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@ -4,17 +4,17 @@
<a href="https://colab.research.google.com/drive/1oW55fBmwzCOrBVX66RcpptL3a99qWBxb?usp=sharing"><img src="./images/try live demo green.png" width="130"></a>
</div>
## 2-5x faster 50% less memory local LLM finetuning
* Manual autograd engine - hand derived backprop steps.
* 2x to 5x faster than QLoRA. 50% less memory usage.
## 2-5x faster 60% less memory local QLoRA finetuning
* Supports Llama 7b, 13b, 70b, CodeLlama 34b, Mistral 7b, TinyLlama and all Llama archs!
* Mistral 7b [(Colab example)](https://colab.research.google.com/drive/1SKrKGV-BZoU4kv5q3g0jtE_OhRgPtrrQ?usp=sharing) on 1 A100 2.2x faster, uses 62% less VRAM (12.4GB).
* CodeLlama 34b [(Colab example)](https://colab.research.google.com/drive/1gdHyAx8XJsz2yNV-DHvbHjR1iCef5Qmh?usp=sharing) does not OOM is 1.9x faster, uses 32% less VRAM (27GB).
* Kaggle 2 Tesla T4s 5.28x faster on Alpaca. [(Kaggle example)](https://www.kaggle.com/danielhanchen/unsloth-laion-t4-ddp)
* All kernels written in [OpenAI's Triton](https://openai.com/research/triton) language.
* 0% loss in accuracy - no approximation methods - all exact.
* No change of hardware necessary. Supports NVIDIA GPUs since 2018+. Minimum CUDA Compute Capability 7.0 (V100, T4, Titan V, RTX 20, 30, 40x, A100, H100, L40 etc) [Check your GPU](https://developer.nvidia.com/cuda-gpus)
* [Flash Attention v2](https://github.com/Dao-AILab/flash-attention) support via [Xformers](https://github.com/facebookresearch/xformers).
* **NEW!** Works on **Linux** and **Windows** via WSL.
* **NEW!** Experimental support for [DPO (Direct Preference Optimization)](https://arxiv.org/abs/2305.18290)!
* Supports 4bit and 16bit QLoRA / LoRA finetuning via [bitsandbytes](https://github.com/TimDettmers/bitsandbytes).
* Train Slim Orca **fully locally in 260 hours from 1301 hours (5x faster).**
* Open source version trains 5x faster or you can check out [Unsloth Pro and Max](https://unsloth.ai/) codepaths for **30x faster training**!
<div class="align-center">
@ -22,9 +22,16 @@
<img src="./images/LAION 2GPU.png" width="400" />
</div>
1. Try our Colab examples for [the Alpaca 52K dataset](https://colab.research.google.com/drive/1oW55fBmwzCOrBVX66RcpptL3a99qWBxb?usp=sharing) or [the Slim Orca 518K dataset](https://colab.research.google.com/drive/1VNqLARpE8N8eYwNrUSDoHVjtbR9W0_c7?usp=sharing).
2. Try our Kaggle example for [the LAION OIG Chip2 dataset](https://www.kaggle.com/danielhanchen/unsloth-laion-chip2-kaggle)
3. Join our [Discord](https://discord.gg/nsS4V5Z6ge)!
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| Alpaca | 1x | 1.04x | 1.98x | 2.48x | 5.32x | **15.64x** |
| LAION Chip2 | 1x | 0.92x | 1.61x | 1.84x | 7.05x | **20.73x** |
| OASST | 1x | 1.19x | 2.17x | 2.66x | 5.04x | **14.83x** |
| Slim Orca | 1x | 1.18x | 2.22x | 2.64x | 5.04x | **14.82x** |
Join our [Discord](https://discord.gg/nsS4V5Z6ge)!
If you trained a model with Unsloth, we made a cool sticker!!
<img src="./images/unsloth made with love.png" width="200" />
# Installation Instructions - Conda
Unsloth currently only supports Linux distros and Pytorch >= 2.1.
