From 8f6900671b4ff5e462ce4b358b4e493c35a00879 Mon Sep 17 00:00:00 2001 From: "Ma, Guokai" Date: Thu, 13 Nov 2025 15:47:33 +0800 Subject: [PATCH 01/20] Muon optimizer blog draft Signed-off-by: Ma, Guokai Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 34 ++++++++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 blogs/muon-optimizer/README.md diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md new file mode 100644 index 000000000000..e27f2308076e --- /dev/null +++ b/blogs/muon-optimizer/README.md @@ -0,0 +1,34 @@ +# Using Muon Optimizer with DeepSpeed +## TL;DR +Muon optimizer has gain momentum with more and more use from community and also from Large Foundation Model like Kimi-K2-Thinking. Now DeepSpeed supports Muon optimizer + +## What is Muon optimizer? +Muon is an optimizer designed for hidden 2D weights of a neural network. It takes gradient of the weight, computes its momentum, and applies NewtonSchulz iterations to orthogonalize the momentum matrix, then use this orthogonalized matrix to update weight[1](https://kellerjordan.github.io/posts/muon/). With Muon optimizer, optimization are less likely to overfit, converge faster, and saves more memory than Adam optimizer. It is used by Keller Jordan’s mod of NanoGPT[2](https://github.com/KellerJordan/modded-nanogpt), Andrej Karpathy’s nanochat[3](https://github.com/karpathy/nanochat), and a variant of Muon (MuonClip) is also used by product level LLM model Kimi-K2 from MoonShot[4](https://arxiv.org/pdf/2507.20534). + +## Muon Optimizer support in DeepSpeed +One of the challenges of applying Muon optimizer to DeepSpeed is that previous optimizers (SGD, Adam) look at gradients as flattened buffers. Thus it is hard to swap in Muon optimizer in the same place because the gradient buffers are already flattened. We move the Muon update to the get_flat_partition function of stage 1 and 2 DeepSpeedZeroOptimizer in which per parameter gradients are still in unflattened stages, thus we can easily apply the Muon updates. + +Muon optimizer works for hidden 2D gradients. We apply a parse in model engine initializer to tag the model parameter with ‘use_muon’, if and only if the model parameter is 2D and is hidden. When Muon optimizer is used, any gradient with parameter match ‘use_muon’ will use Muon optimizer to update weight. + +## Running DeepSpeed finetune with Muon optimizer +Deepspeed finetune demo[5](https://github.com/delock/deepspeed_finetune_demo) is a demo to use different DeepSpeed training features and compare their performance in a single place. You can use it to test finetune LLM models with Muon optimizer: +``` +git clone https://github.com/delock/deepspeed_finetune_demo +cd deepspeed_finetune_demo +./finetune.sh z2_muon.json +``` + +## Muon Optimizer convergence experiment result +[TBD] + +## Muon Optimizer memory overhead +Muon optimizer has smaller memory requirements than Adam optimizer. Adam optimizer has to hold two momentum buffer as training state, Muon only has one momentum buffer. Thus Muon need less memory of optimizer state. For setup that exceeds GPU memory capacity and needs CPU offloading with Adam optimizer, Muon optimizer will need less GPU memory and may still be able to run without CPU offloading, avoid the overhead of CPU offloading. + +## Future plan +Muon optimizer is getting more and more attention, and is verified by product level open LLM model such as Kimi-K2 which has 1T weights. This makes Muon a second choice even potential replacement of Adam optimizer. To make Muon optimizer more accessible in production environment, the following feature is needed: +-[] Muon optimizer with ZeRO stage 3 +-[] CPU Offloading support +-[] MuonClip support +-[] Performance optimization to make Muon optimizer more efficient + +If you have thoughts, feedback and contribution on Muon optimizer, welcome to start an issue for discussion, or submit a PR to DeepSpeed. Let’s make Muon optimizer rock solid and lightning fast in DeepSpeed! From 58612b4ffd0400723f284ca0fd6d4d2078e41614 Mon Sep 17 00:00:00 2001 From: "Ma, Guokai" Date: Thu, 13 Nov 2025 17:57:10 +0800 Subject: [PATCH 02/20] add contributor list Signed-off-by: Ma, Guokai Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index e27f2308076e..66824b309d35 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -32,3 +32,6 @@ Muon optimizer is getting more and more attention, and is verified by product le -[] Performance optimization to make Muon optimizer more efficient If you have thoughts, feedback and contribution on Muon optimizer, welcome to start an issue for discussion, or submit a PR to DeepSpeed. Let’s make Muon optimizer rock solid and lightning fast in DeepSpeed! + +## Contributors +This work is contributed from Wang, Zhipeng (@PKUWZP); Chi McIsaac(@qimcis) and Ma, Guokai (@delock) From 5a1058489d8b05c6b5774a8184d2d1c850c5fa5e Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Fri, 14 Nov 2025 00:02:47 -0800 Subject: [PATCH 03/20] fix checkboxes Signed-off-by: Guokai Ma Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index 66824b309d35..c530872a8bb1 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -26,12 +26,13 @@ Muon optimizer has smaller memory requirements than Adam optimizer. Adam optimi ## Future plan Muon optimizer is getting more and more attention, and is verified by product level open LLM model such as Kimi-K2 which has 1T weights. This makes Muon a second choice even potential replacement of Adam optimizer. To make Muon optimizer more accessible in production environment, the following feature is needed: --[] Muon optimizer with ZeRO stage 3 --[] CPU Offloading support --[] MuonClip support --[] Performance optimization to make Muon optimizer more efficient -If you have thoughts, feedback and contribution on Muon optimizer, welcome to start an issue for discussion, or submit a PR to DeepSpeed. Let’s make Muon optimizer rock solid and lightning fast in DeepSpeed! +- [ ] Muon optimizer with ZeRO stage 3 +- [ ] CPU Offloading support +- [ ] MuonClip support +- [ ] Performance optimization to make Muon optimizer more efficient + +If you have thoughts, feedback and contribution on Muon optimizer, welcome to start an issue for discussion, or submit a PR to DeepSpeed. Let's make Muon optimizer rock solid and lightning fast in DeepSpeed! ## Contributors This work is contributed from Wang, Zhipeng (@PKUWZP); Chi McIsaac(@qimcis) and Ma, Guokai (@delock) From c4e42e71e3fc5e6d07e248613870b74fe395eb3f Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Fri, 14 Nov 2025 00:54:21 -0800 Subject: [PATCH 04/20] expand memory analysis Signed-off-by: Guokai Ma Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 56 +++++++++++++++++++++++++++++++++- 1 file changed, 55 insertions(+), 1 deletion(-) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index c530872a8bb1..2d945cddc56b 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -22,7 +22,61 @@ cd deepspeed_finetune_demo [TBD] ## Muon Optimizer memory overhead -Muon optimizer has smaller memory requirements than Adam optimizer. Adam optimizer has to hold two momentum buffer as training state, Muon only has one momentum buffer. Thus Muon need less memory of optimizer state. For setup that exceeds GPU memory capacity and needs CPU offloading with Adam optimizer, Muon optimizer will need less GPU memory and may still be able to run without CPU offloading, avoid the overhead of CPU offloading. +Muon optimizer has significantly smaller memory requirements than Adam optimizer, making it particularly valuable for large-scale model training. + +### Memory Usage Comparison + +| Optimizer | Momentum Buffers | Memory per Parameter | Example: 3B Model | +|-----------|------------------|---------------------|-------------------| +| **Adam** | 2 (m, v) | 8 bytes | ~24 GB | +| **Muon** | 1 (momentum) | 4 bytes | ~12 GB | + +### Practical Benefits + +1. **Memory Reduction**: Muon uses **50% less memory** for optimizer states compared to Adam +2. **Larger Batch Sizes**: With reduced memory overhead, you can increase batch sizes by up to 25% +3. **Avoid CPU Offloading**: Models that require CPU offloading with Adam may fit entirely in GPU memory with Muon +4. **Better Scaling**: More efficient memory usage enables training larger models on the same hardware + +### Real-world Example: 3B Model - No Offloading Required +In our experiments with a 3B parameter model on 2×A100 (40GB each) using batch size=8 and input length=512: + +**Training Configuration:** +- Model: Qwen2.5-3B +- Dataset: tatsu-lab/alpaca (standard instruction-tuning dataset) +- Batch size: 8 +- Sequence length: 512 tokens (standard for instruction-tuning) +- GPU memory: 80 GB total (2×A100 40GB) +- ZeRO Stage: Stage 2 (distributed optimizer states and gradients) + +**Adam Optimizer Setup:** +- Model parameters: 3B × 4 bytes = 12 GB +- Adam optimizer states: 3B × 8 bytes = 24 GB +- Activation memory (batch=8, seq=512): ~8 GB +- Gradient memory: 3B × 4 bytes = 12 GB +- **Per GPU memory with ZeRO Stage 2**: (12 + 8) + (24 + 12)/2 = 20 + 18 = 38 GB +- **Result**: Fits within 40GB per GPU, but with minimal headroom + +**Muon Optimizer Setup:** +- Model parameters: 3B × 4 bytes = 12 GB +- Muon optimizer states: 3B × 4 bytes = 12 GB +- Activation memory (batch=8, seq=512): ~8 GB +- Gradient memory: 3B × 4 bytes = 12 GB +- **Per GPU memory with ZeRO Stage 2**: (12 + 8) + (12 + 12)/2 = 20 + 12 = 32 GB +- **Result**: Comfortably fits with 8GB headroom per GPU + +**Actual Performance Test Results:** + +BS=8, sequence length=512 + +| Optimizer | Offloading | Iteration Time | Memory Usage | +|-----------|------------|----------------|--------------| +| **Muon** | No | **0.9s** | 32 GB/GPU | +| **Adam** | No | OOM (Crash) | >40 GB/GPU | +| **Adam** | Yes | **4.5s** | 38 GB/GPU | + +**Key Performance Insights:** +From this result, we can see in certain situation, Muon optimizer can use less memory and does not need CPU offloading, while Adam optimizer cannot fit GPU memory and requires CPU offloading. ## Future plan Muon optimizer is getting more and more attention, and is verified by product level open LLM model such as Kimi-K2 which has 1T weights. This makes Muon a second choice even potential replacement of Adam optimizer. To make Muon optimizer more accessible in production environment, the following feature is needed: From 7efd651a526c07942b6e09890f407d872331da17 Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Fri, 14 Nov 2025 01:00:25 -0800 Subject: [PATCH 05/20] trim down Signed-off-by: Guokai Ma Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 38 ++++++++-------------------------- 1 file changed, 9 insertions(+), 29 deletions(-) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index 2d945cddc56b..0ba093fa7dab 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -25,21 +25,17 @@ cd deepspeed_finetune_demo Muon optimizer has significantly smaller memory requirements than Adam optimizer, making it particularly valuable for large-scale model training. ### Memory Usage Comparison +In theory, Muon optimizer has one momentum buffer while Adam has two, this makes Muon optimizer use 50% less memory for optimizer states compared to Adam | Optimizer | Momentum Buffers | Memory per Parameter | Example: 3B Model | |-----------|------------------|---------------------|-------------------| -| **Adam** | 2 (m, v) | 8 bytes | ~24 GB | -| **Muon** | 1 (momentum) | 4 bytes | ~12 GB | +| Adam | 2 (m, v) | 8 bytes | ~24 GB | +| Muon | 1 (momentum) | 4 bytes | ~12 GB | -### Practical Benefits - -1. **Memory Reduction**: Muon uses **50% less memory** for optimizer states compared to Adam -2. **Larger Batch Sizes**: With reduced memory overhead, you can increase batch sizes by up to 25% -3. **Avoid CPU Offloading**: Models that require CPU offloading with Adam may fit entirely in GPU memory with Muon -4. **Better Scaling**: More efficient memory usage enables training larger models on the same hardware +With Muon optimizer, we can potentially use larger batch sizes and avoid CPU offloading. ### Real-world Example: 3B Model - No Offloading Required -In our experiments with a 3B parameter model on 2×A100 (40GB each) using batch size=8 and input length=512: +We tested finetune Qwen2.5-3B model with tatsu-lab/aplaca dataset on 2xA100 (40GB GPU memory each) using batch size=8 and input length=512: **Training Configuration:** - Model: Qwen2.5-3B @@ -49,31 +45,15 @@ In our experiments with a 3B parameter model on 2×A100 (40GB each) using batch - GPU memory: 80 GB total (2×A100 40GB) - ZeRO Stage: Stage 2 (distributed optimizer states and gradients) -**Adam Optimizer Setup:** -- Model parameters: 3B × 4 bytes = 12 GB -- Adam optimizer states: 3B × 8 bytes = 24 GB -- Activation memory (batch=8, seq=512): ~8 GB -- Gradient memory: 3B × 4 bytes = 12 GB -- **Per GPU memory with ZeRO Stage 2**: (12 + 8) + (24 + 12)/2 = 20 + 18 = 38 GB -- **Result**: Fits within 40GB per GPU, but with minimal headroom - -**Muon Optimizer Setup:** -- Model parameters: 3B × 4 bytes = 12 GB -- Muon optimizer states: 3B × 4 bytes = 12 GB -- Activation memory (batch=8, seq=512): ~8 GB -- Gradient memory: 3B × 4 bytes = 12 GB -- **Per GPU memory with ZeRO Stage 2**: (12 + 8) + (12 + 12)/2 = 20 + 12 = 32 GB -- **Result**: Comfortably fits with 8GB headroom per GPU - -**Actual Performance Test Results:** +**Performance Test Results:** BS=8, sequence length=512 | Optimizer | Offloading | Iteration Time | Memory Usage | |-----------|------------|----------------|--------------| -| **Muon** | No | **0.9s** | 32 GB/GPU | -| **Adam** | No | OOM (Crash) | >40 GB/GPU | -| **Adam** | Yes | **4.5s** | 38 GB/GPU | +| Muon | No | 0.9s | 32 GB/GPU | +| Adam | No | OOM (Crash) | >40 GB/GPU | +| Adam | Yes | 4.5s | 38 GB/GPU | **Key Performance Insights:** From this result, we can see in certain situation, Muon optimizer can use less memory and does not need CPU offloading, while Adam optimizer cannot fit GPU memory and requires CPU offloading. From dc7c02bf1905625897eb2cbbaf103a5c5de9fbc2 Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Fri, 14 Nov 2025 01:01:46 -0800 Subject: [PATCH 06/20] remove memory data Signed-off-by: Guokai Ma Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index 0ba093fa7dab..179118677fef 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -49,11 +49,11 @@ We tested finetune Qwen2.5-3B model with tatsu-lab/aplaca dataset on 2xA100 (40G BS=8, sequence length=512 -| Optimizer | Offloading | Iteration Time | Memory Usage | -|-----------|------------|----------------|--------------| -| Muon | No | 0.9s | 32 GB/GPU | -| Adam | No | OOM (Crash) | >40 GB/GPU | -| Adam | Yes | 4.5s | 38 GB/GPU | +| Optimizer | Offloading | Iteration Time | +|-----------|------------|----------------| +| Muon | No | 0.9s | +| Adam | No | OOM (Crash) | +| Adam | Yes | 4.5s | **Key Performance Insights:** From this result, we can see in certain situation, Muon optimizer can use less memory and does not need CPU offloading, while Adam optimizer cannot fit GPU memory and requires CPU offloading. From f2967a1d59a556a401952b81cbdc8b79b37f5ae3 Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Fri, 14 Nov 2025 01:06:56 -0800 Subject: [PATCH 07/20] fix formatting Signed-off-by: Guokai Ma Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index 179118677fef..45e9c0350ba3 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -56,7 +56,8 @@ BS=8, sequence length=512 | Adam | Yes | 4.5s | **Key Performance Insights:** -From this result, we can see in certain situation, Muon optimizer can use less memory and does not need CPU offloading, while Adam optimizer cannot fit GPU memory and requires CPU offloading. + +From this result, we can see in certain situation, Muon optimizer can use less memory and does not need CPU offloading, while Adam optimizer cannot fit GPU memory and requires CPU offloading. This collaterally brings performance benefit even when Muon optimizer needs more computation, because no offloading needed. ## Future plan Muon optimizer is getting more and more attention, and is verified by product level open LLM model such as Kimi-K2 which has 1T weights. This makes Muon a second choice even potential replacement of Adam optimizer. To make Muon optimizer more accessible in production environment, the following feature is needed: From 0890c49575c2dcf562a2ad10393a0e59a8b846e2 Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Sun, 5 Apr 2026 23:48:41 +0800 Subject: [PATCH 08/20] fix gramma Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index 45e9c0350ba3..34d3eeb59358 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -1,6 +1,6 @@ # Using Muon Optimizer with DeepSpeed ## TL;DR -Muon optimizer has gain momentum with more and more use from community and also from Large Foundation Model like Kimi-K2-Thinking. Now DeepSpeed supports Muon optimizer +Muon optimizer has gained momentum with more and more use from community and also from Large Foundation Model like Kimi-K2-Thinking. Now DeepSpeed supports Muon optimizer. ## What is Muon optimizer? Muon is an optimizer designed for hidden 2D weights of a neural network. It takes gradient of the weight, computes its momentum, and applies NewtonSchulz iterations to orthogonalize the momentum matrix, then use this orthogonalized matrix to update weight[1](https://kellerjordan.github.io/posts/muon/). With Muon optimizer, optimization are less likely to overfit, converge faster, and saves more memory than Adam optimizer. It is used by Keller Jordan’s mod of NanoGPT[2](https://github.com/KellerJordan/modded-nanogpt), Andrej Karpathy’s nanochat[3](https://github.com/karpathy/nanochat), and a variant of Muon (MuonClip) is also used by product level LLM model Kimi-K2 from MoonShot[4](https://arxiv.org/pdf/2507.20534). @@ -35,7 +35,7 @@ In theory, Muon optimizer has one momentum buffer while Adam has two, this makes With Muon optimizer, we can potentially use larger batch sizes and avoid CPU offloading. ### Real-world Example: 3B Model - No Offloading Required -We tested finetune Qwen2.5-3B model with tatsu-lab/aplaca dataset on 2xA100 (40GB GPU memory each) using batch size=8 and input length=512: +We tested finetuning a Qwen2.5-3B model with tatsu-lab/alpaca dataset on 2xA100 (40GB GPU memory each) using batch size=8 and input length=512: **Training Configuration:** - Model: Qwen2.5-3B @@ -60,7 +60,7 @@ BS=8, sequence length=512 From this result, we can see in certain situation, Muon optimizer can use less memory and does not need CPU offloading, while Adam optimizer cannot fit GPU memory and requires CPU offloading. This collaterally brings performance benefit even when Muon optimizer needs more computation, because no offloading needed. ## Future plan -Muon optimizer is getting more and more attention, and is verified by product level open LLM model such as Kimi-K2 which has 1T weights. This makes Muon a second choice even potential replacement of Adam optimizer. To make Muon optimizer more accessible in production environment, the following feature is needed: +Muon optimizer is getting more and more attention, and is verified by product level open LLM model such as Kimi-K2 which has 1T weights. This makes Muon a strong second choice and a potential replacement of Adam optimizer. To make Muon optimizer more accessible in production environment, the following feature is needed: - [ ] Muon optimizer with ZeRO stage 3 - [ ] CPU Offloading support From 7c57422eb62b14d8c125a8ef194f045ca4067784 Mon Sep 17 00:00:00 2001 From: Guokai Ma Date: Mon, 6 Apr 2026 23:32:45 +0800 Subject: [PATCH 09/20] Add convergence experiment result and fix typos in Muon blog Signed-off-by: Ma, Guokai --- blogs/muon-optimizer/README.md | 9 +++++++-- .../images/adamw_vs_muon_3b.png | Bin 0 -> 1284781 bytes 2 files changed, 7 insertions(+), 2 deletions(-) create mode 100644 blogs/muon-optimizer/images/adamw_vs_muon_3b.png diff --git a/blogs/muon-optimizer/README.md b/blogs/muon-optimizer/README.md index 34d3eeb59358..a55966355587 100644 --- a/blogs/muon-optimizer/README.md +++ b/blogs/muon-optimizer/README.md @@ -18,8 +18,13 @@ cd deepspeed_finetune_demo ./finetune.sh z2_muon.json ``` -## Muon Optimizer convergence experiment result -[TBD] +## Muon Optimizer Convergence Experiment Result + +We compared Muon optimizer with AdamW optimizer by finetuning a Qwen2.5-3B model on the tatsu-lab/alpaca dataset with the same learning rate. + +![Muon vs AdamW convergence on Qwen2.5-3B](images/adamw_vs_muon_3b.png) + +In one epoch, Muon optimizer achieved approximately 19% lower loss compared to AdamW optimizer. 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