# Retraining-Free Merging of Sparse MoE via Hierarchical Clustering

arXiv: https://arxiv.org/abs/2410.08589 · HTML: https://mlsanity.com/paper/2410.08589/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [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)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [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)
- [Training-Free Pretrained Model Merging](https://mlsanity.com/paper/2403.01753/) (2024)
- [CodeQA: A Question Answering Dataset for Source Code Comprehension](https://mlsanity.com/paper/2109.08365/) (2021)
- [Diversifying the Mixture-of-Experts Representation for Language Models with Orthogonal Optimizer](https://mlsanity.com/paper/2310.09762/) (2023)

## Built on by (most cited first, 30 of 35)

- [MoBE: Mixture-of-Basis-Experts for Compressing MoE-based LLMs](https://mlsanity.com/paper/2508.05257/) (2025)
- [PuzzleMoE: Efficient Compression of Large Mixture-of-Experts Models via Sparse Expert Merging and Bit-packed inference](https://mlsanity.com/paper/2511.04805/) (2025)
- [EvoESAP: Non-Uniform Expert Pruning for Sparse MoE](https://mlsanity.com/paper/2603.06003/) (2026)
- [CAMERA: Multi-Matrix Joint Compression for MoE Models via Micro-Expert Redundancy Analysis](https://mlsanity.com/paper/2508.02322/) (2025)
- [MoE Pathfinder: Trajectory-driven Expert Pruning](https://mlsanity.com/paper/2512.18425/) (2025)
- [How to Score Experts for One-Shot MoE Expert Pruning: A Unified Formulation and Selection Principle](https://mlsanity.com/paper/2606.15716/) (2026)
- [AIMER: Calibration-Free Task-Agnostic MoE Expert Pruning](https://mlsanity.com/paper/2603.18492/) (2026)
- [Is Retraining-Free Enough? The Necessity of Router Calibration for Efficient MoE Compression](https://mlsanity.com/paper/2603.02217/) (2026)
- [Post-Trained MoE Can Skip Half Experts via Self-Distillation](https://mlsanity.com/paper/2605.18643/) (2026)
- [Model Selection for Gaussian-gated Gaussian Mixture of Experts Using Dendrograms of Mixing Measures](https://mlsanity.com/paper/2505.13052/) (2025)
- [HEAPr: Hessian-based Efficient Atomic Expert Pruning in Output Space](https://mlsanity.com/paper/2509.22299/) (2025)
- [SERE: Similarity-based Expert Re-routing for Efficient Batch Decoding in MoE Models](https://mlsanity.com/paper/2602.07616/) (2026)
- [LightMoE: Reducing Mixture-of-Experts Redundancy through Expert Replacing](https://mlsanity.com/paper/2603.12645/) (2026)
- [Less is MoE: Trimming Experts in Domain-Specialist Language Models](https://mlsanity.com/paper/2606.05538/) (2026)
- [It Takes a MAESTRO To Prune Bad Experts](https://mlsanity.com/paper/2607.08601/) (2026)
- [UniMoMo: Expert Merging-Based MoE Acceleration for Large Recommendation Models](https://mlsanity.com/paper/2608.08627/) (2026)
- [HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts](https://mlsanity.com/paper/2605.13997/) (2026)
- [BEAM: Binary Expert Activation Masking for Dynamic Routing in MoE](https://mlsanity.com/paper/2605.14438/) (2026)
- [Pruning and Distilling Mixture-of-Experts into Dense Language Models](https://mlsanity.com/paper/2605.28207/) (2026)
- [ConMoE: Expert-Pool Consolidation via Prototype Reassignment for MoE Compression](https://mlsanity.com/paper/2605.29350/) (2026)
- [On the Utility and Factual Reliability of Pruned Mixture-of-Experts Models in the Biomedical Domain](https://mlsanity.com/paper/2607.01444/) (2026)
- [Beyond Global Routing Aggregation: Phase-Aware Expert Merging for MoE Vision-Language Models](https://mlsanity.com/paper/2608.04454/) (2026)
- [Shape Mutating Expert Compression:LorExperts and BTExperts](https://mlsanity.com/paper/2608.07814/) (2026)
- [Meta-Learning Where to Allocate Experts: Task-Conditioned Layer-Wise Compression for MoEs](https://mlsanity.com/paper/2608.26650/) (2026)
- [Residual Sparsification via Output Importance for Compressing Mixture-of-Experts LLMs](https://mlsanity.com/paper/2609.00575/) (2026)
- [When Load-Balancing Goes Too Far: Expert Pruning in Over-Dispersed Mixture-of-Experts Models](https://mlsanity.com/paper/2609.04453/) (2026)
- [Beyond Retraining-Free MoE Compression: A Cost-Normalized Study of Post-Compression Adjustment](https://mlsanity.com/paper/2609.06076/) (2026)
- [RAZOR: Pruning Replaceable Experts in LLMs](https://mlsanity.com/paper/2609.30465/) (2026)
- [OMP-MoE: Efficient Expert Pruning for Mixture-of-Experts LLMs via Orthogonal Matching Pursuit](https://mlsanity.com/paper/2609.31631/) (2026)
- [SlimWise: Decoupling Expert Pruning Across Prefill and Decode for Efficient MoE Serving](https://mlsanity.com/paper/2609.34117/) (2026)

## Abstract (arXiv)

Sparse Mixture-of-Experts (SMoE) models represent a significant advancement in large language model (LLM) development through their efficient parameter utilization. These models achieve substantial performance improvements at reduced inference costs. However, the deployment of SMoE models faces constraints from extensive memory requirements of expert components in resource-limited environments. To address these limitations, this paper introduces Hierarchical Clustering for Sparsely activated Mixture of Experts (HC-SMoE), a task-agnostic expert merging framework for parameter reduction without retraining. HC-SMoE introduces a novel hierarchical clustering approach based on expert outputs to ensure merging robustness independent of routing decisions. The proposed output-based clustering method enables effective capture of functional relationships between experts for large-scale architectures. We provide theoretical analysis and comprehensive evaluations across multiple zero-shot language tasks to demonstrate HC-SMoE's effectiveness in state-of-the-art models including Qwen and Mixtral. The experimental results validate HC-SMoE's superior performance and practical applicability for real-world deployments.