Towards Efficient Mixture of Experts: A Holistic Study of Compression Techniques

## Abstract

Abstract Scaling large language models has revolutionized the performance across diverse domains, yet the continual growth in model size poses significant challenges for real-world deployment. The Mixture of Experts (MoE) approach addresses this by dynamically selecting and activating only a subset of experts, significantly reducing computational costs while maintaining high performance.
However, MoE introduces potential redundancy (e.g., parameters) and extra costs (e.g., communication overhead).
Despite numerous compression techniques developed for mitigating the redundancy in dense models, the compression of MoE remains under-explored. We first bridge this gap with a cutting-edge unified framework that not only seamlessly integrates mainstream compression methods but also helps systematically understand MoE compression.
This framework approaches compression from two perspectives: Expert Slimming which compresses individual experts and Expert Trimming which removes structured modules.
Within this framework, we explore the optimization space unexplored by existing methods, and further introduce aggressive Expert Trimming techniques, i.e., Layer Drop and Block Drop, to eliminate redundancy at larger scales. Based on these insights, we present a comprehensive recipe to guide practitioners in compressing MoE effectively.
Extensive experimental results demonstrate the effectiveness of the compression methods under our framework and the proposed recipe, achieving a 6.05 × 6.05\times 6.05 × speedup and only 20.0 20.0 20.0 20.0 GB memory usage while maintaining over 92 % percent 92 92\% 92 % of performance on Mixtral-8 × \times × 7B. Code is released at https://github.com/DaizeDong/Unified-MoE-Compression .

## 1 Introduction

While scaling large language models has shown exceptional performance across various domains [, , ], the increasing model size poses significant challenges in real-world deployments [, ] due to excessive computational demands and associated costs.
The Mixture of Experts (MoE) [], which selectively activates a subset of parameters during inference, offers a promising solution to reduce these computational burdens. Additionally, integrating MoE with Large Language Models (LLMs) [, ] has been shown to enhance performance further.

Despite these advancements, existing MoE models still exhibit redundancies that increase deployment costs. Common MoE approaches often replicate feedforward layers multiple times, leading to parameter redundancy. For example, He et al. [] observed that expert parameters could be compressed through parameter-sharing, Liu et al. [] revealed extremely high representational similarity between experts, while Lu et al. [] noted that not all experts are essential, with some being safely removable.
Additionally, MoE models introduce communication overheads compared to dense models [, , ] in distributed settings, as tokens must be distributed among different experts and their outputs subsequently combined.

In this paper, we investigate the issues through the lens of compression to enhance the efficiency of MoE [, ]. Specifically, we propose a unified framework that integrates two complementary perspectives: (1) Expert Slimming that compresses individual experts and (2) Expert Trimming that structurally removes experts.
In the case of Expert Slimming, network pruning [, ] and quantization [, ] are the most widely used techniques, where quantization is hardware-friendly for implementations. In terms of existing Expert Trimming, we utilize Expert Drop [, ], which removes unimportant experts.

This framework facilitates us to systematically understand the efficiency issue of MoE and identify the new design space to further improve the performance.
With the framework, we first reveal the efficiency bottlenecks of existing methods, specifically the communication between experts and costly computation.
Based on this insight, we propose aggressive Expert Trimming methods to enhance MoE efficiency. Specifically, to mitigate communication and computation costs, we present Layer Drop that removes all experts in an MoE layer, i.e., the entire MoE layer. Additionally, given the computation-intensive nature of the attention mechanism within transformer blocks, we propose Block Drop, which removes both attention layers and MoE layers.
We use similarity-based metrics to demonstrate the feasibility of Layer Drop and Block Drop. Surprisingly, these two coarse-grained methods outperform fine-grained Expert Drop by a large margin in balancing performance and efficiency.
Furthermore, since Expert Slimming can be seamlessly integrated with Expert Trimming, we further utilize the unified framework to propose a comprehensive compression recipe that integrates both strategies.

Experimental results on two widely-used MoE models (i.e., Mixtral-8$\times$7B [] and DeepSeek-MoE-16B []) demonstrate the effectiveness of our methods.
For Expert Slimming, quantization performs best, since it significantly compresses by a large margin practically while maintaining comparable performance. For Expert Trimming,
Expert Drop significantly reduces the memory usage but only accelerates the inference marginally; Layer Drop and Block Drop result in both faster inference speed and less memory usage while maintaining comparable performance.
The combined strategy of Expert Slimming and Expert Trimming achieves a 6.05$\times$ speedup and only 20.0GB memory usage while maintaining over 92% of the performance on Mixtral-8$\times$7B. These findings offer valuable insights for enhancing the efficiency of MoE models.

## 2 Related Work

Mixture of Experts.
The Mixture of Experts (MoE) is a kind of dynamic neural network with an extended set of parameters (referred to as “experts”) controlled by a router, which is first introduced in the context of conditional computation [, , ].
The potential of sparse activation in MoE is subsequently exploited by [] for efficient training and inference on pretrained models with special designs, opening the door for MoE in various vision [] and language [, , ] scenarios.
Attributed to its exceptional efficiency, MoE has been adopted as a foundational framework in the designs of large language models (LLMs) [, , , ], achieving superior scaling laws at low costs [].
Further investigations emerge in developing improved expert structures [, , ], router designs [, , , ], and training strategies [, , , ], propelling the continuous evolution on the representation capability and computational efficiency of MoE models.
Despite the success, MoE also suffers from efficiency issues. For instance, MoE replicates the experts, significantly increasing the parameter budget []. On the other hand, adopting multiple experts to process input tokens introduces communication costs and enhances latency [, ].

Compression Methods.
The escalating size of large language models presents considerable hurdles for their practical implementation. Consequently, a range of efficient methods has emerged to address the high-cost deployment issues.
Among them, model quantization [, , , ] and network pruning [, , , ] are widely utilized. Model quantization reduces the precision of neural network weights to lower bits [], while network pruning [] removes redundant parameters or architectures. Although these methods have shown promising results on dense models, they lack consideration for the inductive bias inherent in MoE.
To bridge this gap, Expert Drop, as proposed in studies like [, ], addresses the unique nature of MoE by removing unimportant experts. By eliminating redundant experts, the MoE architecture becomes more compact and can be deployed at a lower cost. However, while Expert Drop leads to a more compact architecture, it may also lead to non-negligible performance drop and rely on post-training procedures for recovery.