@ -39,10 +46,12 @@ pip install "unsloth[kaggle] @ git+https://github.com/unslothai/unsloth.git"
```
import torch; torch.version.cuda
```
2. Select either cu118 for CUDA 11.8 or cu121 for CUDA 12.1
2. Select either cu118 for CUDA 11.8 or cu121 for CUDA 12.1. If you have a RTX 3060 or higher (A100, H100 etc), use the "ampere" path.
```
pip install "unsloth[cu118] @ git+https://github.com/unslothai/unsloth.git"
pip install "unsloth[cu121] @ git+https://github.com/unslothai/unsloth.git"
pip install "unsloth[cu118_ampere] @ git+https://github.com/unslothai/unsloth.git"
pip install "unsloth[cu121_ampere] @ git+https://github.com/unslothai/unsloth.git"
```
3. We only support Pytorch 2.1: You can update Pytorch via Pip:
```
@ -59,7 +68,7 @@ pip install --upgrade pip
# Documentation
We support Huggingface's TRL, Trainer, Seq2SeqTrainer or even Pytorch code!
```
from unsloth import FastLlamaModel
from unsloth import FastLlamaModel, FastMistralModel
import torch
max_seq_length = 2048 # Can change to any number <= 4096
dtype = None # None for auto detection. Float16 for Tesla T4, V100, Bfloat16 for Ampere+
@ -91,16 +100,13 @@ model = FastLlamaModel.get_peft_model(
trainer = .... Use Huggingface's Trainer and dataset loading (TRL, transformers etc)
```
If you trained a model with Unsloth, we made a cool sticker!!
<img src="./images/unsloth made with love.png" width="200" />
# DPO (Direct Preference Optimization) Experimental support
[152334H](https://github.com/152334H) hacked Unsloth to work with DPO via TRL!
1. Hack the model's `config.json` to be llama model. [Example gist](https://gist.github.com/152334H/d8a68b51b83bac008a02e69ecc81d5c1).
2. Use Unsloth for DPO for both base and reference models. [Example gist](https://gist.github.com/152334H/4847f3a8cca12894877e6b30698b0b64).
# Future Milestones and limitations
1. Support sqrt gradient checkpointing which further slashes memory usage by 25%.
1. Support Mixtral.
2. Does not support non Llama models - we do so in the future.
# Performance comparisons on 1 Tesla T4 GPU:
@ -147,9 +153,158 @@ Two Tesla T4s on Kaggle
* Slim Orca `bsz=1` for all benchmarks since `bsz=2` OOMs. We can handle `bsz=2`, but we benchmark it with `bsz=1` for consistency.
### For replication of timings:
* [Huggingface LAION DDP reference implementation](https://www.kaggle.com/code/danielhanchen/huggingface-original-laion-oig) 60 steps on DDP Kaggle 2 Tesla T4 GPUs takes 40 minutes and 46 seconds
* [Unsloth LAION DDP fast implementation](https://www.kaggle.com/code/danielhanchen/unsloth-laion-chip2-kaggle) 60 steps on DDP Kaggle 2 Tesla T4 GPUs - **Unsloth only uses 1 GPU whilst Pro plans use more.** takes 4 minutes and 34 seconds **(8.64x speedup)**
# Full benchmarking tables
Click "Code" for a fully reproducible example.
"Unsloth Equal" is a preview of our PRO version, with code stripped out. All settings and the loss curve remains identical.
