# GRIN: GRadient-INformed MoE

arXiv: https://arxiv.org/abs/2409.12136 · HTML: https://mlsanity.com/paper/2409.12136/

## Key facts

- Cited by 17 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 35 of its 55 references that are in the map.
- First posted on arXiv 18 Sep 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 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [BASE Layers: Simplifying Training of Large, Sparse Models](https://mlsanity.com/paper/2103.16716/) (2021)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [MegaBlocks: Efficient Sparse Training with Mixture-of-Experts](https://mlsanity.com/paper/2211.15841/) (2022)
- [NEFTune: Noisy Embeddings Improve Instruction Finetuning](https://mlsanity.com/paper/2310.05914/) (2023)

## Built on by (most cited first, 17 of 17)

- [ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routing](https://mlsanity.com/paper/2412.14711/) (2024)
- [A Survey on Inference Optimization Techniques for Mixture of Experts Models](https://mlsanity.com/paper/2412.14219/) (2024)
- [Intern-S1-Pro: Scientific Multimodal Foundation Model at Trillion Scale](https://mlsanity.com/paper/2603.25040/) (2026)
- [Instruction-Following Pruning for Large Language Models](https://mlsanity.com/paper/2501.02086/) (2025)
- [Scaling Laws for Upcycling Mixture-of-Experts Language Models](https://mlsanity.com/paper/2502.03009/) (2025)
- [Pangu Ultra MoE: How to Train Your Big MoE on Ascend NPUs](https://mlsanity.com/paper/2505.04519/) (2025)
- [Not All Models Suit Expert Offloading: On Local Routing Consistency of Mixture-of-Expert Models](https://mlsanity.com/paper/2505.16056/) (2025)
- [BlockFFN: Towards End-Side Acceleration-Friendly Mixture-of-Experts with Chunk-Level Activation Sparsity](https://mlsanity.com/paper/2507.08771/) (2025)
- [Continual Pre-training of MoEs: How robust is your router?](https://mlsanity.com/paper/2503.05029/) (2025)
- [Input Domain Aware MoE: Decoupling Routing Decisions from Task Optimization in Mixture of Experts](https://mlsanity.com/paper/2510.16448/) (2025)
- [FLIP Reasoning Challenge](https://mlsanity.com/paper/2504.12256/) (2025)
- [An Introduction to Discrete Variational Autoencoders](https://mlsanity.com/paper/2505.10344/) (2025)
- [PR2: Predictive Routing Replay for MoE-Based LLM Reinforcement Learning](https://mlsanity.com/paper/2606.00395/) (2026)
- [Expert Streaming: Accelerating Low-Batch MoE Inference via Multi-chiplet Architecture and Dynamic Expert Trajectory Scheduling](https://mlsanity.com/paper/2603.27624/) (2026)
- [UB-SMoE: Universally Balanced Sparse Mixture-of-Experts for Resource-adaptive Federated Fine-tuning of Foundation Models](https://mlsanity.com/paper/2605.16690/) (2026)
- [Chimaera: A Mixture-of-Graph-Experts Architecture for Cross-Task and Cross-Dataset Graph Learning](https://mlsanity.com/paper/2609.08709/) (2026)
- [Principled Top-k Selection for Language Models with Hybrid Gradients](https://mlsanity.com/paper/2610.04162/) (2026)

## Abstract (arXiv)

Mixture-of-Experts (MoE) models scale more effectively than dense models due to sparse computation through expert routing, selectively activating only a small subset of expert modules. However, sparse computation challenges traditional training practices, as discrete expert routing hinders standard backpropagation and thus gradient-based optimization, which are the cornerstone of deep learning. To better pursue the scaling power of MoE, we introduce GRIN (GRadient-INformed MoE training), which incorporates sparse gradient estimation for expert routing and configures model parallelism to avoid token dropping. Applying GRIN to autoregressive language modeling, we develop a top-2 16×3.8B MoE model. Our model, with only 6.6B activated parameters, outperforms a 7B dense model and matches the performance of a 14B dense model trained on the same data. Extensive evaluations across diverse tasks demonstrate the potential of GRIN to significantly enhance MoE efficacy, achieving 79.4 on MMLU, 83.7 on HellaSwag, 74.4 on HumanEval, and 58.9 on MATH.