Prune-then-Quantize or Quantize-then-Prune? Understanding the Impact of Compression Order in Joint Model Compression

Minjun Kim; Jaehyeon Choi; Hyunwoo Yang; Jongjin Kim; Jinho Song; U Kang

cs.AIMar 19, 2026

Prune-then-Quantize or Quantize-then-Prune? Understanding the Impact of Compression Order in Joint Model Compression

Authors: Minjun Kim, Jaehyeon Choi, Hyunwoo Yang, Jongjin Kim, Jinho Song, U Kang

Organizations: Seoul National University, Seoul, South Korea

Abstract

What happens when multiple compression methods are combined-does the order in which they are applied matter? Joint model compression has emerged as a powerful strategy to achieve higher efficiency by combining multiple methods such as pruning and quantization. A central but underexplored factor in joint model compression is the compression order, or the sequence of different methods within the compression pipeline. Most prior studies have either sidestepped the issue by assuming orthogonality between techniques, while a few have examined them only in highly constrained cases. Consequently, the broader role of compression order in shaping model performance remains poorly understood. In this paper, we address the overlooked problem of compression order and provide both theoretical and empirical analysis. We formulate the problem of optimizing the compression order and introduce the Progressive Intensity Hypothesis, which states that weaker perturbations should precede stronger ones. We provide theoretical guarantees showing that the relative benefit of one order increases with the underlying performance gap. Extensive experiments on both language and vision models validate the hypothesis, and further show its generality to broader setups such as multi-stage compression and mixed-precision quantization.

Figures & tables

Panel of Figure 1 — Figure 1: The Progressive Intensity Hypothesis: Given two compression techniques, we conjecture that compressed models perform better if the stronger method is applied after the weaker one. That said, the optimal order between pruning and quantization varies with their compression ratios.

Figure 2: A case study of pruning

\mathcal{P}(\cdot)

and quantization

\mathcal{Q}(\cdot)

on model

\phi

. (a) if pruning granularity (green) is coarser or equal to quantization granularity (orange), disjoint selectivity holds. (b) Otherwise, partial removal of quantization units by pruning introduces extra error, termed interference

\Delta

Panel of Figure 3 — Figure 3: Across diverse language models, the compression order advantage $\mathcal{A}\big(\mathcal{Q}\rightarrow\mathcal{P}\big)$ increases monotonically with the CER difference $C^{*}_{\mathcal{P}}-C_{\mathcal{Q}}$ . See Section 5.2 for details.

Figure 4: Compression order advantage $\mathcal{A}\big(\mathcal{Q}\rightarrow\mathcal{P}\big)$ against CER difference $C^{*}_{\mathcal{P}}-C_{\mathcal{Q}}$ for three pruning $\mathcal{P}(\cdot)$ and four quantization $\mathcal{Q}(\cdot)$ methods on a LLaMA 3 8B model. Our hypothesis consistently holds for language models regardless of pruning granularity, rotation, and weight updates.

Figure 5: Rotation impact on pruning. See Section 5.2 for details.

$C_{\mathcal{Q}}$ $(B_{\mathcal{Q}})$	SparseGPT	SLEB
1.78 (9)	0.002	0
2.00 (8)	0.001	0
2.28 (7)	-0.003	0
2.68 (6)	-0.013	0
3.20 (5)	-0.017	-0.057
4.00 (4)	-49.899	-9.379

Table 1:

\mathcal{A}\big(\mathcal{Q}\rightarrow\mathcal{P}\big)

by quantization ratio

C_{\mathcal{Q}}

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description
$\phi$	A pre-trained model
$\phi^{\prime}$	A compressed model
$f(\cdot)\in\mathbb{F}$	Compression method from a set $\mathbb{F}$
$C$	Compression ratio
$\mathcal{M}(\cdot)$	Performance metric
$\mathbf{W}_{i},\mathbf{X}_{i}$	Weight and activation matrices of layer $l_{i}$ , respectively

Appendix

Table 2: Frequently used notations.