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| Alpaca | 1x | 1.04x | 1.98x | 2.48x | 5.32x | **15.64x** |
| code | [Code](https://colab.research.google.com/drive/1u4dBeM-0vGNVmmO6X7cScAut-Hyt4KDF?usp=sharing) | [Code](https://colab.research.google.com/drive/1fgTOxpMbVjloQBvZyz4lF4BacKSZOB2A?usp=sharing) | [Code](https://colab.research.google.com/drive/1YIPY_18xm-K0iJDgvNkRoJsgkPMPAO3G?usp=sharing) | [Code](https://colab.research.google.com/drive/1ANW8EFL3LVyTD7Gq4TkheC1Z7Rxw-rHp?usp=sharing) | | |
| seconds| 1040 | 1001 | 525 | 419 | 196 | 67 |
| memory MB| 18235 | 15365 | 9631 | 8525 | | |
| % saved| | 15.74 | 47.18 | 53.25 | | | |
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| LAION Chip2 | 1x | 0.92x | 1.61x | 1.84x | 7.05x | **20.73x** |
| code |[Code](https://colab.research.google.com/drive/1gjL1TaKwc_xv2TcxJC8QWEWBG1msh3g2?usp=sharing) | [Code](https://colab.research.google.com/drive/15vlPjMr8xDj5BFhGdqunGaOQSMqXPEXU?usp=sharing) | [Code](https://colab.research.google.com/drive/1zPwvf-BmHyHlPMBxDsY8zS0BnQ-KKbCc?usp=sharing) | [Code](https://colab.research.google.com/drive/1X2uHy-arRsZxqWHvKHwwW102JaMwChD2?usp=sharing) | | |
| seconds| 581 | 631 | 361 | 315 | 82 | 28 |
| memory MB| 7763 | 8047 | 7763 | 6441 | | |
| % saved| | -3.66 | 0.00 | 17.03 | | | |
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| OASST | 1x | 1.19x | 2.17x | 2.66x | 5.04x | **14.83x** |
| code |[Code](https://colab.research.google.com/drive/10NzDreFbuWELGUuBv0MOoC7y3MBewaNx?usp=sharing) | [Code](https://colab.research.google.com/drive/1TwdkJ1sHsuEH-kgeCPqSFeCpOnCfz6Ou?usp=sharing) | [Code](https://colab.research.google.com/drive/1AkwjUkOF0XeRBMT_S8Uhh74kitEsZHla?usp=sharing) | [Code](https://colab.research.google.com/drive/1roMkp2UjbeK2t3DkNz50cRs1MT92RPFT?usp=sharing) | | |
| seconds| 1852 | 1558 | 852 | 696 | 367 | 125 |
| memory MB| 26431 | 16565 | 12267| 11223| | |
| % saved| | 37.33 | 53.59 | 57.54 | | |
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| Slim Orca | 1x | 1.18x | 2.22x | 2.64x | 5.04x | **14.82x** |
| code |[Code](https://colab.research.google.com/drive/1UNo1xsMl8YH7xnWnIVjDFnCAPfc0RGgu?usp=sharing) | [Code](https://colab.research.google.com/drive/1zbphER-SKhbSWGjHTfnBLPFyTgIVvaeH?usp=sharing) | [Code](https://colab.research.google.com/drive/156si33585iv4Uh-VILFglUmIMrNCNuc2?usp=sharing) | [Code](https://colab.research.google.com/drive/1_mhZy7dfl9jEnJRuJBZJ5y3OwW06jgQA?usp=sharing) | | |
| seconds| 1824 | 1545 | 821 | 691 | 362 | 123 |
| memory MB| 24557 | 15681 | 10595| 9007 | | |
| % saved| | 36.14 | 56.86 | 63.32 | | |
### Mistral 7b
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| Mistral 7B Slim Orca | 1x | 1.15x | 2.15x | 2.53x | 4.61x | **13.69x** |
| code | [Code](https://colab.research.google.com/drive/1mePk3KzwTD81hr5mcNcs_AX3Kbg_Ha0x?usp=sharing) | [Code](https://colab.research.google.com/drive/1dgHxjvTmX6hb0bPcLp26RXSE6_n9DKj7?usp=sharing) | [Code](https://colab.research.google.com/drive/1SKrKGV-BZoU4kv5q3g0jtE_OhRgPtrrQ?usp=sharing) | [Code](https://colab.research.google.com/drive/18yOiyX0T81mTwZqOALFSCX_tSAqju6aD?usp=sharing) | |