## 3 Preliminary

### 3.1 Mixture of Experts

A standard Mixture of Experts layer comprises a set of $n$ experts $\left\{\boldsymbol{E}_{1},\boldsymbol{E}_{2},\dots,\boldsymbol{E}_{n}\right\}$ associated with corresponding weights $\{\boldsymbol{W}_{1},\boldsymbol{W}_{2},\dots,\boldsymbol{W}_{n}\}$ and a router $\boldsymbol{G}$.
The router determines which experts to activate for a given input $\boldsymbol{x}$ by calculating selection scores $\boldsymbol{G}(\boldsymbol{x})\in\mathbb{R}^{n}$ for all experts. It then selects the top $k$ experts with the highest scores, resulting in a sparse activation pattern.
The input $\boldsymbol{x}$ is then sent to the selected experts, and their outputs are combined into a weighted sum based on the selection scores provided by the router. This process can be described by the following equations:

$$ $\mathcal{K}=\mathrm{TopK}(\mathrm{Softmax}(\boldsymbol{G}(\boldsymbol{x})),k),$ (1) $$

$$ $\boldsymbol{y}=\sum\nolimits_{i\in\mathcal{K}}{\boldsymbol{G}(\boldsymbol{x})_ {i}\cdot\boldsymbol{E}_{i}(\boldsymbol{x}|\boldsymbol{W}_{i})},$ (2) $$

where $\mathcal{K}$ denotes the indices of selected experts, $\boldsymbol{G}(\boldsymbol{x})_{i}$ represents the selection score for the $i$-th expert, and $\boldsymbol{E}_{i}(\boldsymbol{x})$ is the output from the $i$-th expert.
In transformer models, the MoE layer is often used as a replacement for the feed-forward network (FFN). In this context, each expert functions as an independent FFN module, enhancing the model’s capacity without a proportional increase in computational cost [].

Challenges. While MoE models have demonstrated strong performance across various tasks [, ], they also encounter significant deployment issues: On one hand, MoE replicates expert networks multiple times, increasing model size and memory costs. On the other hand, the complexity of managing multiple expert networks and the associated communication between them leads to increased latency and slower inference speeds.

### 3.2 Overview of Previous Compression Methods

To address the challenges arising from MoE, we investigate several mainstream and state-of-the-art efficient methods for MoE.

Pruning: For a MoE layer that includes multiple experts $\{\boldsymbol{E}_{i}\}_{i=1}^{n}$ with corresponding weights $\{\boldsymbol{W}_{i}\}_{i=1}^{n}$, pruning uses binary masks $\{\boldsymbol{M}_{i}\}_{i=1}^{n}$ to selectively disable parts of weights:

$$ $\hat{\boldsymbol{W}}_{i}=\boldsymbol{M}_{i}\odot\boldsymbol{W}_{i}.$ (3) $$

Masking can exhibit unstructured [, ], semi-structured, or structured properties, each resulting in different sparsity patterns.
Unstructured sparsity often exhibits superior performance, while semi-structured sparsity offers a balance between performance and efficiency. Structured sparsity is hardware-friendly, but its performance is currently deemed insufficient.

Quantization: Unlike pruning, which involves masking out unimportant parameters, quantization transforms weights into low-bit representations, thereby reducing memory requirements.

$$ $\hat{\boldsymbol{W}}_{i}=\rm{Quant}(\boldsymbol{W}_{i}),$ (4) $$

where “$\mathrm{Quant}$” denotes the quantization function.
Quantization reduces the complexity of data types but does not impact the FLOPs (floating point operations) or the total number of parameters.

Expert Drop: Different from fine-grained pruning and quantization, Expert Drop entails the removal of expert networks, based on the observation that not all experts are equally important [, ]. Given expert-wise importance scores $\boldsymbol{S}$
(e.g., the routing scores, $\boldsymbol{S}(\boldsymbol{E}_{i})=\boldsymbol{G}(\boldsymbol{x})_{i}$),
Expert Drop retains only the experts with the highest $n^{\prime}$ scores:

$$ $\mathcal{T}^{\prime}=\mathrm{TopK}(\boldsymbol{S}(\{\boldsymbol{E}_{i}\}_{i=1} ^{n}),n^{\prime}),$ (5) $$

$$ $\boldsymbol{E}\leftarrow\{\boldsymbol{E}_{i}\}_{i\in\mathcal{T}^{\prime}}, \quad\boldsymbol{G}\leftarrow\{\boldsymbol{G}_{i}\}_{i\in\mathcal{T}^{\prime}}.$ (6) $$

Figure: Figure 1: The Unified View of MoE Compression. The view integrates two complementary perspectives: Expert Slimming and Expert Trimming. Expert Slimming compresses individual experts, while Expert Trimming directly drops structured modules.
Refer to caption: x1.png

Here, $\mathcal{T}^{\prime}$ denotes the subset of the original expert indices $\mathcal{T}=\{1,2,\dots,n\}$. Expert Drop  reduces FLOPs conditionally: when $\mathcal{T}^{\prime}$ contains more than or equal to $k$ indices, MoE still utilizes the top $k$ experts for each input; otherwise, it uses all remaining experts. While this approach reduces communication between experts, the resulting speedup is not always significant.

Others:
Other efficient methods include Low-Rank compression [, ], which decomposes model weights into smaller weights. In this paper, we mainly focus on the widely-used methods (i.e., pruning, quantization, dropping), deferring discussion on other methods for future exploration.

## 4 A Unified View on MoE Compression

In this section, we propose a general framework that unifies the efficient methods on MoE. This framework enables us to systematically understand the efficiency issues of MoE models and identify new design opportunities to further improve performance.

### 4.1 Unified View for MoE Compression

Existing compression methods address these challenges by focusing on either the internal compression of individual experts or the structural simplification of the model.
Inspired by this insight, we unify the MoE compression into two complementary perspectives: Expert Slimming that compresses individual experts (e.g., Pruning and Quantization), and Expert Trimming that directly removes experts (e.g., Expert Drop).
In doing so, we can better understand their contributions and limitations.
An overview of these perspectives is illustrated in Figure 1.

The compression of individual experts (Expert Slimming) focuses on the transformation and reduction of expert weights, denoted as $\boldsymbol{W}$. We utilize a transformation function $f(\boldsymbol{W})$ to represent this process. The transformation function $f(\boldsymbol{W})$ can be understood as a general mapping that applies various compression techniques to the weights of the model. For example, in pruning, $f(\boldsymbol{W})$ could be a function that sets a subset of the weights to zero. In quantization, $f(\boldsymbol{W})$ might reduce the precision of the weights from 32-bit floats to 8-bit integers.
On the other hand, Expert Trimming  deals with compressing structured modules by selecting and retaining only a subset of the experts, denoted as $\mathcal{T}^{\prime}$. This is represented by the transformation $\mathcal{T}\leftarrow\mathcal{T}^{\prime}$. Methods like Expert Drop, which selectively drops entire experts or layers, are examples of this approach. By integrating these two perspectives, we can derive a general form for efficient MoE models. The compression within and across experts can be expressed as follows:

$$ $\boldsymbol{y}=\sum\nolimits_{i\in\mathcal{T}^{\prime}}\boldsymbol{G}_{i}\cdot \boldsymbol{E}_{i}(\boldsymbol{x}|f(\boldsymbol{W}_{i})).$ (7) $$

**Table 1: Summary of Compression Methods. “✓” means effective and “✗” means ineffective, while “❍” represents conditionally effective, depending on specific settings and environments.**
| Hierarchy | Method | Formulation | Parameter | Memory | FLOPs | Speedup |
| --- | --- | --- | --- | --- | --- | --- |
|  | Pruning | $\boldsymbol{M}\odot\boldsymbol{W}$ | ✓ | ❍ | ✓ | ❍ |
| Expert Slimming | Quantization | Quant($\boldsymbol{W}$) | ✗ | ✓ | ✗ | ✓ |
|  | Expert | $\mathcal{T}\leftarrow\mathcal{T}^{\prime}$ | ✓ | ✓ | ❍ | ❍ |
| \cdashline2-7 | Layer |  |  |  |  |  |
| Expert Trimming | Block | $\mathcal{T}\leftarrow\varnothing$ | ✓ | ✓ | ✓ | ✓ |

In the following sections, we will elaborate on how this framework incorporates existing methods and inspires us to identify new design space for compression.

### 4.2 Expert Slimming

Given that employing multiple experts in MoE significantly escalates parameters and inference costs, Expert Slimming, stemming from single-model compression techniques, targets the compression of individual expert weights $\boldsymbol{W}$ exclusively.
We denote any efficient transformation function as $f(\cdot)$, which encompasses pruning $\boldsymbol{M}\odot\boldsymbol{W}$ and quantization $\mathrm{Quant}(\boldsymbol{W})$.
Through the application of such functions, we reduce the redundancy within each expert and create several light-weighted slim experts, thus improving their intrinsic efficiency.
However, it is important to note that Expert Slimming primarily focuses on compressing individual experts without addressing the redundancy across multiple experts. This brings us to another aspect of the unified framework, which deals with the structural redundancy present across the expert networks. To achieve comprehensive compression and efficiency, we need to consider both within-expert and across-expert redundancies, which will be explored further in the following sections.

### 4.3 Expert Trimming

Expert Trimming, which removes experts, is complementary to Expert Slimming. Therefore, we include Expert Trimming in our framework to provide a comprehensive view of MoE compression. The core operation of Expert Trimming involves updating the set of remaining experts denoted as $\mathcal{T}\leftarrow\mathcal{T}^{\prime}$, where $\mathcal{T}^{\prime}$ is a subset of the original expert indices $\mathcal{T}$. Specifically, Expert Drop updates the experts and their corresponding routing weights as follows: $\boldsymbol{E}\leftarrow\{\boldsymbol{E}_{i}\}_{i\in\mathcal{T}^{\prime}}$ and $\boldsymbol{G}\leftarrow\boldsymbol{G}_{i\in\mathcal{T}^{\prime}}$.

However, Expert Drop carries the risk of collapsing feature transformation. The absence of certain experts can lead to incorrect selections for given inputs, thereby degrading model performance []. Additionally, partially reducing experts can disrupt routing patterns, negatively impacting the model’s overall efficiency and effectiveness.
Despite its benefits, Expert Drop still retains the costly computation within each expert and the complex communication between experts. These limitations highlight the need for further optimization of Expert Trimming within our unified framework. By systematically analyzing the redundancies and inefficiencies inherent in MoE models, our framework helps identify new design spaces for more efficient approaches, i.e., we propose extending beyond expert-level optimizations to identify new design spaces for efficiency improvements.

Figure: Figure 2: Illustration of Similarity Measurements in Layer Drop. Features for calculating $\boldsymbol{S}^{\text{(M)}}$ and $\boldsymbol{S}^{\text{(NM)}}$ are colored with red and blue, respectively.
Refer to caption: x2.png

We propose two novel techniques: Layer Drop and Block Drop. Layer Drop focuses on removing entire MoE layers, which significantly reduces both computation and communication overhead. Block Drop extends this concept by eliminating entire transformer blocks, including attention layers and MoE layers, within transformer models. These advanced techniques aim to streamline the model architecture, improve performance, and enhance overall efficiency.

#### Layer Drop.

Inspired by [, ], we consider a special scenario of Expert Drop where all experts are dropped ($\mathcal{T}\leftarrow\mathcal{T}^{\prime}=\varnothing$), effectively removing entire MoE layers.
We refer to this approach as Layer Drop. To perform Layer Drop, we use a similarity-based metric where high similarity indicates high redundancy in transformation.
One straightforward metric is the cosine similarity between the input $\boldsymbol{x}$ and the output $\boldsymbol{y}=\mathrm{MoE}(\boldsymbol{x})$:

$$ $\displaystyle\boldsymbol{S}^{\text{(M)}}=\frac{\boldsymbol{x}\cdot\boldsymbol{ y}}{||\boldsymbol{x}||_{2}\ ||\boldsymbol{y}||_{2}},~{}~{}\text{where}~{}~{} \boldsymbol{y}=\mathrm{MoE}(\boldsymbol{x}).$ (8) $$

However, this metric alone does not adequately capture the impact of the MoE layer within the context of a transformer block, which includes a layer normalization module ("Norm") [] and residual connections [].
To address this, we propose concurrently removing both the $\mathrm{MoE}$ and $\mathrm{Norm}$ layers. This approach ensures that the similarity metric more accurately reflects the combined functionality of these layers, allowing for a more precise identification of redundancy and a streamlined model architecture, as illustrated in Figure 1. By considering the similarity between the normalized input and output, we can better evaluate the necessity of the MoE layer in the overall architecture:

$$ $\displaystyle\boldsymbol{S}^{\text{(NM)}}=\frac{\boldsymbol{x}^{\prime}\cdot \boldsymbol{y}^{\prime}}{||\boldsymbol{x}^{\prime}||_{2}\ ||\boldsymbol{y}^{ \prime}||_{2}},~{}~{}\text{where}~{}~{}\boldsymbol{y}^{\prime}=\boldsymbol{x}^ {\prime}+\text{MoE}(\text{Norm}(\boldsymbol{x}^{\prime})).$ (9) $$

#### Block Drop.

Within a transformer block, Layer Drop removes the MoE layers but retains the computation-costly attention layers [, ]. To address this issue, we further utilize the same similarity-based metrics to investigate whether the attention layer can be dropped without a significant performance drop. If feasible, this allows us to drop the entire block within MoE models, thus enhancing efficiency.
We introduce Block Drop as an extension of Layer Drop, which also removes the attention layers.

Compared to Expert Drop, both Layer Drop and Block Drop focus on structures beyond expert-level. Additionally, we summarize the efficiency contributions of all the discussed Expert Slimming and Expert Trimming methods in Table 1, highlighting the unique advantages of each approach. Since Expert Trimming is complementary to Expert Slimming, they can be seamlessly integrated to compress both individual experts and high-level structures, further enhancing overall efficiency.

## 5 Experiments

In this section, we first evaluate Expert Slimming and Expert Trimming separately, then investigate their integration for further efficiency. Lastly, we discuss the potential of future works inspired by our proposed framework and experimental results.
Implementation details are provided in Appendix A.

### 5.1 Expert Slimming

**Table 2: Performance of Pruning on MoE. We consider two mainstream pruning methods (i.e., Wanda [] and SparseGPT []) under $50\%$ unstructured sparsity and $2$:$4$ semi-structured sparsity.**
| Mixtral-8$\times$7B |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Method | Sparsity | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | $0\%$ | 59.4 | 84.2 | 84.0 | 67.9 | 46.8 | 83.8 | 70.4 | 75.6 | 71.5 |
| Wanda |  | 56.1 | 85.8 | 81.7 | 64.3 | 46.4 | 82.2 | 65.0 | 76.0 | 69.7 |
| SparseGPT | $50\%$ | 56.4 | 85.7 | 81.5 | 64.6 | 45.0 | 82.4 | 66.8 | 75.8 | 69.8 |
| \hdashlineWanda |  | 51.4 | 79.4 | 77.8 | 60.3 | 44.0 | 80.7 | 65.3 | 74.1 | 66.6 |
| SparseGPT | $2$:$4$ | 49.2 | 81.0 | 77.6 | 59.2 | 44.0 | 80.6 | 63.9 | 74.8 | 66.3 |
| DeepSeek-MoE-16B |  |  |  |  |  |  |  |  |  |  |
| Method | Sparsity | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | $0\%$ | 48.1 | 72.4 | 77.3 | 37.9 | 44.0 | 80.4 | 63.9 | 70.3 | 61.8 |
| Wanda |  | 43.6 | 74.3 | 72.6 | 31.1 | 43.0 | 79.5 | 58.1 | 69.4 | 59.0 |
| SparseGPT | $50\%$ | 43.9 | 73.5 | 74.0 | 33.8 | 41.4 | 79.0 | 61.0 | 68.3 | 59.4 |
| \hdashlineWanda |  | 38.2 | 66.1 | 67.5 | 27.6 | 39.4 | 77.0 | 53.8 | 66.7 | 54.5 |
| SparseGPT | $2$:$4$ | 43.1 | 68.9 | 71.6 | 27.6 | 41.6 | 78.3 | 57.4 | 66.6 | 56.9 |

#### Pruning Maintains Performance but Faces Deployment Limitations.

In Table 2, we evaluate representative pruning algorithms (i.e., Wanda [], SparseGPT []) on Mixtral-8$\times$7B and DeepSeek-MoE-16B. Since DeepSeek-MoE-16B utilizes both shared experts and normal experts, we conduct an ablation study on whether to prune shared experts, as discussed in Appendix D.
We find that unstructured pruning preserves more than $95\%$ of performance. However, it is not compatible with existing hardware. Conversely, the hardware-friendly semi-structured pruning (i.e., $4$:$8$ and $2$:$4$ patterns) undergoes a significant performance drop. Nevertheless, according to Lu et al. [], semi-structured sparsity is ineffective in speeding up MoE models.

**Table 3: Performance of Quantization on MoE. We utilize GPTQ [] and AWQ [] as the quantization methods for 4-bit compression.**
| Mixtral-8$\times$7B |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Method | Bits | Memory | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | $16$ | 87.7GB | 59.4 | 84.2 | 84.0 | 67.9 | 46.8 | 83.8 | 70.4 | 75.6 | 71.5 |
| \hdashlineGPTQ |  |  | 59.0 | 84.4 | 83.4 | 67.1 | 45.2 | 83.1 | 70.1 | 75.2 | 70.9 |
| AWQ | $4$ | 24.4GB | 58.4 | 84.2 | 83.3 | 66.6 | 45.8 | 83.0 | 69.0 | 76.3 | 70.8 |
| DeepSeek-MoE-16B |  |  |  |  |  |  |  |  |  |  |  |
| Method | Bits | Memory | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | $16$ | 30.8GB | 48.1 | 72.4 | 77.3 | 37.9 | 44.0 | 80.4 | 63.9 | 70.3 | 61.8 |
| \hdashlineGPTQ |  |  | 46.3 | 71.8 | 76.8 | 36.4 | 43.4 | 80.0 | 63.9 | 70.2 | 61.1 |
| AWQ | $4$ | 9.8GB | 46.8 | 71.2 | 76.6 | 36.4 | 43.6 | 80.1 | 62.1 | 70.1 | 60.9 |

#### Quantization Demonstrates Promising Performance and Efficiency.

In Table 3, we evaluate the impact of 4-bit quantization on MoE. Quantization offers two major benefits: it maintains the comparable performance of the original models and significantly reduces memory costs. Specifically, the quantized models achieve over $98\%$ of the original performance while using less than $30\%$ of the memory.
Moreover, when quantized with AWQ [], Mixtral-8$\times$7B and DeepSeek-MoE-16B achieve impressive speedups of $\times 5.08$ and $\times 3.16$, respectively. This demonstrates that 4-bit quantization is an effective technique for deploying MoE models in resource-constrained environments.

### 5.2 Expert Trimming

Figure: Figure 3: Evaluation of Expert Drop. We consider two strategies: layer-wise (dotted lines) and global (solid lines).
Refer to caption: x3.png

#### Expert Drop Degrades Performance and Offers Limited Efficient Gains.

While experts are specific structures in MoE, not all experts hold equal significance. Figure 9 visualizes the distribution of expert-wise importance scores, highlighting this variability. To systematically drop experts at varying proportions, we conduct experiments using both layer-wise and global dropping approaches (see Appendix A.3). Given the importance of shared experts in DeepSeek-MoE-16B, we only dropped normal experts. Under both settings, Expert Drop causes consistent performance degradation. For example, dropping $25\%$ of experts in Mixtral-8$\times$7B results in a $23\%$ performance drop on the MMLU task.

Figure: Figure 4: Layer-Wise Similarity. We consider two scenarios, i.e., for “MoE” and “Norm + MoE”.
Refer to caption: x4.png

The efficiency improvement from Expert Drop is also marginal. For instance, dropping $12.5\%$ of experts results in less than a $1\%$ speedup, despite significant performance losses. More results are available in Appendix E.

#### Layer Drop Preserves the Performance Efficiently.

To verify the feasibility of Layer Drop, we visualize feature similarity across different modules in Figure 4. This visualization shows a high level of similarity between the inputs of the MoE layer normalization module (Norm) and the outputs of the MoE layer. In contrast, the low similarity between the inputs and outputs of MoE layers indicates the infeasibility of removing only the MoE layers.
Results from Figure 5 show that Layer Drop preserves performance within a wide range of compression ratio, e.g. $1\%$ performance drop on MMLU when dropping 8 layers for Mixtral-8$\times$7B, revealing significant redundancy in MoE layers.

Figure: Figure 5: Evaluation of Layer Drop. We show results on Mixtral-8$\times$7B and DeepSeek-MoE-16B (solid lines), along with the baseline and random guess performances (dotted lines).
Refer to caption: x5.png

Figure: Figure 6: Evaluation of Block Drop. We show results on Mixtral-8$\times$7B and DeepSeek-MoE-16B (solid lines), along with the baseline and random guess performances (dotted lines).
Refer to caption: x6.png

#### Block Drop Further Promotes Efficiency.

While Layer Drop maintains the performance of the original models, it still retains the computation-costly attention layers. To address this, we extend the approach by dropping larger structures, specifically blocks that include both FFN and attention layers.
We first visualized the similarity for different blocks in Figure 8, where both Mixtral-8$\times$7B and DeepSeek-MoE-16B demonstrate high similarity between specific blocks. Based on this, we conduct the empirical study by varying the number of dropped blocks.
Surprisingly, as shown in Figure 6, even after removing 4 blocks, the models maintained over $90\%$ of the original performance. Since Block Drop removes computationally expensive attention layers, it outperforms Layer Drop by a large margin in terms of both memory and inference cost, as illustrated in Figure 8.
By focusing on higher-level structures, Block Drop and Layer Drop provide significant efficiency improvements while maintaining acceptable performance levels.

Figure: Figure 7: Normalized Block-Wise Similarity. We measure the cosine similarity among hidden features between blocks.
Refer to caption: x7.png

### 5.3 Integration of Expert Slimming and Expert Trimming

We further investigate the integration of Expert Slimming and Expert Trimming techniques. Given the superior average performance and practical efficiency of quantization, we use it for Expert Slimming. For Expert Trimming, we include all three methods to offer a comprehensive comparison.

Quantization Preserves the Performance of Expert Trimming.
As shown in Table 4, the integration of Expert Slimming and Expert Trimming significantly enhances overall efficiency. Quantization can be seamlessly combined with three different levels of dropping, achieving comparable performance.
For instance, after quantization, the average performance of Layer Drop and Block Drop is nearly the same, maintaining more than $90\%$ of the performance of the original models.

The Integration Significantly Promotes Efficiency.
For efficiency considerations, we measure speedup, FLOPs, and memory usage. Since the original Mixtral-8$\times$7B cannot be deployed on a single Nvidia A100 GPU, we utilize two GPUs for all models to ensure a fair comparison. In Table 4, quantization promotes efficiency by a large margin. Different Expert Trimming strategies showcase different advantages. Specifically, Expert Drop contributes to reducing memory usage but its speedup is marginal. Layer Drop and Block Drop excel in speedup as illustrated in Figure 8, with Block Drop demonstrating both higher performance and greater speedup. Considering all settings, the combination of Block Drop and quantization offers the best efficiency with comparable performance: a $6.05\times$ speedup with only $20.0$GB memory usage, while maintaining over $92\%$ of the performance on Mixtral-8$\times$7B, making it available to be deployed on a NVIDIA RTX 3090 GPU.

**Table 4: Experimental Results of the Integration of Expert Slimming and Expert Trimming. “-E$n/m$” denotes dropping $n$ out of $m$ experts per MoE layer on average. “-L$n/m$”, “-B$n/m$” represents dropping $n$ out of $m$ corresponding modules with Layer Drop and Block Drop, respectively. The FLOPs are measured using an input with the $2,048$ sequence length.**
| Mixtral-8$\times$7B |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Method | SpeedUp | FLOPs | Memory | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | – | 54.4T | 87.7GB | 59.4 | 84.2 | 84.0 | 67.9 | 46.8 | 83.8 | 70.4 | 75.6 | 71.5 |
| \hdashlinew/AWQ | $5.08\times$ | 54.4T | 24.4GB | 58.4 | 84.2 | 83.3 | 66.6 | 45.8 | 83.0 | 69.0 | 76.3 | 70.8 |
| + E2/8 | $1.02\times$ | 54.4T | 66.7GB | 53.2 | 77.7 | 80.5 | 52.2 | 46.2 | 81.7 | 55.6 | 76.8 | 65.5 |
| \hdashlinew/AWQ | $5.18\times$ | 54.4T | 20.1GB | 50.7 | 79.1 | 78.9 | 52.4 | 44.2 | 81.2 | 55.6 | 75.9 | 64.8 |
| + L8/32 | $1.19\times$ | 42.9T | 66.6GB | 47.7 | 85.3 | 75.2 | 67.3 | 40.0 | 75.8 | 69.7 | 74.6 | 67.0 |
| \hdashlinew/AWQ | $\mathbf{6.05\times}$ | 42.9T | 20.0GB | 46.2 | 84.2 | 74.2 | 66.2 | 39.0 | 75.5 | 69.3 | 74.2 | 66.1 |
| + B5/32 | $1.17\times$ | 46.0T | 74.1GB | 51.3 | 85.3 | 78.7 | 67.9 | 42.0 | 79.3 | 69.7 | 74.3 | 68.6 |
| \hdashlinew/AWQ | $\mathbf{5.94\times}$ | 46.0T | 21.9GB | 50.6 | 85.1 | 77.5 | 66.9 | 41.4 | 76.1 | 71.8 | 74.5 | 68.0 |
| DeepSeek-MoE-16B |  |  |  |  |  |  |  |  |  |  |  |  |
| Method | SpeedUp | FLOPs | Memory | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | – | 11.7T | 30.8GB | 48.1 | 72.4 | 77.3 | 37.9 | 44.0 | 80.4 | 63.9 | 70.3 | 61.8 |
| \hdashlinew/AWQ | $3.16\times$ | 11.7T | 9.8GB | 46.8 | 71.2 | 76.6 | 36.4 | 43.6 | 80.1 | 62.1 | 70.1 | 60.9 |
| + E16/64 | $1.03\times$ | 11.7T | 23.9GB | 45.0 | 67.1 | 75.6 | 31.8 | 42.2 | 80.2 | 59.9 | 70.0 | 59.0 |
| \hdashlinew/AWQ | $3.25\times$ | 11.7T | 7.7GB | 44.0 | 66.0 | 74.5 | 27.9 | 42.6 | 78.5 | 56.3 | 67.3 | 57.1 |
| + L4/28 | $1.14\times$ | 10.6T | 26.6GB | 39.5 | 70.2 | 67.6 | 35.2 | 40.4 | 75.8 | 48.4 | 65.7 | 55.3 |
| \hdashlinew/AWQ | $\mathbf{3.60\times}$ | 10.6T | 8.5GB | 42.1 | 72.0 | 69.2 | 33.7 | 39.8 | 75.1 | 47.7 | 66.5 | 55.8 |
| + B4/28 | $1.16\times$ | 10.1T | 26.4GB | 40.3 | 71.3 | 69.0 | 36.2 | 37.8 | 75.8 | 51.6 | 68.0 | 56.3 |
| \hdashlinew/AWQ | $\mathbf{3.67\times}$ | 10.1T | 8.4GB | 40.1 | 70.2 | 68.6 | 36.1 | 38.4 | 76.2 | 51.6 | 66.4 | 56.0 |

## 6 Discussion

With the advent of open-source LLMs incorporated with MoE (e.g., Mixtral []), the machine learning community has rallied around the philosophy of utilizing MoE to scale large language models and making MoE models more accessible to real-life applications.
Our research delves into making MoE models more efficient and accessible, bringing forth significant discoveries and future pathways:

Expert Slimming Exhibits Superior Compression Performance.
Anthough MoE scales models with multiple experts, it causes excessive memory usage and slows down the inference.
Expert Slimming mitigates this by directly compressing individual experts, significantly promoting inference speed and memory.

Expert Trimming Further Creates Efficient Architectures. Scaling with MoE architectures also introduces redundant structures that showcase highly similar hidden features. Expert Trimming removes unimportant modules and creates more efficient architectures.

Model/Task-Specific Compression. Mixtral and DeepSeek-MoE exhibit different properties of redundancy: compared to Mixtral, DeepSeek-MoE has higher expert-redundancy (more experts with low importance scores in Figure 9) and lower hidden feature similarities at both layer and block levels, which is shown in Figure 4 and 8.
On the other hand, MoE models can be compressed by varying ratios depending on the task. Establishing an under-explored correlation between the specific task and the corresponding optimal compression ratio.

Post-Compression Training. In this work, we compress MoE models in a training-free manner. However, our framework facilitates the acquisition of compressed, efficient MoE architectures that can be continuously trained to enhance performance [, , , ]. This approach enables MoE architectures to be improved in both efficiency and performance.

## 7 Conclusion

In this paper, we introduced a unified framework of MoE compression, facilitating to systematically understand the efficiency issue of MoE and identify the new design space to further improve the performance.
Based on this framework, we propose a comprehensive recipe that integrates Expert Slimming and Expert Trimming to further enhance efficiency. Our proposed methods and insights not only address current challenges but also set the stage for future advancements in the field of MoE.

## Appendix A Implementation Details

### A.1 Models and Datasets

#### Models.

For our experiments, we employed Mixtral-8$\times$7B [] and DeepSeek-MoE-16B [].
Mixtral-8$\times$7B utilizes 8 experts for MoE layers and activates the top two for each input token. In contrast, DeepSeek-MoE-16B employs an MLP in the first block and utilizes two shared experts with additional 64 experts within MoE layers in other blocks.

#### Datasets.

For compression experiments, we used the C4 dataset [], with 128 samples and an input sequence length of 2,048, following the setup in [, , , ]. To evaluate model performance, we report normalized zero-shot accuracy on the LM-harness benchmark, which includes multiple tasks: ARC-C [], BoolQ [], HellaSwag [], MMLU [], OBQA [], PIQA [], RTE [], and WinoGrande []. The evaluation code is based on EleutherAI LM Harness [].

### A.2 Implementation Details of Expert Slimming

Both Expert Slimming methods (i.e., pruning and quantization) require calibration data to estimate input statistics. To control this variable, we use $128$ samples from the C4 dataset [] as the calibration dataset for pruning. For quantization, we follow the default settings of GPTQ (^1^11https://github.com/AutoGPTQ/AutoGPTQ) and AWQ (^2^22https://github.com/casper-hansen/AutoAWQ), using $128$ random samples from Alpaca [] and Pile [], respectively. We use the default group size $128$ for Mixtral-8$\times$7B and $64$ for DeepSeek-MoE-16B.

### A.3 Implementation Details of Expert Drop

The Expert Drop compresses MoE by preserving only important experts $\{\boldsymbol{E}_{i}\}_{i\in\mathcal{T}^{\prime}}$ while removing others, where $\mathcal{T}^{\prime}$ is determined by the importance scores $\{\boldsymbol{S}(\boldsymbol{E}_{i})\}_{i\in\mathcal{T}}$. Following Muzio et al. [], we measure the importance scores through the averaged routing scores of a batched data $\mathcal{X}$, i.e., $\{\boldsymbol{S}(\boldsymbol{E}_{i})\}=\frac{1}{|\mathcal{X}|}\sum_{
\boldsymbol{x}\in\mathcal{X}}\boldsymbol{G}_{i}(\boldsymbol{x})$, and consider two dropping strategies for Expert Drop: layer-wise dropping and global dropping.

Layer-Wise dropping removes the same number of experts for each layer. Given the total number of experts $n=|\mathcal{T}|$ and the preserved number of experts $n^{\prime}=|\mathcal{T}^{\prime}|<n$ in layer $l$, the preserved expert set $\mathcal{T}^{\prime(l)}$ is obtained by:

$$ $\mathcal{T}^{\prime(l)}=\{\boldsymbol{E}_{t}^{(l)}\},\quad\text{where}\quad \boldsymbol{S}(\boldsymbol{E}_{t}^{(l)})\in\mathrm{TopK}(\{\boldsymbol{S}( \boldsymbol{E}_{i}^{(l)})\}_{i=1}^{n},n^{\prime}).$ (10) $$

Global dropping constrains the total number of preserved experts for the entire model. Given the total number of layers $L$ in the model, the preserved expert set $\mathcal{T}^{\prime(l)}$ for layer $l$ is obtained by:

$$ $\mathcal{T}^{\prime(l)}=\{\boldsymbol{E}_{t}^{(l)}\},\quad\text{where}\quad \boldsymbol{S}(\boldsymbol{E}_{t}^{(l)})\in\mathrm{TopK}\Big{(}\bigcup_{j=1}^{ m}\{\boldsymbol{S}(\boldsymbol{E}_{i}^{(j)})\}_{i=1}^{n},n^{\prime}L\Big{)}.$ (11) $$

For the integration of Expert Slimming and Expert Trimming, we choose the global dropping as the strategy of Expert Drop, which shows competitive performance compared to the layer dropping for Mixtral-8$\times$7B under low dropping ratios, as well as consistent better performance for DeepSeek-MoE-16B in Figure 13.

## Appendix B Analysis on the Dropping Patterns

In this section, we make further analysis on the dropping patterns of Expert Trimming methods.

### B.1 Expert Drop

Figure: Figure 9: Distribution of Normalized Importance Scores $\boldsymbol{S}$ for Expert Drop. We highlight the density of scores under different drop ratios with different colors.
Refer to caption: x9.png

#### Score Distribution Directs Expert Drop.

The distribution of importance scores is informative to determine the proportion of dropped experts. In Figure 9, we visualize the score distribution of Expert Drop for Mixtral-8$\times$7B and DeepSeek-MoE-16B, respectively. DeepSeek-MoE-16B, which allocates more experts, shows a left-skewed distribution where more experts have low importance scores. In contrast, Mixtral-8$\times$7B demonstrates a right-skewed distribution, with only a few experts being deemed unimportant. This significantly different distribution results in different resistance capability against Expert Drop, where DeepSeek-MoE-16B can drop much more experts than Mixtral-8$\times$7B while maintaining competitive performance, as demonstrated in Table 4 and Figure 13.

Figure: Figure 10: Distribution of Dropped Experts for Expert Drop. We visualize of the dropped experts under different drop ratios, where the dropped experts are colored from yellow to blue as the drop ratio increases.
Refer to caption: x10.png

#### Global Expert Drop Removes Experts Fine-Grainedly.

We employed two different strategies for Expert Drop, namely layer-wise and global. Layer-wise dropping treats each layer equally by dropping the same number of experts, while global dropping results in different proportions of remaining experts across layers. We visualize the distribution of remaining experts after global dropping in Figure 10. We find the global dropping shows a more fine-grained pattern on dropping experts, where the bottom layers are more vulnerable under lower dropping ratios (yellow part).

### B.2 Layer Drop & Block Drop

Figure: (a) Layer Drop
Refer to caption: x11.png

Figure 11 visualizes the remaining and dropped layers/blocks as the number of dropped modules increases. Both MoE architectures exhibit similar patterns in Layer Drop and Block Drop: initially, both models tend to drop the deeper layers, followed by the shallower ones. These findings are consistent with Xu et al. [], which suggests that deeper layers tend to be more redundant.

## Appendix C Ablation Study on the Data Choices

The routing scores in MoE models exhibit a significant correlation with the input data, as evidenced by [, , ]. This relationship underscores the importance of data selection in the application of Expert Drop, which assesses the importance of experts by examining their routing scores. Similarly, the same question holds for Layer Drop and Block Drop: Does data selection affect the feature similarity across different layers? To address this, we performed ablation studies on Mixtral-8$\times$7B, scrutinizing both the number of samples and the dataset types used for feature extraction, to determine how data choice impacts decisions to drop layers or blocks. Results are shown in Figure 12.

Figure: (a) Similarities with different number of samples.
Refer to caption: x13.png

#### Layer Drop and Block Drop are Data Robust.

In Figure 12(a), we note that feature similarity remains relatively stable across different layers as the sample size increases, indicating that Layer Drop and Block Drop maintain consistency regardless of sample quantity. This confirms that using $128$ samples suffices for computing similarity, which is adopted for all our experiments. Similarly, Figure 12(b) shows that varying the datasets, from pretraining with C4 to instruction tuning with Lima and MetaMathQA, does not significantly alter feature similarity. This demonstrates the resilience of Layer Drop and Block Drop to variations in data distribution.

## Appendix D Ablation Study on Shared Experts in DeepSeek-MoE-16B

While most MoE models follow Equation 2 to implement the experts, models like DeepSeek-MoE-16B adopt a residual [] form of experts, which brings a special scenario to discuss. In the residual MoE, an extra set of $m$ shared experts $\left\{\bar{\boldsymbol{E}}_{1},\bar{\boldsymbol{E}}_{2},\dots,\bar{
\boldsymbol{E}}_{m}\right\}$ are always selected by the router $\boldsymbol{G}$ and activated for all inputs. Given an input $\boldsymbol{x}$, the output can be represented as a degenerated form of Equation 2, where the scores of shared experts are fixed to $1$:

$$ $\boldsymbol{y}=\sum\nolimits_{i\in\mathcal{K}}{\boldsymbol{G}(\boldsymbol{x})_ {i}\cdot\boldsymbol{E}_{i}(\boldsymbol{x})}+\sum\nolimits_{j=1}^{m}{\bar{ \boldsymbol{E}}_{j}(\boldsymbol{x})}.$ (12) $$

This special form of expert routing may bring a difference in the redundancy distribution of MoE. Here we discuss the influence of shared experts through pruning and present the results in Table 5. We find that pruning without the shared experts will boost the performance at a considerable scale, i.e., $+3.6\%$ and $+1.5\%$ of the averaged accuracy for unstructured pruning with Wanda and SparseGPT, respectively. This finding reveals a different pattern of the inner redundancy in that the shared experts are less compressible compared to the others in residual MoE models, which may inform future work.

**Table 5: Ablation Study of Pruning Shared Experts on DeepSeek-MoE-16B. We consider two scenarios, i.e., pruning both shared experts and normal experts (“w/Pruning Shared Experts”) and pruning normal experts only (“w/o Pruning Shared Experts”). We use two mainstream pruning methods (i.e., Wanda [] and SparseGPT []) under both unstructured sparsity ($50\%$) and semi-structured sparsity ($2$:$4$).**
| DeepSeek-MoE-16B |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Method | Sparsity | ARC-C | BoolQ | HellaSwag | MMLU | OBQA | PIQA | RTE | WinoGrande | Avg. |
| Baseline | $0\%$ | 48.1 | 72.4 | 77.3 | 37.9 | 44.0 | 80.4 | 63.9 | 70.3 | 61.8 |
| w/ Pruning Shared Experts |  |  |  |  |  |  |  |  |  |  |
| Wanda |  | 43.6 | 74.3 | 72.6 | 31.1 | 43.0 | 79.5 | 58.1 | 69.4 | 59.0 |
| SparseGPT | $50\%$ | 43.9 | 73.5 | 74.0 | 33.8 | 41.4 | 79.0 | 61.0 | 68.3 | 59.4 |
| \hdashlineWanda |  | 38.2 | 66.1 | 67.5 | 27.6 | 39.4 | 77.0 | 53.8 | 66.7 | 54.5 |
| SparseGPT | $2$:$4$ | 43.1 | 68.9 | 71.6 | 27.6 | 41.6 | 78.3 | 57.4 | 66.6 | 56.9 |
| w/o Pruning Shared Experts |  |  |  |  |  |  |  |  |  |  |
| Wanda |  | 44.0 | 76.3 | 73.5 | 36.2 | 41.0 | 79.3 | 59.9 | 70.2 | 60.0 |
| SparseGPT | $50\%$ | 45.0 | 75.5 | 74.4 | 36.3 | 41.0 | 79.4 | 64.3 | 69.3 | 60.7 |
| \hdashlineWanda |  | 40.1 | 75.7 | 69.9 | 33.5 | 40.0 | 77.9 | 58.8 | 68.6 | 58.1 |
| SparseGPT | $2$:$4$ | 40.7 | 75.7 | 69.9 | 33.3 | 39.0 | 77.7 | 61.4 | 69.4 | 58.4 |

## Appendix E Full Experimental Results

We provide the full results of Expert Trimming, including Expert Drop, Layer Drop and Block Drop, in Figure 13, 14, and 15, respectively.

Figure: Figure 13: Full Results for Expert Drop. We consider two strategies: layer-wise (dotted lines) and global (solid lines).
Refer to caption: x15.png

Figure: Figure 14: Full Results for Layer Drop. We show results on Mixtral-8$\times$7B and DeepSeek-MoE-16B (solid lines), along with the baseline and random guess performances (dotted lines).
Refer to caption: x17.png

Figure: Figure 15: Full Results for Block Drop. We show results on Mixtral-8$\times$7B and DeepSeek-MoE-16B (solid lines), along with the baseline and random guess performances (dotted lines).
Refer to caption: x18.png

## Peer Reviews

confidence: 3
contribution: 1
initial_rating: 5
presentation: 3
questions: See weeknesses
soundness: 3
strengths: Pros.
1.	Expert Trimming and Expert Slimming are introduced in the paper and are well-studied comprehensively. 
2.	The evaluation result of Expert Trimming analyzes the impact of different compression methods, including Expert Drop, Layer Drop, and Block Drop. The analysis provides the instructive meaning to choose the compression method of Expert Trimming.
3.	The comprehensive compression performance comprised of Expert Trimming and Expert Slimming is provided.
summary: This paper presents a comprehensive study on compression techniques for Mixture of Experts (MoE) architectures to enhance efficiency and scalability in large language models. The authors propose Expert Trimming strategies like Layer Drop and Block Drop, which remove entire MoE layers and transformer blocks, and Expert Slimming to compress individual experts, all aimed at reducing computational costs and memory usage while preserving high performance. Experimental results demonstrate that these methods achieve a 6.05× speedup and 77.1% reduced memory usage, maintaining over 92% of the performance on the Mixtral-8×7B model, offering a promising solution for real-world deployment challenges.
weaknesses: Cons.
1.	The novelty is a big concern. The proposed method is a combination of existing works.
2.	The baselines of SOTA works are expected in the table to show the effectiveness of the proposed methods.

---

confidence: 4
contribution: 2
initial_rating: 5
presentation: 3
questions: N/A
soundness: 2
strengths: 1. The paper is well-written.
2. The figures are easy to understand and visually appealing.
3. The observations related to expert trimming are meaningful, and the trade-offs between expert drop, layer drop, and block drop are well-considered.
summary: This work investigates compression techniques for MoE, including Layer Drop and Block Drop, which remove MoE layers and transformer blocks, respectively, enhancing efficiency without compromising performance.
weaknesses: 1. The approach presented is straightforward, combining expert/layer/block drop with quantization to compress the MoE model. While the authors claim to introduce two novel techniques, Layer Drop and Block Drop, these methods are not truly new [1].
2. In line 371, the authors state, "Mixtral-8×7B maintains over 90% of the original performance"; however, would training from scratch with a similarly compact architecture also achieve comparable accuracy? Authors could conduct an ablation study comparing their compressed model to a model trained from scratch with a similar architecture. 
3. Additionally, the authors propose simultaneously removing both the MoE and Norm layers, yet this strategy lacks sufficient novelty or justification. Authors may conduct ablation studies showing the impact of removing each layer type individually vs. together.
4. There are also typos in lines 311 and 312: “In this section, we evaluate the effectiveness of Expert Trimming techniques." Additionally, there's an extra "-" in line 264.
5. Regarding the results, Table 3 indicates that the combined use of Expert Trimming and Expert Slimming (quantization) provides advantages over using only AWQ. However, the performance improvement is marginal. Please discuss the practical significance of these marginal improvements.
6. There is no clear conclusion about which expert trimming is the best. The authors can include a more discussion. This could help readers quickly understand the trade-offs between the different approaches in terms of performance, efficiency, and ease of implementation.

[1] Reducing transformer depth on demand with structured dropout.

---

confidence: 4
contribution: 2
initial_rating: 3
presentation: 3
questions: 1. In line 292, "we assess its importance score by evaluating the similarity between its inputs x_l and outputs y_l", are x and y here similar as the x' and y' not x and y in layer drop?

2. Regarding Figure 3, it’s intriguing that the layer-wise expert drop consistently surpasses global strategies at high drop percentages. Could there be any underlying mechanism or explanation for why this approach maintains performance better?

3. On the training pipeline for LLMs, the typical stages are: (1) pretraining, (2) supervised fine-tuning (SFT), and (3) alignment. Based on the authors' findings, in which of these stages might the proposed pruning method be most effectively implemented?

4. This proposed expert or layer pruning method utilizes static pruning. Are there any reasons why dynamic pruning, which adjusts layers for different tokens, was not considered? or any comparisons?

5. From Table 3, there appears to be a performance discrepancy between Mistral MoE and DeepSeek MoE. Specifically, block drop or layer drop methods seem to perform considerably worse on DeepSeek. Could there be an underlying reason for this difference? So I am very confuse of the authors' conclusion that "in Layer Drop and Block Drop excel in speedup as illustrated in Figure 8, with Block Drop demonstrating both higher performance and greater speedup".
soundness: 3
strengths: LLMs efficiency is an very important topic for the deployment of large language models. The idea proposed in this paper is simple.
The paper is clearly written.
summary: This paper propose a pruning method for MoE LLMs including experts trimming: layer drop and block drop and Expert slimming: other parameter pruning or quantization strategy. Experiments on some LLM benchmarks are provided.
weaknesses: 1. Some typos: 
(1) line 304: Expert Slimmingand -> Expert Slimming and
(2) line 311: n this Section -> In this Section
(3) line 311: Expert Trimmingtechniques -> Expert Trimming techniques
(4) line 43:  tandard MoE -> Standard MoE
(5) line264: efficiency. - -. efficiency.

2. The primary issue seems to be the paper's contributions. Expert Trimming, as implemented, is essentially layer pruning for LLMs, whether using layer drop or block drop techniques. Additionally, expert slimming does not appear to be a novel contribution here. Given this, the paper's contributions feel somewhat limited in scope.

3. Lack of comparison of important baselines. I believe there are many layer pruning baseline methods, It is important to give some comparisons in experiments.