distribution

In this section, we propose a novel pruning strategy called Long-Tailed Adaptive Pruner (LTAP), aimed at optimizing neural network models on long-tailed distribution datasets. By effectively protecting critical parameters of tail classes, LTAP not only enhances overall model performance but also improves parameter efficiency in long-tailed distribution scenarios. This is achieved through the integration of multiple importance scoring criteria and the dynamic adjustment of pruning weights. The following subsections will provide a detailed explanation of the overall architecture, LTAP optimizer design, pruning strategy implementation, and the alternating process of training and pruning.

LTAP Optimizer Design

To accurately assess parameter importance, LTAP introduces multiple scoring criteria, including magnitude, average magnitude, cosine similarity, Taylor first order, and Taylor second order. These diverse criteria enable a comprehensive evaluation of parameter significance, capturing different aspects of their contributions to the model's performance. By incorporating multiple perspectives, LTAP ensures a more balanced pruning process that takes into account the complex dynamics of long-tailed distributions. Additionally, to capture the multifaceted nature of parameter contributions, we introduce a dynamic weighting mechanism that adjusts the influence of each criterion based on real-time performance metrics.

The comprehensive importance score $S_g$ for each parameter group $g$ is calculated by the following formula:

$$S_g = \sum_{k=1}^K \alpha_k \cdot s_{g,k}$$

Here, $K=5$ represents the number of scoring criteria, $\alpha_k$ is the weight coefficient for each scoring criterion $k$, and $s_{g,k}$ denotes the score value of scoring criterion $k$ for parameter group $g$. The specific scoring criteria are defined as follows: $s_{g,\text{magnitude}} = |\mathbf{w}_g|_2$

$s_{g,\text{avg-magnitude}} = \frac{|\mathbf{w}_g|_2}{n_g}$

$s_{g,\text{cosine}} = \frac{\mathbf{w}g \cdot \mathbf{w}{ref}}{|\mathbf{w}_g|2 |\mathbf{w}{ref}|_2}$

$s_{g,\text{taylor-first}} = \left|\frac{\partial \mathcal{L}}{\partial \mathbf{w}_g}\right| \cdot \mathbf{w}_g$

$s_{g,\text{taylor-second}} = \left|\frac{\partial^2 \mathcal{L}}{\partial \mathbf{w}_g^2}\right| \cdot \mathbf{w}_g^2$

Where $\mathbf{w}_g$ is the weight vector of parameter group $g$, and $n_g$ is the number of parameters in group $g$.

The reference weight vector $\mathbf{w}_{\text{ref}}$ represents the gradients of the current model parameters, serving as a directional reference in the cosine similarity criterion to measure the alignment between parameter updates and the optimization trajectory.

This multifaceted scoring approach allows LTAP to accurately identify and preserve parameters that are crucial for both head and tail classes, thereby maintaining model robustness and enhancing performance across the entire long-tailed distribution.

Pruning Strategy Implementation

We propose a dynamic importance evaluation mechanism that adaptively integrates class distributions with multiple pruning criteria. This integration allows LTAP to dynamically prioritize parameters based on the specific needs of each class, ensuring that tail classes receive the necessary attention during the pruning process. By leveraging both the inherent class distribution and the multifaceted parameter importance scores, LTAP can effectively balance model compression with the retention of critical information necessary for accurate classification across all classes. The importance score is computed through a novel interaction framework:

$$I_c = D \cdot N_c$$

Where $I_c \in \mathbb{R}^K$ represents the comprehensive importance scores across criteria for class $c$, $D \in \mathbb{R}^{K \times C}$ denotes the criteria weight matrix, and $N_c \in \mathbb{R}^C$ represents the class distribution vector.

Dear Reviewer hf3A,

We have done our best to provide a response to your comments and hope that you can re-evaluate our submission based on the revisions. If there are any further concerns or questions, please don't hesitate to bring them up.

Q1: Theoretical basis for enhanced tail class parameter retention:

Thank you for your question. We agree that fully explaining how our method enhances tail class parameter retention would increase the paper's contribution. As per your request, we have provided the best proof possible. Due to time constraints, we made some assumptions and simplifications regarding the model, distribution, and algorithmic details without compromising our method's applicability. The proof is included in Appendix D, pages 19-23.

Q2: Verification of parameter preservation for tail classes:

Thank you for raising this concern. We have conducted additional experiments to demonstrate "preserves more parameters for tail classes":

We performed additional ablation studies on datasets with two imbalance ratios. "ours w.o. $\kappa$" represents our method with tail protection ablated. As shown, with the same pruning rate F, significant performance degradation occurs in tail classes across different imbalance ratios (ir=50 and 100) and loss functions after ablation. This indicates that our original method retained more parameters beneficial for tail class performance. (Note that retained parameters beneficial for tail classes don't necessarily mean they're useless for head classes - pruned parameters might contribute to both head and tail classes, only to certain classes, or have minimal contribution overall.)

