# Soft Merging of Experts with Adaptive Routing

arXiv: https://arxiv.org/abs/2306.03745 · HTML: https://mlsanity.com/paper/2306.03745/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 94 of its 112 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 94)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Multilingual Denoising Pre-training for Neural Machine Translation](https://mlsanity.com/paper/2001.08210/) (2020)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [How multilingual is Multilingual BERT?](https://mlsanity.com/paper/1906.01502/) (2019)

## Built on by (most cited first, 30 of 90)

- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)
- [From Sparse to Soft Mixtures of Experts](https://mlsanity.com/paper/2308.00951/) (2023)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Pushing Mixture of Experts to the Limit: Extremely Parameter Efficient MoE for Instruction Tuning](https://mlsanity.com/paper/2309.05444/) (2023)
- [SAM-CLIP: Merging Vision Foundation Models towards Semantic and Spatial Understanding](https://mlsanity.com/paper/2310.15308/) (2023)
- [Merge, Then Compress: Demystify Efficient SMoE with Hints from Its Routing Policy](https://mlsanity.com/paper/2310.01334/) (2023)
- [Towards Modular LLMs by Building and Reusing a Library of LoRAs](https://mlsanity.com/paper/2405.11157/) (2024)
- [LoraRetriever: Input-Aware LoRA Retrieval and Composition for Mixed Tasks in the Wild](https://mlsanity.com/paper/2402.09997/) (2024)
- [Learning to Route Among Specialized Experts for Zero-Shot Generalization](https://mlsanity.com/paper/2402.05859/) (2024)
- [ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routing](https://mlsanity.com/paper/2412.14711/) (2024)
- [A Survey on Model MoErging: Recycling and Routing Among Specialized Experts for Collaborative Learning](https://mlsanity.com/paper/2408.07057/) (2024)
- [MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selection](https://mlsanity.com/paper/2403.19888/) (2024)
- [Lory: Fully Differentiable Mixture-of-Experts for Autoregressive Language Model Pre-training](https://mlsanity.com/paper/2405.03133/) (2024)
- [LLM Augmented LLMs: Expanding Capabilities through Composition](https://mlsanity.com/paper/2401.02412/) (2024)
- [FlyLoRA: Boosting Task Decoupling and Parameter Efficiency via Implicit Rank-Wise Mixture-of-Experts](https://mlsanity.com/paper/2510.08396/) (2025)
- [Efficient and Effective Weight-Ensembling Mixture of Experts for Multi-Task Model Merging](https://mlsanity.com/paper/2410.21804/) (2024)
- [DAM: Dynamic Adapter Merging for Continual Video QA Learning](https://mlsanity.com/paper/2403.08755/) (2024)
- [Retrieval-Augmented Mixture of LoRA Experts for Uploadable Machine Learning](https://mlsanity.com/paper/2406.16989/) (2024)
- [Each Rank Could be an Expert: Single-Ranked Mixture of Experts LoRA for Multi-Task Learning](https://mlsanity.com/paper/2501.15103/) (2025)
- [Sweeping Heterogeneity with Smart MoPs: Mixture of Prompts for LLM Task Adaptation](https://mlsanity.com/paper/2310.02842/) (2023)
- [Realistic Evaluation of Model Merging for Compositional Generalization](https://mlsanity.com/paper/2409.18314/) (2024)
- [Conditional computation in neural networks: principles and research trends](https://mlsanity.com/paper/2403.07965/) (2024)
- [Revisiting Model Interpolation for Efficient Reasoning](https://mlsanity.com/paper/2510.10977/) (2025)
- [REAM: Merging Improves Pruning of Experts in LLMs](https://mlsanity.com/paper/2604.04356/) (2026)
- [MoE Jetpack: From Dense Checkpoints to Adaptive Mixture of Experts for Vision Tasks](https://mlsanity.com/paper/2406.04801/) (2024)
- [Revisiting SMoE Language Models by Evaluating Inefficiencies with Task Specific Expert Pruning](https://mlsanity.com/paper/2409.01483/) (2024)
- [Not All Models Suit Expert Offloading: On Local Routing Consistency of Mixture-of-Expert Models](https://mlsanity.com/paper/2505.16056/) (2025)
- [Dynamic Mixture of Progressive Parameter-Efficient Expert Library for Lifelong Robot Learning](https://mlsanity.com/paper/2506.05985/) (2025)

## Abstract (arXiv)

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.