# A Provably Effective Method for Pruning Experts in Fine-tuned Sparse Mixture-of-Experts

arXiv: https://arxiv.org/abs/2405.16646 · HTML: https://mlsanity.com/paper/2405.16646/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 58 of its 69 references that are in the map.
- First posted on arXiv 26 May 2024.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 30 of 58)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [PaLI: A Jointly-Scaled Multilingual Language-Image Model](https://mlsanity.com/paper/2209.06794/) (2022)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [BASE Layers: Simplifying Training of Large, Sparse Models](https://mlsanity.com/paper/2103.16716/) (2021)

## Built on by (most cited first, 21 of 21)

- [MoE-Pruner: Pruning Mixture-of-Experts Large Language Model using the Hints from Its Router](https://mlsanity.com/paper/2410.12013/) (2024)
- [A Survey on Inference Optimization Techniques for Mixture of Experts Models](https://mlsanity.com/paper/2412.14219/) (2024)
- [Diversifying the Expert Knowledge for Task-Agnostic Pruning in Sparse Mixture-of-Experts](https://mlsanity.com/paper/2407.09590/) (2024)
- [Dropping Experts, Recombining Neurons: Retraining-Free Pruning for Sparse Mixture-of-Experts LLMs](https://mlsanity.com/paper/2509.10377/) (2025)
- [Unveiling Super Experts in Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2507.23279/) (2025)
- [MoE Pathfinder: Trajectory-driven Expert Pruning](https://mlsanity.com/paper/2512.18425/) (2025)
- [SHAPE: Coalition-Aware Expert Pruning for Sparse Mixture-of-Experts LLMs](https://mlsanity.com/paper/2606.09886/) (2026)
- [How Can Mamba Learn In Context with Outliers and Generalize Provably?](https://mlsanity.com/paper/2510.00399/) (2025)
- [Guided by the Experts: Provable Feature Learning Dynamic of Soft-Routed Mixture-of-Experts](https://mlsanity.com/paper/2510.07205/) (2025)
- [Efficient Quantization of Mixture-of-Experts with Theoretical Generalization Guarantees](https://mlsanity.com/paper/2604.06515/) (2026)
- [Does a Global Perspective Help Prune Sparse MoEs Elegantly?](https://mlsanity.com/paper/2604.06542/) (2026)
- [dMoE: dLLMs with Learnable Block Experts](https://mlsanity.com/paper/2605.30876/) (2026)
- [Federated Fine-Tuning of Sparsely-Activated Large Language Models on Resource-Constrained Devices](https://mlsanity.com/paper/2508.19078/) (2025)
- [MoEITS: A Green AI approach for simplifying MoE-LLMs](https://mlsanity.com/paper/2604.10603/) (2026)
- [QoS-Efficient Serving of Multiple Mixture-of-Expert LLMs Using Partial Runtime Reconfiguration](https://mlsanity.com/paper/2505.06481/) (2025)
- [SlimMoE: Structured Compression of Large MoE Models via Expert Slimming and Distillation](https://mlsanity.com/paper/2506.18349/) (2025)
- [Robust Heterogeneous Analog-Digital Computing for Mixture-of-Experts Models with Theoretical Generalization Guarantees](https://mlsanity.com/paper/2603.02633/) (2026)
- [Attribution-Guided and Coverage-Maximized Pruning for Structural MoE Compression](https://mlsanity.com/paper/2606.18304/) (2026)
- [Communication-Aware Placement and Pruning for Efficient Mixture-of-Experts Inference](https://mlsanity.com/paper/2607.05116/) (2026)
- [Router Sensitivity Under Lightweight Fine-Tuning Identifies Prunable Experts in Mixture-of-Experts Models](https://mlsanity.com/paper/2608.07890/) (2026)
- [RAZOR: Pruning Replaceable Experts in LLMs](https://mlsanity.com/paper/2609.30465/) (2026)

## Abstract (arXiv)

The sparsely gated mixture of experts (MoE) architecture sends different inputs to different subnetworks, i.e., experts, through trainable routers. MoE reduces the training computation significantly for large models, but its deployment can be still memory or computation expensive for some downstream tasks. Model pruning is a popular approach to reduce inference computation, but its application in MoE architecture is largely unexplored. To the best of our knowledge, this paper provides the first provably efficient technique for pruning experts in finetuned MoE models. We theoretically prove that prioritizing the pruning of the experts with a smaller change of the routers l2 norm from the pretrained model guarantees the preservation of test accuracy, while significantly reducing the model size and the computational requirements. Although our theoretical analysis is centered on binary classification tasks on simplified MoE architecture, our expert pruning method is verified on large vision MoE models such as VMoE and E3MoE finetuned on benchmark datasets such as CIFAR10, CIFAR100, and ImageNet.