Table 1: Experiments on CIFAR with ir=50, testing different losses (ce and Logit Adjustment) and pruning methods. w.o. $\kappa$ represents ablation of our tail protection mechanism

Table 1: Experiments on CIFAR with ir=100, testing different losses (ce and Logit Adjustment) and pruning methods. w.o. $\kappa$ represents ablation of our tail protection mechanism

Our method actually has relatively low costs in the pruning strategy. The time complexity of our pruning method is O(d), where d is the model parameter scale. This is significantly lower than ATO's O(Dd), where D is the scale of the hypernetwork used in their method. The additional complexity of dynamic scoring and balancing mechanisms is O(nk), where n is the number of classes and k is the number of criteria, which is much smaller than O(d) even on long-tailed datasets, as our total complexity remains O(d).

Q4: Other minor issues:

We have added the requested pseudocode to the revision and will incorporate it into the main text. We have also thoroughly revised notation errors and missing references. We sincerely appreciate your contributions to improving the manuscript's quality.

Thank you for your detailed response.

For the theoretical analysis, I appreciate your acknowledgment of the assumptions and simplifications made in the theoretical analysis due to time constraints. From my perspective, your explanation is ok to address my concern to some extent.

For your additional experiments, your results indicate a high correlation between tail protection mechanism and improved performance especially on tail classes. While the results do not directly confirm whether more parameters are retained for tail classes, your additional theoretical analysis in Appendix D supports the likelihood of this being the case.

In summary, based on your response and the feedback from other reviewers, I find your rebuttal reasonable and well-prepared. I will keep my score unchanged.

Q1: Explanation of wk:

w is a 5x100 matrix that records the weights of each criterion for each class. wk is a 1x100 matrix for one specific criterion, with initial values all set to 1. Thank you for pointing out this ambiguity. We have replaced w with the symbol D in the manuscript and clearly annotated its dimensions and update mechanism to avoid any potential misunderstandings.

Q2: Explanation of αk:

We sincerely apologize for the unclear explanation of the αk derivation process. We have rewritten this section using more comprehensible language, breaking down lengthy formulas into shorter ones, and adding necessary textual explanations. These changes are highlighted in red.

Furthermore, let me clarify your question: αk is shared across all classes. However, the calculation of αk is determined by wk and γ for each class. γ can be set as the weight for classes, and the transformation of wk fully considers the performance changes of each class. In other words, we consider performance changes class by class to ultimately derive the weights for the strategy.

Q3: Relationship between adjusting scoring criteria weights and protecting tail classes:

We influence the selection of parameter groups by introducing weights for different criteria. During weight adjustments, the performance changes of each class are considered. This process inherently accounts for long-tailed distributions and tail class protection. For instance, if a pruning operation sacrifices multiple tail classes while improving head class performance, such pruning methods would be penalized. Additionally, we introduced γ, a variable with the same dimension as the classes, which can be used to weight tail classes according to distribution preferences.

Formally, while directly incorporating fixed tail class consideration metrics (or simply setting wk according to distribution) might seem more beneficial for protecting tail classes, this would somewhat reduce the method's generality. Our goal is to develop a pruning strategy that is both universal and adaptable to long-tailed environments.

Q4: Results on ImageNet-LT dataset:

Thank you for your question. To clarify, our method's core focus is on improving the usability of pruning methods in long-tailed learning. Tail class performance is one of the key concerns in this context (as the performance degradation and additional bias introduced by pruning can further exacerbate the insufficient performance of tail classes in long-tailed learning), rather than specifically designing a method biased towards tail classes compared to traditional pruning (in fact, pruned parameters might significantly affect both head and tail classes, or have minimal impact on both).

Class-aware selection rules replacing overall performance as pruning criteria prevent further bias against tail classes while improving performance across all classes compared to existing pruning methods. We have also retained the capability to introduce preference control vectors for specific requirements (though specific preferences were not introduced in the original experiments).

Your observation that our method shows larger improvements in head classes than tail classes on ImageNet-LT is valid. Due to random factors and dataset imbalance, the actual improvements from our method may vary. However, this doesn't conflict with our motivation - improving usability in long-tailed learning while avoiding introducing additional bias and performance degradation for tail classes. More specifically, this might indicate that our method has found pruning combinations in ImageNet-LT that avoid further performance degradation in most tail classes while satisfying head class requirements (which is indeed the case compared to baselines). Additionally, if you're particularly interested in the underlying reasons for tail class preservation effects, our provided proofs may offer supplementary information.

We greatly appreciate your attention to detail and responsibility. Your contributions have been invaluable in helping us clarify misunderstandings and improve the manuscript's quality.