# Lory: Fully Differentiable Mixture-of-Experts for Autoregressive Language Model Pre-training

arXiv: https://arxiv.org/abs/2405.03133 · HTML: https://mlsanity.com/paper/2405.03133/

## Key facts

- Cited by 37 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 40 of its 48 references that are in the map.
- First posted on arXiv 6 May 2024.

## Placed in

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

## Builds on (most cited first, 30 of 40)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [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)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [CCNet: Extracting High Quality Monolingual Datasets from Web Crawl Data](https://mlsanity.com/paper/1911.00359/) (2019)
- [MetaICL: Learning to Learn In Context](https://mlsanity.com/paper/2110.15943/) (2021)

## Built on by (most cited first, 30 of 37)

- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Mixture-of-Transformers: A Sparse and Scalable Architecture for Multi-Modal Foundation Models](https://mlsanity.com/paper/2411.04996/) (2024)
- [ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routing](https://mlsanity.com/paper/2412.14711/) (2024)
- [Demons in the Detail: On Implementing Load Balancing Loss for Training Specialized Mixture-of-Expert Models](https://mlsanity.com/paper/2501.11873/) (2025)
- [Sparser is Faster and Less is More: Efficient Sparse Attention for Long-Range Transformers](https://mlsanity.com/paper/2406.16747/) (2024)
- [A Survey: Collaborative Hardware and Software Design in the Era of Large Language Models](https://mlsanity.com/paper/2410.07265/) (2024)
- [Mixture of Parrots: Experts improve memorization more than reasoning](https://mlsanity.com/paper/2410.19034/) (2024)
- [LD-MoLE: Learnable Dynamic Routing for Mixture of LoRA Experts](https://mlsanity.com/paper/2509.25684/) (2025)
- [Ensembles of Low-Rank Expert Adapters](https://mlsanity.com/paper/2502.00089/) (2025)
- [GW-MoE: Resolving Uncertainty in MoE Router with Global Workspace Theory](https://mlsanity.com/paper/2406.12375/) (2024)
- [Analytical FFN-to-MoE Restructuring via Activation Pattern Analysis](https://mlsanity.com/paper/2502.04416/) (2025)
- [Not All Models Suit Expert Offloading: On Local Routing Consistency of Mixture-of-Expert Models](https://mlsanity.com/paper/2505.16056/) (2025)
- [GRAPHMOE: Amplifying Cognitive Depth of Mixture-of-Experts Network via Introducing Self-Rethinking Mechanism](https://mlsanity.com/paper/2501.07890/) (2025)
- [Long-Tailed Distribution-Aware Router For Mixture-of-Experts in Large Vision-Language Model](https://mlsanity.com/paper/2507.01351/) (2025)
- [The Expert Strikes Back: Interpreting Mixture-of-Experts Language Models at Expert Level](https://mlsanity.com/paper/2604.02178/) (2026)
- [First Activations Matter: Training-Free Methods for Dynamic Activation in Large Language Models](https://mlsanity.com/paper/2408.11393/) (2024)
- [LIBMoE: A Library for comprehensive benchmarking Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2411.00918/) (2024)
- [Efficiently Editing Mixture-of-Experts Models with Compressed Experts](https://mlsanity.com/paper/2503.00634/) (2025)
- [BlockFFN: Towards End-Side Acceleration-Friendly Mixture-of-Experts with Chunk-Level Activation Sparsity](https://mlsanity.com/paper/2507.08771/) (2025)
- [CAMEx: Curvature-aware Merging of Experts](https://mlsanity.com/paper/2502.18821/) (2025)
- [Grouter: Decoupling Routing from Representation for Accelerated MoE Training](https://mlsanity.com/paper/2603.06626/) (2026)
- [Expert Divergence Learning for MoE-based Language Models](https://mlsanity.com/paper/2603.00054/) (2026)
- [SAMoE-VLA: A Scene Adaptive Mixture-of-Experts Vision-Language-Action Model for Autonomous Driving](https://mlsanity.com/paper/2603.08113/) (2026)
- [Sparse Brains are Also Adaptive Brains: Cognitive-Load-Aware Dynamic Activation for LLMs](https://mlsanity.com/paper/2502.19078/) (2025)
- [Expert Merging in Sparse Mixture of Experts with Nash Bargaining](https://mlsanity.com/paper/2510.16138/) (2025)
- [RANGER: Sparsely-Gated Mixture-of-Experts with Adaptive Retrieval Re-ranking for Pathology Report Generation](https://mlsanity.com/paper/2603.04348/) (2026)
- [Expert Threshold Routing for Autoregressive Language Modeling with Dynamic Computation Allocation and Load Balancing](https://mlsanity.com/paper/2603.11535/) (2026)
- [Guiding the Experts: Semantic Priors for Efficient and Focused MoE Routing](https://mlsanity.com/paper/2505.18586/) (2025)
- [DirMoE: Dirichlet-routed Mixture of Experts](https://mlsanity.com/paper/2602.09001/) (2026)

## Abstract (arXiv)

Mixture-of-experts (MoE) models facilitate efficient scaling; however, training the router network introduces the challenge of optimizing a non-differentiable, discrete objective. Recently, a fully-differentiable MoE architecture, SMEAR, was proposed (Muqeeth et al., 2023), which softly merges experts in the parameter space; nevertheless, its effectiveness was only demonstrated in downstream fine-tuning on classification tasks. In this paper, we present Lory, the first approach that scales such architectures to autoregressive language model pre-training. Lory introduces two key techniques: (1) a causal segment routing strategy that achieves high efficiency for expert merging operations while preserving the autoregressive nature of language models; (2) a similarity-based data batching method that encourages expert specialization by grouping similar documents in training instances. We pre-train a series of Lory models on 150B tokens from scratch, with up to 32 experts and 30B (1.5B active) parameters. Experimental results show significant performance gains over parameter-matched dense models on both perplexity (+13.9%) and a variety of downstream tasks (+1.5%-11.1%). Despite segment-level routing, Lory models achieve competitive performance compared to state-of-the-art MoE models with token-level routing. We further demonstrate that the trained experts in Lory capture domain-level specialization without supervision. Our work highlights the potential of fully-differentiable MoE architectures for language model pre-training and advocates future research in this area.