# PRIME: Frequency-Aware Unified Pruning and Merging for MoE Compression

arXiv: https://arxiv.org/abs/2610.13982 · HTML: https://mlsanity.com/paper/2610.13982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 27 of 27)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Not All Experts are Equal: Efficient Expert Pruning and Skipping for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2402.14800/) (2024)
- [Merge, Then Compress: Demystify Efficient SMoE with Hints from Its Routing Policy](https://mlsanity.com/paper/2310.01334/) (2023)
- [Task-Specific Expert Pruning for Sparse Mixture-of-Experts](https://mlsanity.com/paper/2206.00277/) (2022)
- [MoE-Pruner: Pruning Mixture-of-Experts Large Language Model using the Hints from Its Router](https://mlsanity.com/paper/2410.12013/) (2024)
- [Efficient Expert Pruning for Sparse Mixture-of-Experts Language Models: Enhancing Performance and Reducing Inference Costs](https://mlsanity.com/paper/2407.00945/) (2024)
- [REAP the Experts: Why Pruning Prevails for One-Shot MoE compression](https://mlsanity.com/paper/2510.13999/) (2025)
- [Mixture Compressor for Mixture-of-Experts LLMs Gains More](https://mlsanity.com/paper/2410.06270/) (2024)
- [Diversifying the Expert Knowledge for Task-Agnostic Pruning in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2407.09590/) (2024)
- [Retraining-Free Merging of Sparse MoE via Hierarchical Clustering](https://mlsanity.com/paper/2410.08589/) (2024)
- [DiEP: Adaptive Mixture-of-Experts Compression through Differentiable Expert Pruning](https://mlsanity.com/paper/2509.16105/) (2025)
- [MergeMoE: Efficient Compression of MoE Models via Expert Output Merging](https://mlsanity.com/paper/2510.14436/) (2025)
- [Cluster-Driven Expert Pruning for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2504.07807/) (2025)

## Abstract (arXiv)

Mixture-of-Experts (MoE) models have emerged as an effective paradigm for scaling large language models, yet their massive parameter footprint poses severe memory challenges for deployment. Existing compression methods typically treat expert pruning and merging as disjoint operations and rely on greedy heuristics, often leading to irreversible information loss or representational pollution. In this paper, we propose PRIME, a unified optimization framework for MoE compression via adaptive PRunIng and MErging. PRIME casts the discrete prune-merge assignment step as a global Integer Linear Programming over a frequency-weighted surrogate objective, jointly selecting pruning and merging decisions while accounting for expert usage. We motivate the frequency-aware objective through an error-bound analysis under fixed representative assignments, and show that the formulation favors high-frequency experts as centroids, promoting routing stability. Extensive experiments on Qwen3-30B-A3B and Qwen3.5-122B-A10B demonstrate that PRIME achieves strong accuracy retention across knowledge, coding, math, and long-context tasks, while serving benchmarks of merged models quantify the memory and throughput benefits of expert compression in vLLM.