| seconds | 1813 | 1571 | 842 | 718 | 393 | 132 |
| memory MB | 32853 | 19385 | 12465 | 10271 | | |
| % saved| | 40.99 | 62.06 | 68.74 | | |
### CodeLlama 34b
| 1 A100 40GB | Hugging Face | Flash Attention 2 | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-------------|-----------------|--------------|---------------|-------------|
| Code Llama 34B | OOM ❌ | 0.99x | 1.87x | 2.61x | 4.27x | 12.82x |
| code | [Code](https://colab.research.google.com/drive/1ykfz3BqrtC_AUFegCzUQjjfUNlxp6Otc?usp=sharing) | [Code](https://colab.research.google.com/drive/12ZypxQh7OC6kBXvWZI-5d05I4m-B_hoR?usp=sharing) | [Code](https://colab.research.google.com/drive/1gdHyAx8XJsz2yNV-DHvbHjR1iCef5Qmh?usp=sharing) | [Code](https://colab.research.google.com/drive/1fm7wqx9MJ0kRrwKOfmLkK1Rmw-pySahB?usp=sharing) | |
| seconds | 1953 | 1982 | 1043 | 748 | 458 | 152 |
| memory MB | 40000 | 33217 | 27413 | 22161 | | |
| % saved| | 16.96| 31.47 | 44.60 | | | |
### 1 Tesla T4
| 1 T4 16GB | Hugging Face | Flash Attention | Unsloth Open | Unsloth Pro Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-----------------|-----------------|---------------|---------------|-------------|
| Alpaca | 1x | 1.09x | 1.69x | 1.79x | 2.93x | **8.3x** |
| code | [Code](https://colab.research.google.com/drive/1XpLIV4s8Bj5uryB-X2gqM88oRGHEGdaB?usp=sharing) | [Code](https://colab.research.google.com/drive/1LyXu6CjuymQg6ddHX8g1dpUvrMa1nn4L?usp=sharing) | [Code](https://colab.research.google.com/drive/1gsv4LpY7C32otl1rgRo5wXTk4HIitXoM?usp=sharing) | [Code](https://colab.research.google.com/drive/1VtULwRQwhEnVdNryjm27zXfdSM1tNfFK?usp=sharing) | | |
| seconds | 1599 | 1468 | 942 | 894 | 545 | 193 |
| memory MB | 7199 | 7059 | 6459 | 5443 | | |
| % saved | | 1.94 | 10.28 | 24.39 | | |
| 1 T4 16GB | Hugging Face | Flash Attention | Unsloth Open | Unsloth Pro Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-----------------|-----------------|---------------|---------------|-------------|
| LAION Chip2 | 1x | 0.99x | 1.80x | 1.75x | 4.15x | **11.75x** |
| code | [Code](https://colab.research.google.com/drive/1EtdStADehE4FVJnU2Cu6O8p9jDYdqG2L?usp=sharing) | [Code](https://colab.research.google.com/drive/1Ik4jO68odUiQIJ_szZ3xok5fk58WpA5Q?usp=sharing) | [Code](https://colab.research.google.com/drive/1E2nR4V3bXIWBQIUE7uR39lYPr3UikzqH?usp=sharing) | [Code](https://colab.research.google.com/drive/13jbj8D8FOt9KyXwZt9Yf2MsYkD8CyCVR?usp=sharing) | | |
| seconds | 952 | 955 | 529 | 543 | 229 | 81 |
| memory MB | 6037 | 6033 | 5797 | 4855 | | |
| % saved | | 0.07 | 3.98 | 19.58 | | |
| 1 T4 16GB | Hugging Face | Flash Attention | Unsloth Open | Unsloth Pro Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-----------------|-----------------|---------------|---------------|-------------|
| OASST | 1x | 1.19x | 1.95x | 1.86x | 2.58x | **7.3x** |