Figure 11: We partition all units

u

into four disjoint groups. Only groups

\mathbb{G}_{1}

and

\mathbb{G}_{2}

influence

\mathcal{A}\big(f_{1}\rightarrow f_{2}\big)

Compression	Modality	Target Models	Baseline Methods
Pruning $\mathcal{P}(\cdot)$	Language models	Decoder-only models	SparseGPT ( Frantar and Alistarh, 2023 ) , Wanda ( Sun et al., 2024 ) , SLEB ( Song et al., 2024 )
	Language models	Encoder-based models	K-prune ( Park et al., 2024 )
	Vision models	CNNs	PRACTISE ( Wang and Wu, 2023 )
	Vision models	ViTs	SAViT ( Chuanyang et al., 2022 )
Quantization $\mathcal{Q}(\cdot)$	Language models	Decoder-only models	RTN ( Gupta et al., 2015 ) , OPTQ ( Frantar et al., 2023 ) , QuaRoT ( Ashkboos et al., 2024b )
	Language models	Encoder-based models	UniQuanF ( Park et al., 2025a )

Appendix

Table 3: Baseline methods covered in our experiments across different settings.

Panel of Figure 12 — Figure 12: The compression order advantage $\mathcal{A}\big(\mathcal{Q}\rightarrow\mathcal{P}\big)$ increases monotonically with the CER difference $C^{*}_{\mathcal{P}}-C_{\mathcal{Q}}$ also for Mistral herd models. See Appendix D.1 for details.

Figure 13: The hypothesis holds for encoder-based language models. See Appendix D.2 for details.

Panel of Figure 14 — Figure 14: Commonsense reasoning task performance of a LLaMA 3 8B model for SparseGPT and QuaRot. See Appendix D.3 for details.

Pruning Ratio	SLEB			SparseGPT
Pruning Ratio	No rotation	Rotation	Difference	No rotation	Rotation	Difference
Original	6.137
0.05	6.857	6.871	0.014	6.140	6.154	0.014
0.1	8.792	8.828	0.036	6.159	6.205	0.046
0.15	12.603	12.615	0.012	6.213	6.352	0.139
0.2	25.289	25.295	0.006	6.330	6.629	0.299

Appendix

Table 4: WikiText-2 perplexity comparison of a LLaMA 3 8B model pruned by SLEB ( Song et al., 2024 ) and SparseGPT ( Frantar and Alistarh, 2023 ) under varying pruning ratios, with and without rotation following QuaRot ( Ashkboos et al., 2024b ) . See Section D.4 for details.

Figure 15: Two cases of errors when pruning rotated units. See Section D.4 for details.

Figure 16: If the number of pruned units increases by one, the change in unit allocation across groups fall into three distinct cases. See Appendix D.6 for details.

Model Compression

Model compression reduces the storage, computation, or latency of machine-learning models while preserving task performance.

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Prune-Quantize-Distill: An Ordered Pipeline for Efficient Neural Network Compression

Longsheng Zhou, Yu Shen

Institute of Advanced Technology University of Science and Technology of China Hefei, China · Supercomputing Center University of Science and Technology of China Hefei, China

Neural Network Compression Efficient Neural Network Inference Neural Network Pruning

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Modern deployment often requires trading accuracy for efficiency under tight CPU and memory constraints, yet common compression proxies such as parameter count or FLOPs do not reliably predict wall-clock inference time. In particular, unstructured sparsity can reduce model storage while failing to accelerate (and sometimes slightly slowing down) standard CPU execution due to irregular memory access and sparse kernel overhead. Motivated by this gap between compression and acceleration, we study a practical, ordered pipeline that targets measured latency by combining three widely used techniques: unstructured pruning, INT8 quantization-aware training (QAT), and knowledge distillation (KD). Empirically, INT8 QAT provides the dominant runtime benefit, while pruning mainly acts as a capacity-reduction pre-conditioner that improves the robustness of subsequent low-precision optimization; KD, applied last, recovers accuracy within the already constrained sparse INT8 regime without changing the deployment form. We evaluate on CIFAR-10/100 using three backbones (ResNet-18, WRN-28-10, and VGG-16-BN). Across all settings, the ordered pipeline achieves a stronger accuracy-size-latency frontier than any single technique alone, reaching 0.99-1.42 ms CPU latency with competitive accuracy and compact checkpoints. Controlled ordering ablations with a fixed 20/40/40 epoch allocation further confirm that stage order is consequential, with the proposed ordering generally performing best among the tested permutations. Overall, our results provide a simple guideline for edge deployment: evaluate compression choices in the joint accuracy-size-latency space using measured runtime, rather than proxy metrics alone.

Abstract

Model Compression

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