| code | [Code](https://colab.research.google.com/drive/1aXzGgEM3yYB6SWy_XR81nQFWME40ksSy?usp=sharing) | [Code](https://colab.research.google.com/drive/1-5MdIOp0cM0scC-CdRZhh8OYhnGHqct4?usp=sharing) | [Code](https://colab.research.google.com/drive/1n-fgduZhRUsSjgpqNtVkXA3rSfE7iBdg?usp=sharing) | [Code](https://colab.research.google.com/drive/1z_GlHr2M_bB4lQrPhdWC7dseZv23cBIy?usp=sharing) | | |
| seconds | 2640 | 2222 | 1355 | 1421 | 1024 | 362 |
| memory MB | 14827 | 10391 | 8413 | 7031 | | |
| % saved | | 29.92 | 43.26 | 52.58 | | |
| 1 T4 16GB | Hugging Face | Flash Attention | Unsloth Open | Unsloth Pro Equal | Unsloth Pro | Unsloth Max |
|--------------|-------------|-----------------|-----------------|---------------|---------------|-------------|
| Slim Orca | 1x | 1.21x | 1.77x | 1.85x | 2.71x | **7.67x** |
| code | [Code](https://colab.research.google.com/drive/15yLlJx9IE84kzx7ikky45pRcarPyUtEs?usp=sharing) | [Code](https://colab.research.google.com/drive/16IShIBmjKULWy87I-xURpj4nztTkAF13?usp=sharing) | [Code](https://colab.research.google.com/drive/1CJG3XLg_OQpCz71eB7Uqx7wuK_n2b-a8?usp=sharing) | [Code](https://colab.research.google.com/drive/1UmwuWHtlrC6MAfl9mX7A_TRfo5iSHDa-?usp=sharing) | | |
| seconds | 2735 | 2262 | 1545 | 1478 | 1009 | 356 |
| memory MB | 13933 | 10489 | 7661 | 6563 | | |
| % saved | | 24.72 | 45.02 | 52.90 | | |
### 2 Tesla T4s via DDP
| 2 T4 DDP | Hugging Face | Flash Attention | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|----------|-------------|-----------------|--------------|---------------|-------------|
| Alpaca | 1x | 0.99x | 4.95x | 4.44x | 7.28x | **20.61x** |
| code | [Code](https://www.kaggle.com/danielhanchen/hf-original-alpaca-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/hf-sdpa-alpaca-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/unsloth-alpaca-t4-ddp) | | |
| seconds | 9882 | 9946 | 1996 | 2227 | 1357 | 480 |
| memory MB| 9176 | 9128 | 6904 | 6782 | | |
| % saved | | 0.52 | 24.76 | 26.09 | | | |
| 2 T4 DDP | Hugging Face | Flash Attention | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|----------|-------------|-----------------|--------------|---------------|-------------|
| LAION Chip2 | 1x | 1.12x | 5.28x | 4.21x | 10.01x | **28.32x** |
| code | [Code](https://www.kaggle.com/danielhanchen/hf-original-laion-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/hf-sdpa-laion-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/unsloth-laion-t4-ddp) | | |
| seconds | 5418 | 4854 | 1027 | 1286 | 541 | 191 |
| memory MB| 7316 | 7316 | 5732 | 5934 | | |
| % saved | | 0.00 | 21.65 | 18.89 | | |
| 2 T4 DDP | Hugging Face | Flash Attention | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|----------|-------------|-----------------|--------------|---------------|-------------|
| OASST (bsz=1) | 1x | 1.14x | 5.56x | 5.09x | 5.64x | **15.97x** |
| code | [Code](https://www.kaggle.com/danielhanchen/hf-original-oasst-bsz1-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/hf-sdpa-oasst-bsz1-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/unsloth-oasst-bsz1-t4-ddp) | | | |
| seconds | 4503 | 3955 | 811 | 885 | 798 | 282 |
| memory MB | 11896 | 11628 | 6616 | 7105 | | |
| % saved | | 2.25 | 44.38 | 40.27 | | |
| 2 T4 DDP | Hugging Face | Flash Attention | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|----------|-------------|-----------------|--------------|---------------|-------------|
| Slim Orca (bsz=1) | 1x | 0.97x | 5.54x | 4.68x | 6.88x | **19.46x** |
| code | [Code](https://www.kaggle.com/danielhanchen/hf-original-slimorca-bsz1-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/hf-sdpa-slimorca-bsz1-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/unsloth-slimorca-bsz1-t4-ddp) | | |
| seconds | 4042 | 4158 | 729 | 863 | 588 | 208 |
| memory MB| 11010 | 11042 | 6492 | 7410 | | |
| % saved | | -0.29| 41.04 | 32.70 | | | |
| 2 T4 DDP | Hugging Face | Flash Attention | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|----------|-------------|-----------------|--------------|---------------|-------------|
| OASST (bsz=2) | OOM ❌ | OOM ❌ | ✓ | ✓ | ✓ | ✓ |
| code | [Code](https://www.kaggle.com/danielhanchen/hf-original-oasst-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/hf-sdpa-oasst-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/unsloth-oasst-t4-ddp) | | | |
| seconds | OOM | OOM | 2719 | 3391 | 2794 | 987 |
| memory MB| OOM | OOM | 8134 | 9600 | | |
| % saved | OOM | OOM | | | | |
| 2 T4 DDP | Hugging Face | Flash Attention | Unsloth Open | Unsloth Equal | Unsloth Pro | Unsloth Max |
|--------------|----------|-------------|-----------------|--------------|---------------|-------------|
| Slim Orca (bsz=2) | OOM ❌ | OOM ❌ | ✓ | ✓ | ✓ |✓ |
| code | [Code](https://www.kaggle.com/danielhanchen/hf-original-slimorca-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/hf-sdpa-slimorca-t4-ddp) | [Code](https://www.kaggle.com/danielhanchen/unsloth-slimorca-t4-ddp) | | |
| seconds | OOM | OOM | 2990 | 3444 | 2351 | 831 |
| memory MB| OOM | OOM | 7594 | 8881 | | |
| % saved | OOM | OOM | | | | |
# How did we make it faster?
Manual autograd, Triton kernels etc. See our [Benchmark Breakdown](https://unsloth.ai/blog/mistral-benchmark) for more info!
$$
\begin{align}
\text{RMSLayernorm}(X) &= y = \frac{x_i}{\sqrt{\frac{1}{n}\sum{x_i^2}+\epsilon}} \cdot w \\
\frac{dC}{dX} &= \frac{1}{n} \frac{1}{\sqrt{\frac{1}{n}\sum{x_i^2}+\epsilon}} \bigg( n (dY \cdot w) - \bigg( \frac{x_i}{\sqrt{\frac{1}{n}\sum{x_i^2}+\epsilon}} \cdot \sum{dY \cdot \frac{x_i}{\sqrt{\frac{1}{n}\sum{x_i^2}+\epsilon}} \cdot w } \bigg) \bigg) \\
y &= \frac{x_i}{\sqrt{\frac{1}{n}\sum{x_i^2}+\epsilon}} \cdot w \\
r &= \frac{1}{\sqrt{\frac{1}{n}\sum{x_i^2}+\epsilon}} \\
\frac{dC}{dX} &= \frac{1}{n} r \bigg( n (dY \cdot w) - \bigg( x_i \cdot r \cdot \sum{dY \cdot y_i } \bigg) \bigg)
\end{align}
$$
# Troubleshooting
1. Sometimes `bitsandbytes` or `xformers` does not link properly. Try running: