Repository: kozistr/pytorch_optimizer

Issue:
Support AdaGC, Simplified-Ademamix
AdaGC
https://arxiv.org/abs/2502.11034

Simplified-Ademamix 
https://arxiv.org/abs/2502.02431
https://github.com/[DepenM/Simplified-AdEMAMix](https://github.com/DepenM/Simplified-AdEMAMix/)/

Thank you!

Hints from issue comments:

Solution patch:
diff --git a/README.md b/README.md
index 000850cf..b28037cf 100644
--- a/README.md
+++ b/README.md
@@ -10,7 +10,7 @@
 
 ## The reasons why you use `pytorch-optimizer`.
 
-* Wide range of supported optimizers. Currently, **100 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
+* Wide range of supported optimizers. Currently, **102 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
 * Including many variants such as `ADOPT`, `Cautious`, `AdamD`, `StableAdamW`, and `Gradient Centrailiaztion`
 * Easy to use, clean, and tested codes
 * Active maintenance
@@ -105,110 +105,112 @@ get_supported_optimizers(['adam*', 'ranger*'])
 # ['adamax', 'adamg', 'adammini', 'adamod', 'adamp', 'adams', 'adamw', 'ranger', 'ranger21']
 ```
 
-| Optimizer     | Description                                                                                       | Official Code                                                                                                  | Paper                                                                                       | Citation                                                                                                                            |
-|---------------|---------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------|
-| AdaBelief     | *Adapting Step-sizes by the Belief in Observed Gradients*                                         | [github](https://github.com/juntang-zhuang/Adabelief-Optimizer)                                                | <https://arxiv.org/abs/2010.07468>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201007468Z/exportcitation)                                                        |
-| AdaBound      | *Adaptive Gradient Methods with Dynamic Bound of Learning Rate*                                   | [github](https://github.com/Luolc/AdaBound/blob/master/adabound/adabound.py)                                   | <https://openreview.net/forum?id=Bkg3g2R9FX>                                                | [cite](https://github.com/Luolc/AdaBound#citing)                                                                                    |
-| AdaHessian    | *An Adaptive Second Order Optimizer for Machine Learning*                                         | [github](https://github.com/amirgholami/adahessian)                                                            | <https://arxiv.org/abs/2006.00719>                                                          | [cite](https://github.com/amirgholami/adahessian#citation)                                                                          |
-| AdamD         | *Improved bias-correction in Adam*                                                                |                                                                                                                | <https://arxiv.org/abs/2110.10828>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv211010828S/exportcitation)                                                        |
-| AdamP         | *Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights*                    | [github](https://github.com/clovaai/AdamP)                                                                     | <https://arxiv.org/abs/2006.08217>                                                          | [cite](https://github.com/clovaai/AdamP#how-to-cite)                                                                                |
-| diffGrad      | *An Optimization Method for Convolutional Neural Networks*                                        | [github](https://github.com/shivram1987/diffGrad)                                                              | <https://arxiv.org/abs/1909.11015v3>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190911015D/exportcitation)                                                        |
-| MADGRAD       | *A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic*                          | [github](https://github.com/facebookresearch/madgrad)                                                          | <https://arxiv.org/abs/2101.11075>                                                          | [cite](https://github.com/facebookresearch/madgrad#tech-report)                                                                     |
-| RAdam         | *On the Variance of the Adaptive Learning Rate and Beyond*                                        | [github](https://github.com/LiyuanLucasLiu/RAdam)                                                              | <https://arxiv.org/abs/1908.03265>                                                          | [cite](https://github.com/LiyuanLucasLiu/RAdam#citation)                                                                            |
-| Ranger        | *a synergistic optimizer combining RAdam and LookAhead, and now GC in one optimizer*              | [github](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer)                                          | <https://bit.ly/3zyspC3>                                                                    | [cite](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer#citing-this-work)                                                |
-| Ranger21      | *a synergistic deep learning optimizer*                                                           | [github](https://github.com/lessw2020/Ranger21)                                                                | <https://arxiv.org/abs/2106.13731>                                                          | [cite](https://github.com/lessw2020/Ranger21#referencing-this-work)                                                                 |
-| Lamb          | *Large Batch Optimization for Deep Learning*                                                      | [github](https://github.com/cybertronai/pytorch-lamb)                                                          | <https://arxiv.org/abs/1904.00962>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190400962Y/exportcitation)                                                        |
-| Shampoo       | *Preconditioned Stochastic Tensor Optimization*                                                   | [github](https://github.com/moskomule/shampoo.pytorch)                                                         | <https://arxiv.org/abs/1802.09568>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180209568G/exportcitation)                                                        |
-| Nero          | *Learning by Turning: Neural Architecture Aware Optimisation*                                     | [github](https://github.com/jxbz/nero)                                                                         | <https://arxiv.org/abs/2102.07227>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210207227L/exportcitation)                                                        |
-| Adan          | *Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models*                          | [github](https://github.com/sail-sg/Adan)                                                                      | <https://arxiv.org/abs/2208.06677>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220806677X/exportcitation)                                                        |
-| Adai          | *Disentangling the Effects of Adaptive Learning Rate and Momentum*                                | [github](https://github.com/zeke-xie/adaptive-inertia-adai)                                                    | <https://arxiv.org/abs/2006.15815>                                                          | [cite](https://github.com/zeke-xie/adaptive-inertia-adai#citing)                                                                    |
-| SAM           | *Sharpness-Aware Minimization*                                                                    | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2010.01412>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201001412F/exportcitation)                                                        |
-| ASAM          | *Adaptive Sharpness-Aware Minimization*                                                           | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2102.11600>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210211600K/exportcitation)                                                        |
-| GSAM          | *Surrogate Gap Guided Sharpness-Aware Minimization*                                               | [github](https://github.com/juntang-zhuang/GSAM)                                                               | <https://openreview.net/pdf?id=edONMAnhLu->                                                 | [cite](https://github.com/juntang-zhuang/GSAM#citation)                                                                             |
-| D-Adaptation  | *Learning-Rate-Free Learning by D-Adaptation*                                                     | [github](https://github.com/facebookresearch/dadaptation)                                                      | <https://arxiv.org/abs/2301.07733>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230107733D/exportcitation)                                                        |
-| AdaFactor     | *Adaptive Learning Rates with Sublinear Memory Cost*                                              | [github](https://github.com/DeadAt0m/adafactor-pytorch)                                                        | <https://arxiv.org/abs/1804.04235>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180404235S/exportcitation)                                                        |
-| Apollo        | *An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization*   | [github](https://github.com/XuezheMax/apollo)                                                                  | <https://arxiv.org/abs/2009.13586>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv200913586M/exportcitation)                                                        |
-| NovoGrad      | *Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks*      | [github](https://github.com/lonePatient/NovoGrad-pytorch)                                                      | <https://arxiv.org/abs/1905.11286>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190511286G/exportcitation)                                                        |
-| Lion          | *Symbolic Discovery of Optimization Algorithms*                                                   | [github](https://github.com/google/automl/tree/master/lion)                                                    | <https://arxiv.org/abs/2302.06675>                                                          | [cite](https://github.com/google/automl/tree/master/lion#citation)                                                                  |
-| Ali-G         | *Adaptive Learning Rates for Interpolation with Gradients*                                        | [github](https://github.com/oval-group/ali-g)                                                                  | <https://arxiv.org/abs/1906.05661>                                                          | [cite](https://github.com/oval-group/ali-g#adaptive-learning-rates-for-interpolation-with-gradients)                                |
-| SM3           | *Memory-Efficient Adaptive Optimization*                                                          | [github](https://github.com/google-research/google-research/tree/master/sm3)                                   | <https://arxiv.org/abs/1901.11150>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190111150A/exportcitation)                                                        |
-| AdaNorm       | *Adaptive Gradient Norm Correction based Optimizer for CNNs*                                      | [github](https://github.com/shivram1987/AdaNorm)                                                               | <https://arxiv.org/abs/2210.06364>                                                          | [cite](https://github.com/shivram1987/AdaNorm/tree/main#citation)                                                                   |
-| RotoGrad      | *Gradient Homogenization in Multitask Learning*                                                   | [github](https://github.com/adrianjav/rotograd)                                                                | <https://openreview.net/pdf?id=T8wHz4rnuGL>                                                 | [cite](https://github.com/adrianjav/rotograd#citing)                                                                                |
-| A2Grad        | *Optimal Adaptive and Accelerated Stochastic Gradient Descent*                                    | [github](https://github.com/severilov/A2Grad_optimizer)                                                        | <https://arxiv.org/abs/1810.00553>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000553D/exportcitation)                                                        |
-| AccSGD        | *Accelerating Stochastic Gradient Descent For Least Squares Regression*                           | [github](https://github.com/rahulkidambi/AccSGD)                                                               | <https://arxiv.org/abs/1704.08227>                                                          | [cite](https://github.com/rahulkidambi/AccSGD#citation)                                                                             |
-| SGDW          | *Decoupled Weight Decay Regularization*                                                           | [github](https://github.com/loshchil/AdamW-and-SGDW)                                                           | <https://arxiv.org/abs/1711.05101>                                                          | [cite](https://github.com/loshchil/AdamW-and-SGDW#contact)                                                                          |
-| ASGD          | *Adaptive Gradient Descent without Descent*                                                       | [github](https://github.com/ymalitsky/adaptive_GD)                                                             | <https://arxiv.org/abs/1910.09529>                                                          | [cite](https://github.com/ymalitsky/adaptive_GD#reference)                                                                          |
-| Yogi          | *Adaptive Methods for Nonconvex Optimization*                                                     |                                                                                                                | [NIPS 2018](https://papers.nips.cc/paper/8186-adaptive-methods-for-nonconvex-optimization)  | [cite](https://proceedings.neurips.cc/paper_files/paper/2018/hash/90365351ccc7437a1309dc64e4db32a3-Abstract.html)                   |
-| SWATS         | *Improving Generalization Performance by Switching from Adam to SGD*                              |                                                                                                                | <https://arxiv.org/abs/1712.07628>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2017arXiv171207628S/exportcitation)                                                        |
-| Fromage       | *On the distance between two neural networks and the stability of learning*                       | [github](https://github.com/jxbz/fromage)                                                                      | <https://arxiv.org/abs/2002.03432>                                                          | [cite](https://github.com/jxbz/fromage#citation)                                                                                    |
-| MSVAG         | *Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients*                       | [github](https://github.com/lballes/msvag)                                                                     | <https://arxiv.org/abs/1705.07774>                                                          | [cite](https://github.com/lballes/msvag#citation)                                                                                   |
-| AdaMod        | *An Adaptive and Momental Bound Method for Stochastic Learning*                                   | [github](https://github.com/lancopku/AdaMod)                                                                   | <https://arxiv.org/abs/1910.12249>                                                          | [cite](https://github.com/lancopku/AdaMod#citation)                                                                                 |
-| AggMo         | *Aggregated Momentum: Stability Through Passive Damping*                                          | [github](https://github.com/AtheMathmo/AggMo)                                                                  | <https://arxiv.org/abs/1804.00325>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180400325L/exportcitation)                                                        |
-| QHAdam        | *Quasi-hyperbolic momentum and Adam for deep learning*                                            | [github](https://github.com/facebookresearch/qhoptim)                                                          | <https://arxiv.org/abs/1810.06801>                                                          | [cite](https://github.com/facebookresearch/qhoptim#reference)                                                                       |
-| PID           | *A PID Controller Approach for Stochastic Optimization of Deep Networks*                          | [github](https://github.com/tensorboy/PIDOptimizer)                                                            | [CVPR 18](http://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdf)                     | [cite](https://github.com/tensorboy/PIDOptimizer#citation)                                                                          |
-| Gravity       | *a Kinematic Approach on Optimization in Deep Learning*                                           | [github](https://github.com/dariush-bahrami/gravity.optimizer)                                                 | <https://arxiv.org/abs/2101.09192>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210109192B/exportcitation)                                                        |
-| AdaSmooth     | *An Adaptive Learning Rate Method based on Effective Ratio*                                       |                                                                                                                | <https://arxiv.org/abs/2204.00825v1>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220400825L/exportcitation)                                                        |
-| SRMM          | *Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates* | [github](https://github.com/HanbaekLyu/SRMM)                                                                   | <https://arxiv.org/abs/2201.01652>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220101652L/exportcitation)                                                        |
-| AvaGrad       | *Domain-independent Dominance of Adaptive Methods*                                                | [github](https://github.com/lolemacs/avagrad)                                                                  | <https://arxiv.org/abs/1912.01823>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191201823S/exportcitation)                                                        |
-| PCGrad        | *Gradient Surgery for Multi-Task Learning*                                                        | [github](https://github.com/tianheyu927/PCGrad)                                                                | <https://arxiv.org/abs/2001.06782>                                                          | [cite](https://github.com/tianheyu927/PCGrad#reference)                                                                             |
-| AMSGrad       | *On the Convergence of Adam and Beyond*                                                           |                                                                                                                | <https://openreview.net/pdf?id=ryQu7f-RZ>                                                   | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190409237R/exportcitation)                                                        |
-| Lookahead     | *k steps forward, 1 step back*                                                                    | [github](https://github.com/pytorch/examples/tree/main/imagenet)                                               | <https://arxiv.org/abs/1907.08610>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190708610Z/exportcitation)                                                        |
-| PNM           | *Manipulating Stochastic Gradient Noise to Improve Generalization*                                | [github](https://github.com/zeke-xie/Positive-Negative-Momentum)                                               | <https://arxiv.org/abs/2103.17182>                                                          | [cite](https://github.com/zeke-xie/Positive-Negative-Momentum#citing)                                                               |
-| GC            | *Gradient Centralization*                                                                         | [github](https://github.com/Yonghongwei/Gradient-Centralization)                                               | <https://arxiv.org/abs/2004.01461>                                                          | [cite](https://github.com/Yonghongwei/Gradient-Centralization#citation)                                                             |
-| AGC           | *Adaptive Gradient Clipping*                                                                      | [github](https://github.com/deepmind/deepmind-research/tree/master/nfnets)                                     | <https://arxiv.org/abs/2102.06171>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210206171B/exportcitation)                                                        |
-| Stable WD     | *Understanding and Scheduling Weight Decay*                                                       | [github](https://github.com/zeke-xie/stable-weight-decay-regularization)                                       | <https://arxiv.org/abs/2011.11152>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201111152X/exportcitation)                                                        |
-| Softplus T    | *Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM*                           |                                                                                                                | <https://arxiv.org/abs/1908.00700>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190800700T/exportcitation)                                                        |
-| Un-tuned w/u  | *On the adequacy of untuned warmup for adaptive optimization*                                     |                                                                                                                | <https://arxiv.org/abs/1910.04209>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191004209M/exportcitation)                                                        |
-| Norm Loss     | *An efficient yet effective regularization method for deep neural networks*                       |                                                                                                                | <https://arxiv.org/abs/2103.06583>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210306583G/exportcitation)                                                        |
-| AdaShift      | *Decorrelation and Convergence of Adaptive Learning Rate Methods*                                 | [github](https://github.com/MichaelKonobeev/adashift)                                                          | <https://arxiv.org/abs/1810.00143v4>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000143Z/exportcitation)                                                        |
-| AdaDelta      | *An Adaptive Learning Rate Method*                                                                |                                                                                                                | <https://arxiv.org/abs/1212.5701v1>                                                         | [cite](https://ui.adsabs.harvard.edu/abs/2012arXiv1212.5701Z/exportcitation)                                                        |
-| Amos          | *An Adam-style Optimizer with Adaptive Weight Decay towards Model-Oriented Scale*                 | [github](https://github.com/google-research/jestimator)                                                        | <https://arxiv.org/abs/2210.11693>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221011693T/exportcitation)                                                        |
-| SignSGD       | *Compressed Optimisation for Non-Convex Problems*                                                 | [github](https://github.com/jxbz/signSGD)                                                                      | <https://arxiv.org/abs/1802.04434>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180204434B/exportcitation)                                                        |
-| Sophia        | *A Scalable Stochastic Second-order Optimizer for Language Model Pre-training*                    | [github](https://github.com/Liuhong99/Sophia)                                                                  | <https://arxiv.org/abs/2305.14342>                                                          | [cite](https://github.com/Liuhong99/Sophia)                                                                                         |
-| Prodigy       | *An Expeditiously Adaptive Parameter-Free Learner*                                                | [github](https://github.com/konstmish/prodigy)                                                                 | <https://arxiv.org/abs/2306.06101>                                                          | [cite](https://github.com/konstmish/prodigy#how-to-cite)                                                                            |
-| PAdam         | *Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks*    | [github](https://github.com/uclaml/Padam)                                                                      | <https://arxiv.org/abs/1806.06763>                                                          | [cite](https://github.com/uclaml/Padam#citation)                                                                                    |
-| LOMO          | *Full Parameter Fine-tuning for Large Language Models with Limited Resources*                     | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2306.09782>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
-| AdaLOMO       | *Low-memory Optimization with Adaptive Learning Rate*                                             | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2310.10195>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
-| Tiger         | *A Tight-fisted Optimizer, an optimizer that is extremely budget-conscious*                       | [github](https://github.com/bojone/tiger)                                                                      |                                                                                             | [cite](https://github.com/bojone/tiger/blob/main/README_en.md#citation)                                                             |
-| CAME          | *Confidence-guided Adaptive Memory Efficient Optimization*                                        | [github](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME)                            | <https://aclanthology.org/2023.acl-long.243/>                                               | [cite](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME#citation)                                          |
-| WSAM          | *Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Term*             | [github](https://github.com/intelligent-machine-learning/dlrover/blob/master/atorch/atorch/optimizers/wsam.py) | <https://arxiv.org/abs/2305.15817>                                                          | [cite](https://github.com/intelligent-machine-learning/dlrover)                                                                     |
-| Aida          | *A DNN Optimizer that Improves over AdaBelief by Suppression of the Adaptive Stepsize Range*      | [github](https://github.com/guoqiang-zhang-x/Aida-Optimizer)                                                   | <https://arxiv.org/abs/2203.13273>                                                          | [cite](https://github.com/guoqiang-zhang-x/Aida-Optimizer?tab=readme-ov-file#1-brief-description-of-aida)                           |
-| GaLore        | *Memory-Efficient LLM Training by Gradient Low-Rank Projection*                                   | [github](https://github.com/jiaweizzhao/GaLore)                                                                | <https://arxiv.org/abs/2403.03507>                                                          | [cite](https://github.com/jiaweizzhao/GaLore/tree/master?tab=readme-ov-file#citation)                                               |
-| Adalite       | *Adalite optimizer*                                                                               | [github](https://github.com/VatsaDev/adalite)                                                                  | <https://github.com/VatsaDev/adalite>                                                       | [cite](https://github.com/VatsaDev/adalite)                                                                                         |
-| bSAM          | *SAM as an Optimal Relaxation of Bayes*                                                           | [github](https://github.com/team-approx-bayes/bayesian-sam)                                                    | <https://arxiv.org/abs/2210.01620>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221001620M/exportcitation)                                                        |
-| Schedule-Free | *Schedule-Free Optimizers*                                                                        | [github](https://github.com/facebookresearch/schedule_free)                                                    | <https://github.com/facebookresearch/schedule_free>                                         | [cite](https://github.com/facebookresearch/schedule_free)                                                                           |
-| FAdam         | *Adam is a natural gradient optimizer using diagonal empirical Fisher information*                | [github](https://github.com/lessw2020/fadam_pytorch)                                                           | <https://arxiv.org/abs/2405.12807>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240512807H/exportcitation)                                                        |
-| Grokfast      | *Accelerated Grokking by Amplifying Slow Gradients*                                               | [github](https://github.com/ironjr/grokfast)                                                                   | <https://arxiv.org/abs/2405.20233>                                                          | [cite](https://github.com/ironjr/grokfast?tab=readme-ov-file#citation)                                                              |
-| Kate          | *Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad*                     | [github](https://github.com/nazya/KATE)                                                                        | <https://arxiv.org/abs/2403.02648>                                                          | [cite](https://github.com/nazya/KATE?tab=readme-ov-file#remove-that-square-root-a-new-efficient-scale-invariant-version-of-adagrad) |
-| StableAdamW   | *Stable and low-precision training for large-scale vision-language models*                        |                                                                                                                | <https://arxiv.org/abs/2304.13013>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230413013W/exportcitation)                                                        |
-| AdamMini      | *Use Fewer Learning Rates To Gain More*                                                           | [github](https://github.com/zyushun/Adam-mini)                                                                 | <https://arxiv.org/abs/2406.16793>                                                          | [cite](https://github.com/zyushun/Adam-mini?tab=readme-ov-file#citation)                                                            |
-| TRAC          | *Adaptive Parameter-free Optimization*                                                            | [github](https://github.com/ComputationalRobotics/TRAC)                                                        | <https://arxiv.org/abs/2405.16642>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240516642M/exportcitation)                                                        |
-| AdamG         | *Towards Stability of Parameter-free Optimization*                                                |                                                                                                                | <https://arxiv.org/abs/2405.04376>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240504376P/exportcitation)                                                        |
-| AdEMAMix      | *Better, Faster, Older*                                                                           | [github](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch)                                               | <https://arxiv.org/abs/2409.03137>                                                          | [cite](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch?tab=readme-ov-file#reference)                                         |
-| SOAP          | *Improving and Stabilizing Shampoo using Adam*                                                    | [github](https://github.com/nikhilvyas/SOAP)                                                                   | <https://arxiv.org/abs/2409.11321>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240911321V/exportcitation)                                                        |
-| ADOPT         | *Modified Adam Can Converge with Any β2 with the Optimal Rate*                                    | [github](https://github.com/iShohei220/adopt)                                                                  | <https://arxiv.org/abs/2411.02853>                                                          | [cite](https://github.com/iShohei220/adopt?tab=readme-ov-file#citation)                                                             |
-| FTRL          | *Follow The Regularized Leader*                                                                   |                                                                                                                | <https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/41159.pdf> |                                                                                                                                     |
-| Cautious      | *Improving Training with One Line of Code*                                                        | [github](https://github.com/kyleliang919/C-Optim)                                                              | <https://arxiv.org/pdf/2411.16085v1>                                                        | [cite](https://github.com/kyleliang919/C-Optim?tab=readme-ov-file#citation)                                                         |
-| DeMo          | *Decoupled Momentum Optimization*                                                                 | [github](https://github.com/bloc97/DeMo)                                                                       | <https://arxiv.org/abs/2411.19870>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241119870P/exportcitation)                                                        |
-| MicroAdam     | *Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence*                 | [github](https://github.com/IST-DASLab/MicroAdam)                                                              | <https://arxiv.org/abs/2405.15593>                                                          | [cite](https://github.com/IST-DASLab/MicroAdam?tab=readme-ov-file#citing)                                                           |
-| Muon          | *MomentUm Orthogonalized by Newton-schulz*                                                        | [github](https://github.com/KellerJordan/Muon)                                                                 | <https://x.com/kellerjordan0/status/1842300916864844014>                                    | [cite](https://github.com/KellerJordan/Muon)                                                                                        |
-| LaProp        | *Separating Momentum and Adaptivity in Adam*                                                      | [github](https://github.com/Z-T-WANG/LaProp-Optimizer)                                                         | <https://arxiv.org/abs/2002.04839>                                                          | [cite](https://github.com/Z-T-WANG/LaProp-Optimizer?tab=readme-ov-file#citation)                                                    |
-| APOLLO        | *SGD-like Memory, AdamW-level Performance*                                                        | [github](https://github.com/zhuhanqing/APOLLO)                                                                 | <https://arxiv.org/abs/2412.05270>                                                          | [cite](https://github.com/zhuhanqing/APOLLO?tab=readme-ov-file#-citation)                                                           |
-| MARS          | *Unleashing the Power of Variance Reduction for Training Large Models*                            | [github](https://github.com/AGI-Arena/MARS)                                                                    | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AGI-Arena/MARS/tree/main?tab=readme-ov-file#citation)                                                     |
-| SGDSaI        | *No More Adam: Learning Rate Scaling at Initialization is All You Need*                           | [github](https://github.com/AnonymousAlethiometer/SGD_SaI)                                                     | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AnonymousAlethiometer/SGD_SaI?tab=readme-ov-file#citation)                                                |
-| Grams         | *Gradient Descent with Adaptive Momentum Scaling*                                                 |                                                                                                                | <https://arxiv.org/abs/2412.17107>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241217107C/exportcitation)                                                        |
-| OrthoGrad     | *Grokking at the Edge of Numerical Stability*                                                     | [github](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability)                         | <https://arxiv.org/abs/2501.04697>                                                          | [cite](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability?tab=readme-ov-file#citation)                    |
-| Adam-ATAN2    | *Scaling Exponents Across Parameterizations and Optimizers*                                       |                                                                                                                | <https://arxiv.org/abs/2407.05872>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240705872E/exportcitation)                                                        |
-| SPAM          | *Spike-Aware Adam with Momentum Reset for Stable LLM Training*                                    | [github](https://github.com/TianjinYellow/SPAM-Optimizer)                                                      | <https://arxiv.org/abs/2501.06842>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250106842H/exportcitation)                                                        |
-| TAM           | *Torque-Aware Momentum*                                                                           |                                                                                                                | <https://arxiv.org/abs/2412.18790>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241218790M/exportcitation)                                                        |
-| FOCUS         | *First Order Concentrated Updating Scheme*                                                        | [github](https://github.com/liuyz0/FOCUS)                                                                      | <https://arxiv.org/abs/2501.12243>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250112243M/exportcitation)                                                        |
-| PSGD          | *Preconditioned Stochastic Gradient Descent*                                                      | [github](https://github.com/lixilinx/psgd_torch)                                                               | <https://arxiv.org/abs/1512.04202>                                                          | [cite](https://github.com/lixilinx/psgd_torch?tab=readme-ov-file#resources)                                                         |
-| EXAdam        | *The Power of Adaptive Cross-Moments*                                                             | [github](https://github.com/AhmedMostafa16/EXAdam)                                                             | <https://arxiv.org/abs/2412.20302>                                                          | [cite](https://github.com/AhmedMostafa16/EXAdam?tab=readme-ov-file#citation)                                                        |
-| GCSAM         | *Gradient Centralized Sharpness Aware Minimization*                                               | [github](https://github.com/mhassann22/GCSAM)                                                                  | <https://arxiv.org/abs/2501.11584>                                                          | [cite](https://github.com/mhassann22/GCSAM?tab=readme-ov-file#citation)                                                             |
-| LookSAM       | *Towards Efficient and Scalable Sharpness-Aware Minimization*                                     | [github](https://github.com/rollovd/LookSAM)                                                                   | <https://arxiv.org/abs/2203.02714>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220302714L/exportcitation)                                                        |
-| SCION         | *Training Deep Learning Models with Norm-Constrained LMOs*                                        |                                                                                                                | <https://arxiv.org/abs/2502.07529>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250207529P/exportcitation)                                                        |
-| COSMOS        | *SOAP with Muon*                                                                                  | [github](https://github.com/lliu606/COSMOS)                                                                    |                                                                                             |                                                                                                                                     |
-| StableSPAM    | *How to Train in 4-Bit More Stably than 16-Bit Adam                                               | [github](https://github.com/TianjinYellow/StableSPAM)                                                          | <https://arxiv.org/abs/2502.17055>                                                          |                                                                                                                                     |
+| Optimizer           | Description                                                                                       | Official Code                                                                                                  | Paper                                                                                       | Citation                                                                                                                            |
+|---------------------|---------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------|
+| AdaBelief           | *Adapting Step-sizes by the Belief in Observed Gradients*                                         | [github](https://github.com/juntang-zhuang/Adabelief-Optimizer)                                                | <https://arxiv.org/abs/2010.07468>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201007468Z/exportcitation)                                                        |
+| AdaBound            | *Adaptive Gradient Methods with Dynamic Bound of Learning Rate*                                   | [github](https://github.com/Luolc/AdaBound/blob/master/adabound/adabound.py)                                   | <https://openreview.net/forum?id=Bkg3g2R9FX>                                                | [cite](https://github.com/Luolc/AdaBound#citing)                                                                                    |
+| AdaHessian          | *An Adaptive Second Order Optimizer for Machine Learning*                                         | [github](https://github.com/amirgholami/adahessian)                                                            | <https://arxiv.org/abs/2006.00719>                                                          | [cite](https://github.com/amirgholami/adahessian#citation)                                                                          |
+| AdamD               | *Improved bias-correction in Adam*                                                                |                                                                                                                | <https://arxiv.org/abs/2110.10828>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv211010828S/exportcitation)                                                        |
+| AdamP               | *Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights*                    | [github](https://github.com/clovaai/AdamP)                                                                     | <https://arxiv.org/abs/2006.08217>                                                          | [cite](https://github.com/clovaai/AdamP#how-to-cite)                                                                                |
+| diffGrad            | *An Optimization Method for Convolutional Neural Networks*                                        | [github](https://github.com/shivram1987/diffGrad)                                                              | <https://arxiv.org/abs/1909.11015v3>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190911015D/exportcitation)                                                        |
+| MADGRAD             | *A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic*                          | [github](https://github.com/facebookresearch/madgrad)                                                          | <https://arxiv.org/abs/2101.11075>                                                          | [cite](https://github.com/facebookresearch/madgrad#tech-report)                                                                     |
+| RAdam               | *On the Variance of the Adaptive Learning Rate and Beyond*                                        | [github](https://github.com/LiyuanLucasLiu/RAdam)                                                              | <https://arxiv.org/abs/1908.03265>                                                          | [cite](https://github.com/LiyuanLucasLiu/RAdam#citation)                                                                            |
+| Ranger              | *a synergistic optimizer combining RAdam and LookAhead, and now GC in one optimizer*              | [github](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer)                                          | <https://bit.ly/3zyspC3>                                                                    | [cite](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer#citing-this-work)                                                |
+| Ranger21            | *a synergistic deep learning optimizer*                                                           | [github](https://github.com/lessw2020/Ranger21)                                                                | <https://arxiv.org/abs/2106.13731>                                                          | [cite](https://github.com/lessw2020/Ranger21#referencing-this-work)                                                                 |
+| Lamb                | *Large Batch Optimization for Deep Learning*                                                      | [github](https://github.com/cybertronai/pytorch-lamb)                                                          | <https://arxiv.org/abs/1904.00962>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190400962Y/exportcitation)                                                        |
+| Shampoo             | *Preconditioned Stochastic Tensor Optimization*                                                   | [github](https://github.com/moskomule/shampoo.pytorch)                                                         | <https://arxiv.org/abs/1802.09568>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180209568G/exportcitation)                                                        |
+| Nero                | *Learning by Turning: Neural Architecture Aware Optimisation*                                     | [github](https://github.com/jxbz/nero)                                                                         | <https://arxiv.org/abs/2102.07227>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210207227L/exportcitation)                                                        |
+| Adan                | *Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models*                          | [github](https://github.com/sail-sg/Adan)                                                                      | <https://arxiv.org/abs/2208.06677>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220806677X/exportcitation)                                                        |
+| Adai                | *Disentangling the Effects of Adaptive Learning Rate and Momentum*                                | [github](https://github.com/zeke-xie/adaptive-inertia-adai)                                                    | <https://arxiv.org/abs/2006.15815>                                                          | [cite](https://github.com/zeke-xie/adaptive-inertia-adai#citing)                                                                    |
+| SAM                 | *Sharpness-Aware Minimization*                                                                    | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2010.01412>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201001412F/exportcitation)                                                        |
+| ASAM                | *Adaptive Sharpness-Aware Minimization*                                                           | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2102.11600>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210211600K/exportcitation)                                                        |
+| GSAM                | *Surrogate Gap Guided Sharpness-Aware Minimization*                                               | [github](https://github.com/juntang-zhuang/GSAM)                                                               | <https://openreview.net/pdf?id=edONMAnhLu->                                                 | [cite](https://github.com/juntang-zhuang/GSAM#citation)                                                                             |
+| D-Adaptation        | *Learning-Rate-Free Learning by D-Adaptation*                                                     | [github](https://github.com/facebookresearch/dadaptation)                                                      | <https://arxiv.org/abs/2301.07733>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230107733D/exportcitation)                                                        |
+| AdaFactor           | *Adaptive Learning Rates with Sublinear Memory Cost*                                              | [github](https://github.com/DeadAt0m/adafactor-pytorch)                                                        | <https://arxiv.org/abs/1804.04235>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180404235S/exportcitation)                                                        |
+| Apollo              | *An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization*   | [github](https://github.com/XuezheMax/apollo)                                                                  | <https://arxiv.org/abs/2009.13586>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv200913586M/exportcitation)                                                        |
+| NovoGrad            | *Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks*      | [github](https://github.com/lonePatient/NovoGrad-pytorch)                                                      | <https://arxiv.org/abs/1905.11286>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190511286G/exportcitation)                                                        |
+| Lion                | *Symbolic Discovery of Optimization Algorithms*                                                   | [github](https://github.com/google/automl/tree/master/lion)                                                    | <https://arxiv.org/abs/2302.06675>                                                          | [cite](https://github.com/google/automl/tree/master/lion#citation)                                                                  |
+| Ali-G               | *Adaptive Learning Rates for Interpolation with Gradients*                                        | [github](https://github.com/oval-group/ali-g)                                                                  | <https://arxiv.org/abs/1906.05661>                                                          | [cite](https://github.com/oval-group/ali-g#adaptive-learning-rates-for-interpolation-with-gradients)                                |
+| SM3                 | *Memory-Efficient Adaptive Optimization*                                                          | [github](https://github.com/google-research/google-research/tree/master/sm3)                                   | <https://arxiv.org/abs/1901.11150>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190111150A/exportcitation)                                                        |
+| AdaNorm             | *Adaptive Gradient Norm Correction based Optimizer for CNNs*                                      | [github](https://github.com/shivram1987/AdaNorm)                                                               | <https://arxiv.org/abs/2210.06364>                                                          | [cite](https://github.com/shivram1987/AdaNorm/tree/main#citation)                                                                   |
+| RotoGrad            | *Gradient Homogenization in Multitask Learning*                                                   | [github](https://github.com/adrianjav/rotograd)                                                                | <https://openreview.net/pdf?id=T8wHz4rnuGL>                                                 | [cite](https://github.com/adrianjav/rotograd#citing)                                                                                |
+| A2Grad              | *Optimal Adaptive and Accelerated Stochastic Gradient Descent*                                    | [github](https://github.com/severilov/A2Grad_optimizer)                                                        | <https://arxiv.org/abs/1810.00553>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000553D/exportcitation)                                                        |
+| AccSGD              | *Accelerating Stochastic Gradient Descent For Least Squares Regression*                           | [github](https://github.com/rahulkidambi/AccSGD)                                                               | <https://arxiv.org/abs/1704.08227>                                                          | [cite](https://github.com/rahulkidambi/AccSGD#citation)                                                                             |
+| SGDW                | *Decoupled Weight Decay Regularization*                                                           | [github](https://github.com/loshchil/AdamW-and-SGDW)                                                           | <https://arxiv.org/abs/1711.05101>                                                          | [cite](https://github.com/loshchil/AdamW-and-SGDW#contact)                                                                          |
+| ASGD                | *Adaptive Gradient Descent without Descent*                                                       | [github](https://github.com/ymalitsky/adaptive_GD)                                                             | <https://arxiv.org/abs/1910.09529>                                                          | [cite](https://github.com/ymalitsky/adaptive_GD#reference)                                                                          |
+| Yogi                | *Adaptive Methods for Nonconvex Optimization*                                                     |                                                                                                                | [NIPS 2018](https://papers.nips.cc/paper/8186-adaptive-methods-for-nonconvex-optimization)  | [cite](https://proceedings.neurips.cc/paper_files/paper/2018/hash/90365351ccc7437a1309dc64e4db32a3-Abstract.html)                   |
+| SWATS               | *Improving Generalization Performance by Switching from Adam to SGD*                              |                                                                                                                | <https://arxiv.org/abs/1712.07628>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2017arXiv171207628S/exportcitation)                                                        |
+| Fromage             | *On the distance between two neural networks and the stability of learning*                       | [github](https://github.com/jxbz/fromage)                                                                      | <https://arxiv.org/abs/2002.03432>                                                          | [cite](https://github.com/jxbz/fromage#citation)                                                                                    |
+| MSVAG               | *Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients*                       | [github](https://github.com/lballes/msvag)                                                                     | <https://arxiv.org/abs/1705.07774>                                                          | [cite](https://github.com/lballes/msvag#citation)                                                                                   |
+| AdaMod              | *An Adaptive and Momental Bound Method for Stochastic Learning*                                   | [github](https://github.com/lancopku/AdaMod)                                                                   | <https://arxiv.org/abs/1910.12249>                                                          | [cite](https://github.com/lancopku/AdaMod#citation)                                                                                 |
+| AggMo               | *Aggregated Momentum: Stability Through Passive Damping*                                          | [github](https://github.com/AtheMathmo/AggMo)                                                                  | <https://arxiv.org/abs/1804.00325>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180400325L/exportcitation)                                                        |
+| QHAdam              | *Quasi-hyperbolic momentum and Adam for deep learning*                                            | [github](https://github.com/facebookresearch/qhoptim)                                                          | <https://arxiv.org/abs/1810.06801>                                                          | [cite](https://github.com/facebookresearch/qhoptim#reference)                                                                       |
+| PID                 | *A PID Controller Approach for Stochastic Optimization of Deep Networks*                          | [github](https://github.com/tensorboy/PIDOptimizer)                                                            | [CVPR 18](http://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdf)                     | [cite](https://github.com/tensorboy/PIDOptimizer#citation)                                                                          |
+| Gravity             | *a Kinematic Approach on Optimization in Deep Learning*                                           | [github](https://github.com/dariush-bahrami/gravity.optimizer)                                                 | <https://arxiv.org/abs/2101.09192>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210109192B/exportcitation)                                                        |
+| AdaSmooth           | *An Adaptive Learning Rate Method based on Effective Ratio*                                       |                                                                                                                | <https://arxiv.org/abs/2204.00825v1>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220400825L/exportcitation)                                                        |
+| SRMM                | *Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates* | [github](https://github.com/HanbaekLyu/SRMM)                                                                   | <https://arxiv.org/abs/2201.01652>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220101652L/exportcitation)                                                        |
+| AvaGrad             | *Domain-independent Dominance of Adaptive Methods*                                                | [github](https://github.com/lolemacs/avagrad)                                                                  | <https://arxiv.org/abs/1912.01823>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191201823S/exportcitation)                                                        |
+| PCGrad              | *Gradient Surgery for Multi-Task Learning*                                                        | [github](https://github.com/tianheyu927/PCGrad)                                                                | <https://arxiv.org/abs/2001.06782>                                                          | [cite](https://github.com/tianheyu927/PCGrad#reference)                                                                             |
+| AMSGrad             | *On the Convergence of Adam and Beyond*                                                           |                                                                                                                | <https://openreview.net/pdf?id=ryQu7f-RZ>                                                   | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190409237R/exportcitation)                                                        |
+| Lookahead           | *k steps forward, 1 step back*                                                                    | [github](https://github.com/pytorch/examples/tree/main/imagenet)                                               | <https://arxiv.org/abs/1907.08610>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190708610Z/exportcitation)                                                        |
+| PNM                 | *Manipulating Stochastic Gradient Noise to Improve Generalization*                                | [github](https://github.com/zeke-xie/Positive-Negative-Momentum)                                               | <https://arxiv.org/abs/2103.17182>                                                          | [cite](https://github.com/zeke-xie/Positive-Negative-Momentum#citing)                                                               |
+| GC                  | *Gradient Centralization*                                                                         | [github](https://github.com/Yonghongwei/Gradient-Centralization)                                               | <https://arxiv.org/abs/2004.01461>                                                          | [cite](https://github.com/Yonghongwei/Gradient-Centralization#citation)                                                             |
+| AGC                 | *Adaptive Gradient Clipping*                                                                      | [github](https://github.com/deepmind/deepmind-research/tree/master/nfnets)                                     | <https://arxiv.org/abs/2102.06171>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210206171B/exportcitation)                                                        |
+| Stable WD           | *Understanding and Scheduling Weight Decay*                                                       | [github](https://github.com/zeke-xie/stable-weight-decay-regularization)                                       | <https://arxiv.org/abs/2011.11152>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201111152X/exportcitation)                                                        |
+| Softplus T          | *Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM*                           |                                                                                                                | <https://arxiv.org/abs/1908.00700>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190800700T/exportcitation)                                                        |
+| Un-tuned w/u        | *On the adequacy of untuned warmup for adaptive optimization*                                     |                                                                                                                | <https://arxiv.org/abs/1910.04209>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191004209M/exportcitation)                                                        |
+| Norm Loss           | *An efficient yet effective regularization method for deep neural networks*                       |                                                                                                                | <https://arxiv.org/abs/2103.06583>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210306583G/exportcitation)                                                        |
+| AdaShift            | *Decorrelation and Convergence of Adaptive Learning Rate Methods*                                 | [github](https://github.com/MichaelKonobeev/adashift)                                                          | <https://arxiv.org/abs/1810.00143v4>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000143Z/exportcitation)                                                        |
+| AdaDelta            | *An Adaptive Learning Rate Method*                                                                |                                                                                                                | <https://arxiv.org/abs/1212.5701v1>                                                         | [cite](https://ui.adsabs.harvard.edu/abs/2012arXiv1212.5701Z/exportcitation)                                                        |
+| Amos                | *An Adam-style Optimizer with Adaptive Weight Decay towards Model-Oriented Scale*                 | [github](https://github.com/google-research/jestimator)                                                        | <https://arxiv.org/abs/2210.11693>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221011693T/exportcitation)                                                        |
+| SignSGD             | *Compressed Optimisation for Non-Convex Problems*                                                 | [github](https://github.com/jxbz/signSGD)                                                                      | <https://arxiv.org/abs/1802.04434>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180204434B/exportcitation)                                                        |
+| Sophia              | *A Scalable Stochastic Second-order Optimizer for Language Model Pre-training*                    | [github](https://github.com/Liuhong99/Sophia)                                                                  | <https://arxiv.org/abs/2305.14342>                                                          | [cite](https://github.com/Liuhong99/Sophia)                                                                                         |
+| Prodigy             | *An Expeditiously Adaptive Parameter-Free Learner*                                                | [github](https://github.com/konstmish/prodigy)                                                                 | <https://arxiv.org/abs/2306.06101>                                                          | [cite](https://github.com/konstmish/prodigy#how-to-cite)                                                                            |
+| PAdam               | *Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks*    | [github](https://github.com/uclaml/Padam)                                                                      | <https://arxiv.org/abs/1806.06763>                                                          | [cite](https://github.com/uclaml/Padam#citation)                                                                                    |
+| LOMO                | *Full Parameter Fine-tuning for Large Language Models with Limited Resources*                     | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2306.09782>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
+| AdaLOMO             | *Low-memory Optimization with Adaptive Learning Rate*                                             | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2310.10195>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
+| Tiger               | *A Tight-fisted Optimizer, an optimizer that is extremely budget-conscious*                       | [github](https://github.com/bojone/tiger)                                                                      |                                                                                             | [cite](https://github.com/bojone/tiger/blob/main/README_en.md#citation)                                                             |
+| CAME                | *Confidence-guided Adaptive Memory Efficient Optimization*                                        | [github](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME)                            | <https://aclanthology.org/2023.acl-long.243/>                                               | [cite](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME#citation)                                          |
+| WSAM                | *Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Term*             | [github](https://github.com/intelligent-machine-learning/dlrover/blob/master/atorch/atorch/optimizers/wsam.py) | <https://arxiv.org/abs/2305.15817>                                                          | [cite](https://github.com/intelligent-machine-learning/dlrover)                                                                     |
+| Aida                | *A DNN Optimizer that Improves over AdaBelief by Suppression of the Adaptive Stepsize Range*      | [github](https://github.com/guoqiang-zhang-x/Aida-Optimizer)                                                   | <https://arxiv.org/abs/2203.13273>                                                          | [cite](https://github.com/guoqiang-zhang-x/Aida-Optimizer?tab=readme-ov-file#1-brief-description-of-aida)                           |
+| GaLore              | *Memory-Efficient LLM Training by Gradient Low-Rank Projection*                                   | [github](https://github.com/jiaweizzhao/GaLore)                                                                | <https://arxiv.org/abs/2403.03507>                                                          | [cite](https://github.com/jiaweizzhao/GaLore/tree/master?tab=readme-ov-file#citation)                                               |
+| Adalite             | *Adalite optimizer*                                                                               | [github](https://github.com/VatsaDev/adalite)                                                                  | <https://github.com/VatsaDev/adalite>                                                       | [cite](https://github.com/VatsaDev/adalite)                                                                                         |
+| bSAM                | *SAM as an Optimal Relaxation of Bayes*                                                           | [github](https://github.com/team-approx-bayes/bayesian-sam)                                                    | <https://arxiv.org/abs/2210.01620>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221001620M/exportcitation)                                                        |
+| Schedule-Free       | *Schedule-Free Optimizers*                                                                        | [github](https://github.com/facebookresearch/schedule_free)                                                    | <https://github.com/facebookresearch/schedule_free>                                         | [cite](https://github.com/facebookresearch/schedule_free)                                                                           |
+| FAdam               | *Adam is a natural gradient optimizer using diagonal empirical Fisher information*                | [github](https://github.com/lessw2020/fadam_pytorch)                                                           | <https://arxiv.org/abs/2405.12807>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240512807H/exportcitation)                                                        |
+| Grokfast            | *Accelerated Grokking by Amplifying Slow Gradients*                                               | [github](https://github.com/ironjr/grokfast)                                                                   | <https://arxiv.org/abs/2405.20233>                                                          | [cite](https://github.com/ironjr/grokfast?tab=readme-ov-file#citation)                                                              |
+| Kate                | *Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad*                     | [github](https://github.com/nazya/KATE)                                                                        | <https://arxiv.org/abs/2403.02648>                                                          | [cite](https://github.com/nazya/KATE?tab=readme-ov-file#remove-that-square-root-a-new-efficient-scale-invariant-version-of-adagrad) |
+| StableAdamW         | *Stable and low-precision training for large-scale vision-language models*                        |                                                                                                                | <https://arxiv.org/abs/2304.13013>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230413013W/exportcitation)                                                        |
+| AdamMini            | *Use Fewer Learning Rates To Gain More*                                                           | [github](https://github.com/zyushun/Adam-mini)                                                                 | <https://arxiv.org/abs/2406.16793>                                                          | [cite](https://github.com/zyushun/Adam-mini?tab=readme-ov-file#citation)                                                            |
+| TRAC                | *Adaptive Parameter-free Optimization*                                                            | [github](https://github.com/ComputationalRobotics/TRAC)                                                        | <https://arxiv.org/abs/2405.16642>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240516642M/exportcitation)                                                        |
+| AdamG               | *Towards Stability of Parameter-free Optimization*                                                |                                                                                                                | <https://arxiv.org/abs/2405.04376>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240504376P/exportcitation)                                                        |
+| AdEMAMix            | *Better, Faster, Older*                                                                           | [github](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch)                                               | <https://arxiv.org/abs/2409.03137>                                                          | [cite](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch?tab=readme-ov-file#reference)                                         |
+| SOAP                | *Improving and Stabilizing Shampoo using Adam*                                                    | [github](https://github.com/nikhilvyas/SOAP)                                                                   | <https://arxiv.org/abs/2409.11321>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240911321V/exportcitation)                                                        |
+| ADOPT               | *Modified Adam Can Converge with Any β2 with the Optimal Rate*                                    | [github](https://github.com/iShohei220/adopt)                                                                  | <https://arxiv.org/abs/2411.02853>                                                          | [cite](https://github.com/iShohei220/adopt?tab=readme-ov-file#citation)                                                             |
+| FTRL                | *Follow The Regularized Leader*                                                                   |                                                                                                                | <https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/41159.pdf> |                                                                                                                                     |
+| Cautious            | *Improving Training with One Line of Code*                                                        | [github](https://github.com/kyleliang919/C-Optim)                                                              | <https://arxiv.org/pdf/2411.16085v1>                                                        | [cite](https://github.com/kyleliang919/C-Optim?tab=readme-ov-file#citation)                                                         |
+| DeMo                | *Decoupled Momentum Optimization*                                                                 | [github](https://github.com/bloc97/DeMo)                                                                       | <https://arxiv.org/abs/2411.19870>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241119870P/exportcitation)                                                        |
+| MicroAdam           | *Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence*                 | [github](https://github.com/IST-DASLab/MicroAdam)                                                              | <https://arxiv.org/abs/2405.15593>                                                          | [cite](https://github.com/IST-DASLab/MicroAdam?tab=readme-ov-file#citing)                                                           |
+| Muon                | *MomentUm Orthogonalized by Newton-schulz*                                                        | [github](https://github.com/KellerJordan/Muon)                                                                 | <https://x.com/kellerjordan0/status/1842300916864844014>                                    | [cite](https://github.com/KellerJordan/Muon)                                                                                        |
+| LaProp              | *Separating Momentum and Adaptivity in Adam*                                                      | [github](https://github.com/Z-T-WANG/LaProp-Optimizer)                                                         | <https://arxiv.org/abs/2002.04839>                                                          | [cite](https://github.com/Z-T-WANG/LaProp-Optimizer?tab=readme-ov-file#citation)                                                    |
+| APOLLO              | *SGD-like Memory, AdamW-level Performance*                                                        | [github](https://github.com/zhuhanqing/APOLLO)                                                                 | <https://arxiv.org/abs/2412.05270>                                                          | [cite](https://github.com/zhuhanqing/APOLLO?tab=readme-ov-file#-citation)                                                           |
+| MARS                | *Unleashing the Power of Variance Reduction for Training Large Models*                            | [github](https://github.com/AGI-Arena/MARS)                                                                    | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AGI-Arena/MARS/tree/main?tab=readme-ov-file#citation)                                                     |
+| SGDSaI              | *No More Adam: Learning Rate Scaling at Initialization is All You Need*                           | [github](https://github.com/AnonymousAlethiometer/SGD_SaI)                                                     | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AnonymousAlethiometer/SGD_SaI?tab=readme-ov-file#citation)                                                |
+| Grams               | *Gradient Descent with Adaptive Momentum Scaling*                                                 |                                                                                                                | <https://arxiv.org/abs/2412.17107>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241217107C/exportcitation)                                                        |
+| OrthoGrad           | *Grokking at the Edge of Numerical Stability*                                                     | [github](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability)                         | <https://arxiv.org/abs/2501.04697>                                                          | [cite](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability?tab=readme-ov-file#citation)                    |
+| Adam-ATAN2          | *Scaling Exponents Across Parameterizations and Optimizers*                                       |                                                                                                                | <https://arxiv.org/abs/2407.05872>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240705872E/exportcitation)                                                        |
+| SPAM                | *Spike-Aware Adam with Momentum Reset for Stable LLM Training*                                    | [github](https://github.com/TianjinYellow/SPAM-Optimizer)                                                      | <https://arxiv.org/abs/2501.06842>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250106842H/exportcitation)                                                        |
+| TAM                 | *Torque-Aware Momentum*                                                                           |                                                                                                                | <https://arxiv.org/abs/2412.18790>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241218790M/exportcitation)                                                        |
+| FOCUS               | *First Order Concentrated Updating Scheme*                                                        | [github](https://github.com/liuyz0/FOCUS)                                                                      | <https://arxiv.org/abs/2501.12243>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250112243M/exportcitation)                                                        |
+| PSGD                | *Preconditioned Stochastic Gradient Descent*                                                      | [github](https://github.com/lixilinx/psgd_torch)                                                               | <https://arxiv.org/abs/1512.04202>                                                          | [cite](https://github.com/lixilinx/psgd_torch?tab=readme-ov-file#resources)                                                         |
+| EXAdam              | *The Power of Adaptive Cross-Moments*                                                             | [github](https://github.com/AhmedMostafa16/EXAdam)                                                             | <https://arxiv.org/abs/2412.20302>                                                          | [cite](https://github.com/AhmedMostafa16/EXAdam?tab=readme-ov-file#citation)                                                        |
+| GCSAM               | *Gradient Centralized Sharpness Aware Minimization*                                               | [github](https://github.com/mhassann22/GCSAM)                                                                  | <https://arxiv.org/abs/2501.11584>                                                          | [cite](https://github.com/mhassann22/GCSAM?tab=readme-ov-file#citation)                                                             |
+| LookSAM             | *Towards Efficient and Scalable Sharpness-Aware Minimization*                                     | [github](https://github.com/rollovd/LookSAM)                                                                   | <https://arxiv.org/abs/2203.02714>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220302714L/exportcitation)                                                        |
+| SCION               | *Training Deep Learning Models with Norm-Constrained LMOs*                                        |                                                                                                                | <https://arxiv.org/abs/2502.07529>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250207529P/exportcitation)                                                        |
+| COSMOS              | *SOAP with Muon*                                                                                  | [github](https://github.com/lliu606/COSMOS)                                                                    |                                                                                             |                                                                                                                                     |
+| StableSPAM          | *How to Train in 4-Bit More Stably than 16-Bit Adam*                                              | [github](https://github.com/TianjinYellow/StableSPAM)                                                          | <https://arxiv.org/abs/2502.17055>                                                          |                                                                                                                                     |
+| AdaGC               | *Improving Training Stability for Large Language Model Pretraining*                               |                                                                                                                | <https://arxiv.org/abs/2502.11034>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250211034W/exportcitation)                                                        |
+| Simplified-Ademamix | *Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants*            | [github](https://github.com/DepenM/Simplified-AdEMAMix/)                                                       | <https://arxiv.org/abs/2502.02431>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250202431M/exportcitation)                                                        |
 
 ## Supported LR Scheduler
 
diff --git a/docs/changelogs/v3.4.3.md b/docs/changelogs/v3.5.0.md
similarity index 69%
rename from docs/changelogs/v3.4.3.md
rename to docs/changelogs/v3.5.0.md
index 240873a9..e4ca2c7a 100644
--- a/docs/changelogs/v3.4.3.md
+++ b/docs/changelogs/v3.5.0.md
@@ -5,6 +5,10 @@
 * Support `StableSPAM` optimizer. (#358, #359)
     * [How to Train in 4-Bit More Stably than 16-Bit Adam](https://arxiv.org/abs/2502.17055?)
 * Support `ScheduleFreeWrapper`. (#334, #360)
+* Implement `AdaGC` optimizer. (#364, #366)
+    * [Improving Training Stability for Large Language Model Pretraining](https://arxiv.org/abs/2502.11034)
+* Implement `Simplified-Ademamix` optimizer. (#364, #366)
+    * [Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants](https://arxiv.org/abs/2502.02431)
 
 ### Update
 
diff --git a/docs/index.md b/docs/index.md
index 000850cf..b28037cf 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -10,7 +10,7 @@
 
 ## The reasons why you use `pytorch-optimizer`.
 
-* Wide range of supported optimizers. Currently, **100 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
+* Wide range of supported optimizers. Currently, **102 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
 * Including many variants such as `ADOPT`, `Cautious`, `AdamD`, `StableAdamW`, and `Gradient Centrailiaztion`
 * Easy to use, clean, and tested codes
 * Active maintenance
@@ -105,110 +105,112 @@ get_supported_optimizers(['adam*', 'ranger*'])
 # ['adamax', 'adamg', 'adammini', 'adamod', 'adamp', 'adams', 'adamw', 'ranger', 'ranger21']
 ```
 
-| Optimizer     | Description                                                                                       | Official Code                                                                                                  | Paper                                                                                       | Citation                                                                                                                            |
-|---------------|---------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------|
-| AdaBelief     | *Adapting Step-sizes by the Belief in Observed Gradients*                                         | [github](https://github.com/juntang-zhuang/Adabelief-Optimizer)                                                | <https://arxiv.org/abs/2010.07468>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201007468Z/exportcitation)                                                        |
-| AdaBound      | *Adaptive Gradient Methods with Dynamic Bound of Learning Rate*                                   | [github](https://github.com/Luolc/AdaBound/blob/master/adabound/adabound.py)                                   | <https://openreview.net/forum?id=Bkg3g2R9FX>                                                | [cite](https://github.com/Luolc/AdaBound#citing)                                                                                    |
-| AdaHessian    | *An Adaptive Second Order Optimizer for Machine Learning*                                         | [github](https://github.com/amirgholami/adahessian)                                                            | <https://arxiv.org/abs/2006.00719>                                                          | [cite](https://github.com/amirgholami/adahessian#citation)                                                                          |
-| AdamD         | *Improved bias-correction in Adam*                                                                |                                                                                                                | <https://arxiv.org/abs/2110.10828>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv211010828S/exportcitation)                                                        |
-| AdamP         | *Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights*                    | [github](https://github.com/clovaai/AdamP)                                                                     | <https://arxiv.org/abs/2006.08217>                                                          | [cite](https://github.com/clovaai/AdamP#how-to-cite)                                                                                |
-| diffGrad      | *An Optimization Method for Convolutional Neural Networks*                                        | [github](https://github.com/shivram1987/diffGrad)                                                              | <https://arxiv.org/abs/1909.11015v3>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190911015D/exportcitation)                                                        |
-| MADGRAD       | *A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic*                          | [github](https://github.com/facebookresearch/madgrad)                                                          | <https://arxiv.org/abs/2101.11075>                                                          | [cite](https://github.com/facebookresearch/madgrad#tech-report)                                                                     |
-| RAdam         | *On the Variance of the Adaptive Learning Rate and Beyond*                                        | [github](https://github.com/LiyuanLucasLiu/RAdam)                                                              | <https://arxiv.org/abs/1908.03265>                                                          | [cite](https://github.com/LiyuanLucasLiu/RAdam#citation)                                                                            |
-| Ranger        | *a synergistic optimizer combining RAdam and LookAhead, and now GC in one optimizer*              | [github](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer)                                          | <https://bit.ly/3zyspC3>                                                                    | [cite](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer#citing-this-work)                                                |
-| Ranger21      | *a synergistic deep learning optimizer*                                                           | [github](https://github.com/lessw2020/Ranger21)                                                                | <https://arxiv.org/abs/2106.13731>                                                          | [cite](https://github.com/lessw2020/Ranger21#referencing-this-work)                                                                 |
-| Lamb          | *Large Batch Optimization for Deep Learning*                                                      | [github](https://github.com/cybertronai/pytorch-lamb)                                                          | <https://arxiv.org/abs/1904.00962>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190400962Y/exportcitation)                                                        |
-| Shampoo       | *Preconditioned Stochastic Tensor Optimization*                                                   | [github](https://github.com/moskomule/shampoo.pytorch)                                                         | <https://arxiv.org/abs/1802.09568>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180209568G/exportcitation)                                                        |
-| Nero          | *Learning by Turning: Neural Architecture Aware Optimisation*                                     | [github](https://github.com/jxbz/nero)                                                                         | <https://arxiv.org/abs/2102.07227>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210207227L/exportcitation)                                                        |
-| Adan          | *Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models*                          | [github](https://github.com/sail-sg/Adan)                                                                      | <https://arxiv.org/abs/2208.06677>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220806677X/exportcitation)                                                        |
-| Adai          | *Disentangling the Effects of Adaptive Learning Rate and Momentum*                                | [github](https://github.com/zeke-xie/adaptive-inertia-adai)                                                    | <https://arxiv.org/abs/2006.15815>                                                          | [cite](https://github.com/zeke-xie/adaptive-inertia-adai#citing)                                                                    |
-| SAM           | *Sharpness-Aware Minimization*                                                                    | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2010.01412>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201001412F/exportcitation)                                                        |
-| ASAM          | *Adaptive Sharpness-Aware Minimization*                                                           | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2102.11600>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210211600K/exportcitation)                                                        |
-| GSAM          | *Surrogate Gap Guided Sharpness-Aware Minimization*                                               | [github](https://github.com/juntang-zhuang/GSAM)                                                               | <https://openreview.net/pdf?id=edONMAnhLu->                                                 | [cite](https://github.com/juntang-zhuang/GSAM#citation)                                                                             |
-| D-Adaptation  | *Learning-Rate-Free Learning by D-Adaptation*                                                     | [github](https://github.com/facebookresearch/dadaptation)                                                      | <https://arxiv.org/abs/2301.07733>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230107733D/exportcitation)                                                        |
-| AdaFactor     | *Adaptive Learning Rates with Sublinear Memory Cost*                                              | [github](https://github.com/DeadAt0m/adafactor-pytorch)                                                        | <https://arxiv.org/abs/1804.04235>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180404235S/exportcitation)                                                        |
-| Apollo        | *An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization*   | [github](https://github.com/XuezheMax/apollo)                                                                  | <https://arxiv.org/abs/2009.13586>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv200913586M/exportcitation)                                                        |
-| NovoGrad      | *Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks*      | [github](https://github.com/lonePatient/NovoGrad-pytorch)                                                      | <https://arxiv.org/abs/1905.11286>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190511286G/exportcitation)                                                        |
-| Lion          | *Symbolic Discovery of Optimization Algorithms*                                                   | [github](https://github.com/google/automl/tree/master/lion)                                                    | <https://arxiv.org/abs/2302.06675>                                                          | [cite](https://github.com/google/automl/tree/master/lion#citation)                                                                  |
-| Ali-G         | *Adaptive Learning Rates for Interpolation with Gradients*                                        | [github](https://github.com/oval-group/ali-g)                                                                  | <https://arxiv.org/abs/1906.05661>                                                          | [cite](https://github.com/oval-group/ali-g#adaptive-learning-rates-for-interpolation-with-gradients)                                |
-| SM3           | *Memory-Efficient Adaptive Optimization*                                                          | [github](https://github.com/google-research/google-research/tree/master/sm3)                                   | <https://arxiv.org/abs/1901.11150>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190111150A/exportcitation)                                                        |
-| AdaNorm       | *Adaptive Gradient Norm Correction based Optimizer for CNNs*                                      | [github](https://github.com/shivram1987/AdaNorm)                                                               | <https://arxiv.org/abs/2210.06364>                                                          | [cite](https://github.com/shivram1987/AdaNorm/tree/main#citation)                                                                   |
-| RotoGrad      | *Gradient Homogenization in Multitask Learning*                                                   | [github](https://github.com/adrianjav/rotograd)                                                                | <https://openreview.net/pdf?id=T8wHz4rnuGL>                                                 | [cite](https://github.com/adrianjav/rotograd#citing)                                                                                |
-| A2Grad        | *Optimal Adaptive and Accelerated Stochastic Gradient Descent*                                    | [github](https://github.com/severilov/A2Grad_optimizer)                                                        | <https://arxiv.org/abs/1810.00553>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000553D/exportcitation)                                                        |
-| AccSGD        | *Accelerating Stochastic Gradient Descent For Least Squares Regression*                           | [github](https://github.com/rahulkidambi/AccSGD)                                                               | <https://arxiv.org/abs/1704.08227>                                                          | [cite](https://github.com/rahulkidambi/AccSGD#citation)                                                                             |
-| SGDW          | *Decoupled Weight Decay Regularization*                                                           | [github](https://github.com/loshchil/AdamW-and-SGDW)                                                           | <https://arxiv.org/abs/1711.05101>                                                          | [cite](https://github.com/loshchil/AdamW-and-SGDW#contact)                                                                          |
-| ASGD          | *Adaptive Gradient Descent without Descent*                                                       | [github](https://github.com/ymalitsky/adaptive_GD)                                                             | <https://arxiv.org/abs/1910.09529>                                                          | [cite](https://github.com/ymalitsky/adaptive_GD#reference)                                                                          |
-| Yogi          | *Adaptive Methods for Nonconvex Optimization*                                                     |                                                                                                                | [NIPS 2018](https://papers.nips.cc/paper/8186-adaptive-methods-for-nonconvex-optimization)  | [cite](https://proceedings.neurips.cc/paper_files/paper/2018/hash/90365351ccc7437a1309dc64e4db32a3-Abstract.html)                   |
-| SWATS         | *Improving Generalization Performance by Switching from Adam to SGD*                              |                                                                                                                | <https://arxiv.org/abs/1712.07628>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2017arXiv171207628S/exportcitation)                                                        |
-| Fromage       | *On the distance between two neural networks and the stability of learning*                       | [github](https://github.com/jxbz/fromage)                                                                      | <https://arxiv.org/abs/2002.03432>                                                          | [cite](https://github.com/jxbz/fromage#citation)                                                                                    |
-| MSVAG         | *Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients*                       | [github](https://github.com/lballes/msvag)                                                                     | <https://arxiv.org/abs/1705.07774>                                                          | [cite](https://github.com/lballes/msvag#citation)                                                                                   |
-| AdaMod        | *An Adaptive and Momental Bound Method for Stochastic Learning*                                   | [github](https://github.com/lancopku/AdaMod)                                                                   | <https://arxiv.org/abs/1910.12249>                                                          | [cite](https://github.com/lancopku/AdaMod#citation)                                                                                 |
-| AggMo         | *Aggregated Momentum: Stability Through Passive Damping*                                          | [github](https://github.com/AtheMathmo/AggMo)                                                                  | <https://arxiv.org/abs/1804.00325>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180400325L/exportcitation)                                                        |
-| QHAdam        | *Quasi-hyperbolic momentum and Adam for deep learning*                                            | [github](https://github.com/facebookresearch/qhoptim)                                                          | <https://arxiv.org/abs/1810.06801>                                                          | [cite](https://github.com/facebookresearch/qhoptim#reference)                                                                       |
-| PID           | *A PID Controller Approach for Stochastic Optimization of Deep Networks*                          | [github](https://github.com/tensorboy/PIDOptimizer)                                                            | [CVPR 18](http://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdf)                     | [cite](https://github.com/tensorboy/PIDOptimizer#citation)                                                                          |
-| Gravity       | *a Kinematic Approach on Optimization in Deep Learning*                                           | [github](https://github.com/dariush-bahrami/gravity.optimizer)                                                 | <https://arxiv.org/abs/2101.09192>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210109192B/exportcitation)                                                        |
-| AdaSmooth     | *An Adaptive Learning Rate Method based on Effective Ratio*                                       |                                                                                                                | <https://arxiv.org/abs/2204.00825v1>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220400825L/exportcitation)                                                        |
-| SRMM          | *Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates* | [github](https://github.com/HanbaekLyu/SRMM)                                                                   | <https://arxiv.org/abs/2201.01652>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220101652L/exportcitation)                                                        |
-| AvaGrad       | *Domain-independent Dominance of Adaptive Methods*                                                | [github](https://github.com/lolemacs/avagrad)                                                                  | <https://arxiv.org/abs/1912.01823>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191201823S/exportcitation)                                                        |
-| PCGrad        | *Gradient Surgery for Multi-Task Learning*                                                        | [github](https://github.com/tianheyu927/PCGrad)                                                                | <https://arxiv.org/abs/2001.06782>                                                          | [cite](https://github.com/tianheyu927/PCGrad#reference)                                                                             |
-| AMSGrad       | *On the Convergence of Adam and Beyond*                                                           |                                                                                                                | <https://openreview.net/pdf?id=ryQu7f-RZ>                                                   | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190409237R/exportcitation)                                                        |
-| Lookahead     | *k steps forward, 1 step back*                                                                    | [github](https://github.com/pytorch/examples/tree/main/imagenet)                                               | <https://arxiv.org/abs/1907.08610>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190708610Z/exportcitation)                                                        |
-| PNM           | *Manipulating Stochastic Gradient Noise to Improve Generalization*                                | [github](https://github.com/zeke-xie/Positive-Negative-Momentum)                                               | <https://arxiv.org/abs/2103.17182>                                                          | [cite](https://github.com/zeke-xie/Positive-Negative-Momentum#citing)                                                               |
-| GC            | *Gradient Centralization*                                                                         | [github](https://github.com/Yonghongwei/Gradient-Centralization)                                               | <https://arxiv.org/abs/2004.01461>                                                          | [cite](https://github.com/Yonghongwei/Gradient-Centralization#citation)                                                             |
-| AGC           | *Adaptive Gradient Clipping*                                                                      | [github](https://github.com/deepmind/deepmind-research/tree/master/nfnets)                                     | <https://arxiv.org/abs/2102.06171>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210206171B/exportcitation)                                                        |
-| Stable WD     | *Understanding and Scheduling Weight Decay*                                                       | [github](https://github.com/zeke-xie/stable-weight-decay-regularization)                                       | <https://arxiv.org/abs/2011.11152>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201111152X/exportcitation)                                                        |
-| Softplus T    | *Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM*                           |                                                                                                                | <https://arxiv.org/abs/1908.00700>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190800700T/exportcitation)                                                        |
-| Un-tuned w/u  | *On the adequacy of untuned warmup for adaptive optimization*                                     |                                                                                                                | <https://arxiv.org/abs/1910.04209>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191004209M/exportcitation)                                                        |
-| Norm Loss     | *An efficient yet effective regularization method for deep neural networks*                       |                                                                                                                | <https://arxiv.org/abs/2103.06583>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210306583G/exportcitation)                                                        |
-| AdaShift      | *Decorrelation and Convergence of Adaptive Learning Rate Methods*                                 | [github](https://github.com/MichaelKonobeev/adashift)                                                          | <https://arxiv.org/abs/1810.00143v4>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000143Z/exportcitation)                                                        |
-| AdaDelta      | *An Adaptive Learning Rate Method*                                                                |                                                                                                                | <https://arxiv.org/abs/1212.5701v1>                                                         | [cite](https://ui.adsabs.harvard.edu/abs/2012arXiv1212.5701Z/exportcitation)                                                        |
-| Amos          | *An Adam-style Optimizer with Adaptive Weight Decay towards Model-Oriented Scale*                 | [github](https://github.com/google-research/jestimator)                                                        | <https://arxiv.org/abs/2210.11693>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221011693T/exportcitation)                                                        |
-| SignSGD       | *Compressed Optimisation for Non-Convex Problems*                                                 | [github](https://github.com/jxbz/signSGD)                                                                      | <https://arxiv.org/abs/1802.04434>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180204434B/exportcitation)                                                        |
-| Sophia        | *A Scalable Stochastic Second-order Optimizer for Language Model Pre-training*                    | [github](https://github.com/Liuhong99/Sophia)                                                                  | <https://arxiv.org/abs/2305.14342>                                                          | [cite](https://github.com/Liuhong99/Sophia)                                                                                         |
-| Prodigy       | *An Expeditiously Adaptive Parameter-Free Learner*                                                | [github](https://github.com/konstmish/prodigy)                                                                 | <https://arxiv.org/abs/2306.06101>                                                          | [cite](https://github.com/konstmish/prodigy#how-to-cite)                                                                            |
-| PAdam         | *Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks*    | [github](https://github.com/uclaml/Padam)                                                                      | <https://arxiv.org/abs/1806.06763>                                                          | [cite](https://github.com/uclaml/Padam#citation)                                                                                    |
-| LOMO          | *Full Parameter Fine-tuning for Large Language Models with Limited Resources*                     | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2306.09782>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
-| AdaLOMO       | *Low-memory Optimization with Adaptive Learning Rate*                                             | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2310.10195>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
-| Tiger         | *A Tight-fisted Optimizer, an optimizer that is extremely budget-conscious*                       | [github](https://github.com/bojone/tiger)                                                                      |                                                                                             | [cite](https://github.com/bojone/tiger/blob/main/README_en.md#citation)                                                             |
-| CAME          | *Confidence-guided Adaptive Memory Efficient Optimization*                                        | [github](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME)                            | <https://aclanthology.org/2023.acl-long.243/>                                               | [cite](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME#citation)                                          |
-| WSAM          | *Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Term*             | [github](https://github.com/intelligent-machine-learning/dlrover/blob/master/atorch/atorch/optimizers/wsam.py) | <https://arxiv.org/abs/2305.15817>                                                          | [cite](https://github.com/intelligent-machine-learning/dlrover)                                                                     |
-| Aida          | *A DNN Optimizer that Improves over AdaBelief by Suppression of the Adaptive Stepsize Range*      | [github](https://github.com/guoqiang-zhang-x/Aida-Optimizer)                                                   | <https://arxiv.org/abs/2203.13273>                                                          | [cite](https://github.com/guoqiang-zhang-x/Aida-Optimizer?tab=readme-ov-file#1-brief-description-of-aida)                           |
-| GaLore        | *Memory-Efficient LLM Training by Gradient Low-Rank Projection*                                   | [github](https://github.com/jiaweizzhao/GaLore)                                                                | <https://arxiv.org/abs/2403.03507>                                                          | [cite](https://github.com/jiaweizzhao/GaLore/tree/master?tab=readme-ov-file#citation)                                               |
-| Adalite       | *Adalite optimizer*                                                                               | [github](https://github.com/VatsaDev/adalite)                                                                  | <https://github.com/VatsaDev/adalite>                                                       | [cite](https://github.com/VatsaDev/adalite)                                                                                         |
-| bSAM          | *SAM as an Optimal Relaxation of Bayes*                                                           | [github](https://github.com/team-approx-bayes/bayesian-sam)                                                    | <https://arxiv.org/abs/2210.01620>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221001620M/exportcitation)                                                        |
-| Schedule-Free | *Schedule-Free Optimizers*                                                                        | [github](https://github.com/facebookresearch/schedule_free)                                                    | <https://github.com/facebookresearch/schedule_free>                                         | [cite](https://github.com/facebookresearch/schedule_free)                                                                           |
-| FAdam         | *Adam is a natural gradient optimizer using diagonal empirical Fisher information*                | [github](https://github.com/lessw2020/fadam_pytorch)                                                           | <https://arxiv.org/abs/2405.12807>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240512807H/exportcitation)                                                        |
-| Grokfast      | *Accelerated Grokking by Amplifying Slow Gradients*                                               | [github](https://github.com/ironjr/grokfast)                                                                   | <https://arxiv.org/abs/2405.20233>                                                          | [cite](https://github.com/ironjr/grokfast?tab=readme-ov-file#citation)                                                              |
-| Kate          | *Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad*                     | [github](https://github.com/nazya/KATE)                                                                        | <https://arxiv.org/abs/2403.02648>                                                          | [cite](https://github.com/nazya/KATE?tab=readme-ov-file#remove-that-square-root-a-new-efficient-scale-invariant-version-of-adagrad) |
-| StableAdamW   | *Stable and low-precision training for large-scale vision-language models*                        |                                                                                                                | <https://arxiv.org/abs/2304.13013>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230413013W/exportcitation)                                                        |
-| AdamMini      | *Use Fewer Learning Rates To Gain More*                                                           | [github](https://github.com/zyushun/Adam-mini)                                                                 | <https://arxiv.org/abs/2406.16793>                                                          | [cite](https://github.com/zyushun/Adam-mini?tab=readme-ov-file#citation)                                                            |
-| TRAC          | *Adaptive Parameter-free Optimization*                                                            | [github](https://github.com/ComputationalRobotics/TRAC)                                                        | <https://arxiv.org/abs/2405.16642>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240516642M/exportcitation)                                                        |
-| AdamG         | *Towards Stability of Parameter-free Optimization*                                                |                                                                                                                | <https://arxiv.org/abs/2405.04376>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240504376P/exportcitation)                                                        |
-| AdEMAMix      | *Better, Faster, Older*                                                                           | [github](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch)                                               | <https://arxiv.org/abs/2409.03137>                                                          | [cite](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch?tab=readme-ov-file#reference)                                         |
-| SOAP          | *Improving and Stabilizing Shampoo using Adam*                                                    | [github](https://github.com/nikhilvyas/SOAP)                                                                   | <https://arxiv.org/abs/2409.11321>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240911321V/exportcitation)                                                        |
-| ADOPT         | *Modified Adam Can Converge with Any β2 with the Optimal Rate*                                    | [github](https://github.com/iShohei220/adopt)                                                                  | <https://arxiv.org/abs/2411.02853>                                                          | [cite](https://github.com/iShohei220/adopt?tab=readme-ov-file#citation)                                                             |
-| FTRL          | *Follow The Regularized Leader*                                                                   |                                                                                                                | <https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/41159.pdf> |                                                                                                                                     |
-| Cautious      | *Improving Training with One Line of Code*                                                        | [github](https://github.com/kyleliang919/C-Optim)                                                              | <https://arxiv.org/pdf/2411.16085v1>                                                        | [cite](https://github.com/kyleliang919/C-Optim?tab=readme-ov-file#citation)                                                         |
-| DeMo          | *Decoupled Momentum Optimization*                                                                 | [github](https://github.com/bloc97/DeMo)                                                                       | <https://arxiv.org/abs/2411.19870>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241119870P/exportcitation)                                                        |
-| MicroAdam     | *Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence*                 | [github](https://github.com/IST-DASLab/MicroAdam)                                                              | <https://arxiv.org/abs/2405.15593>                                                          | [cite](https://github.com/IST-DASLab/MicroAdam?tab=readme-ov-file#citing)                                                           |
-| Muon          | *MomentUm Orthogonalized by Newton-schulz*                                                        | [github](https://github.com/KellerJordan/Muon)                                                                 | <https://x.com/kellerjordan0/status/1842300916864844014>                                    | [cite](https://github.com/KellerJordan/Muon)                                                                                        |
-| LaProp        | *Separating Momentum and Adaptivity in Adam*                                                      | [github](https://github.com/Z-T-WANG/LaProp-Optimizer)                                                         | <https://arxiv.org/abs/2002.04839>                                                          | [cite](https://github.com/Z-T-WANG/LaProp-Optimizer?tab=readme-ov-file#citation)                                                    |
-| APOLLO        | *SGD-like Memory, AdamW-level Performance*                                                        | [github](https://github.com/zhuhanqing/APOLLO)                                                                 | <https://arxiv.org/abs/2412.05270>                                                          | [cite](https://github.com/zhuhanqing/APOLLO?tab=readme-ov-file#-citation)                                                           |
-| MARS          | *Unleashing the Power of Variance Reduction for Training Large Models*                            | [github](https://github.com/AGI-Arena/MARS)                                                                    | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AGI-Arena/MARS/tree/main?tab=readme-ov-file#citation)                                                     |
-| SGDSaI        | *No More Adam: Learning Rate Scaling at Initialization is All You Need*                           | [github](https://github.com/AnonymousAlethiometer/SGD_SaI)                                                     | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AnonymousAlethiometer/SGD_SaI?tab=readme-ov-file#citation)                                                |
-| Grams         | *Gradient Descent with Adaptive Momentum Scaling*                                                 |                                                                                                                | <https://arxiv.org/abs/2412.17107>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241217107C/exportcitation)                                                        |
-| OrthoGrad     | *Grokking at the Edge of Numerical Stability*                                                     | [github](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability)                         | <https://arxiv.org/abs/2501.04697>                                                          | [cite](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability?tab=readme-ov-file#citation)                    |
-| Adam-ATAN2    | *Scaling Exponents Across Parameterizations and Optimizers*                                       |                                                                                                                | <https://arxiv.org/abs/2407.05872>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240705872E/exportcitation)                                                        |
-| SPAM          | *Spike-Aware Adam with Momentum Reset for Stable LLM Training*                                    | [github](https://github.com/TianjinYellow/SPAM-Optimizer)                                                      | <https://arxiv.org/abs/2501.06842>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250106842H/exportcitation)                                                        |
-| TAM           | *Torque-Aware Momentum*                                                                           |                                                                                                                | <https://arxiv.org/abs/2412.18790>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241218790M/exportcitation)                                                        |
-| FOCUS         | *First Order Concentrated Updating Scheme*                                                        | [github](https://github.com/liuyz0/FOCUS)                                                                      | <https://arxiv.org/abs/2501.12243>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250112243M/exportcitation)                                                        |
-| PSGD          | *Preconditioned Stochastic Gradient Descent*                                                      | [github](https://github.com/lixilinx/psgd_torch)                                                               | <https://arxiv.org/abs/1512.04202>                                                          | [cite](https://github.com/lixilinx/psgd_torch?tab=readme-ov-file#resources)                                                         |
-| EXAdam        | *The Power of Adaptive Cross-Moments*                                                             | [github](https://github.com/AhmedMostafa16/EXAdam)                                                             | <https://arxiv.org/abs/2412.20302>                                                          | [cite](https://github.com/AhmedMostafa16/EXAdam?tab=readme-ov-file#citation)                                                        |
-| GCSAM         | *Gradient Centralized Sharpness Aware Minimization*                                               | [github](https://github.com/mhassann22/GCSAM)                                                                  | <https://arxiv.org/abs/2501.11584>                                                          | [cite](https://github.com/mhassann22/GCSAM?tab=readme-ov-file#citation)                                                             |
-| LookSAM       | *Towards Efficient and Scalable Sharpness-Aware Minimization*                                     | [github](https://github.com/rollovd/LookSAM)                                                                   | <https://arxiv.org/abs/2203.02714>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220302714L/exportcitation)                                                        |
-| SCION         | *Training Deep Learning Models with Norm-Constrained LMOs*                                        |                                                                                                                | <https://arxiv.org/abs/2502.07529>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250207529P/exportcitation)                                                        |
-| COSMOS        | *SOAP with Muon*                                                                                  | [github](https://github.com/lliu606/COSMOS)                                                                    |                                                                                             |                                                                                                                                     |
-| StableSPAM    | *How to Train in 4-Bit More Stably than 16-Bit Adam                                               | [github](https://github.com/TianjinYellow/StableSPAM)                                                          | <https://arxiv.org/abs/2502.17055>                                                          |                                                                                                                                     |
+| Optimizer           | Description                                                                                       | Official Code                                                                                                  | Paper                                                                                       | Citation                                                                                                                            |
+|---------------------|---------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------|
+| AdaBelief           | *Adapting Step-sizes by the Belief in Observed Gradients*                                         | [github](https://github.com/juntang-zhuang/Adabelief-Optimizer)                                                | <https://arxiv.org/abs/2010.07468>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201007468Z/exportcitation)                                                        |
+| AdaBound            | *Adaptive Gradient Methods with Dynamic Bound of Learning Rate*                                   | [github](https://github.com/Luolc/AdaBound/blob/master/adabound/adabound.py)                                   | <https://openreview.net/forum?id=Bkg3g2R9FX>                                                | [cite](https://github.com/Luolc/AdaBound#citing)                                                                                    |
+| AdaHessian          | *An Adaptive Second Order Optimizer for Machine Learning*                                         | [github](https://github.com/amirgholami/adahessian)                                                            | <https://arxiv.org/abs/2006.00719>                                                          | [cite](https://github.com/amirgholami/adahessian#citation)                                                                          |
+| AdamD               | *Improved bias-correction in Adam*                                                                |                                                                                                                | <https://arxiv.org/abs/2110.10828>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv211010828S/exportcitation)                                                        |
+| AdamP               | *Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights*                    | [github](https://github.com/clovaai/AdamP)                                                                     | <https://arxiv.org/abs/2006.08217>                                                          | [cite](https://github.com/clovaai/AdamP#how-to-cite)                                                                                |
+| diffGrad            | *An Optimization Method for Convolutional Neural Networks*                                        | [github](https://github.com/shivram1987/diffGrad)                                                              | <https://arxiv.org/abs/1909.11015v3>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190911015D/exportcitation)                                                        |
+| MADGRAD             | *A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic*                          | [github](https://github.com/facebookresearch/madgrad)                                                          | <https://arxiv.org/abs/2101.11075>                                                          | [cite](https://github.com/facebookresearch/madgrad#tech-report)                                                                     |
+| RAdam               | *On the Variance of the Adaptive Learning Rate and Beyond*                                        | [github](https://github.com/LiyuanLucasLiu/RAdam)                                                              | <https://arxiv.org/abs/1908.03265>                                                          | [cite](https://github.com/LiyuanLucasLiu/RAdam#citation)                                                                            |
+| Ranger              | *a synergistic optimizer combining RAdam and LookAhead, and now GC in one optimizer*              | [github](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer)                                          | <https://bit.ly/3zyspC3>                                                                    | [cite](https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer#citing-this-work)                                                |
+| Ranger21            | *a synergistic deep learning optimizer*                                                           | [github](https://github.com/lessw2020/Ranger21)                                                                | <https://arxiv.org/abs/2106.13731>                                                          | [cite](https://github.com/lessw2020/Ranger21#referencing-this-work)                                                                 |
+| Lamb                | *Large Batch Optimization for Deep Learning*                                                      | [github](https://github.com/cybertronai/pytorch-lamb)                                                          | <https://arxiv.org/abs/1904.00962>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190400962Y/exportcitation)                                                        |
+| Shampoo             | *Preconditioned Stochastic Tensor Optimization*                                                   | [github](https://github.com/moskomule/shampoo.pytorch)                                                         | <https://arxiv.org/abs/1802.09568>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180209568G/exportcitation)                                                        |
+| Nero                | *Learning by Turning: Neural Architecture Aware Optimisation*                                     | [github](https://github.com/jxbz/nero)                                                                         | <https://arxiv.org/abs/2102.07227>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210207227L/exportcitation)                                                        |
+| Adan                | *Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models*                          | [github](https://github.com/sail-sg/Adan)                                                                      | <https://arxiv.org/abs/2208.06677>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220806677X/exportcitation)                                                        |
+| Adai                | *Disentangling the Effects of Adaptive Learning Rate and Momentum*                                | [github](https://github.com/zeke-xie/adaptive-inertia-adai)                                                    | <https://arxiv.org/abs/2006.15815>                                                          | [cite](https://github.com/zeke-xie/adaptive-inertia-adai#citing)                                                                    |
+| SAM                 | *Sharpness-Aware Minimization*                                                                    | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2010.01412>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201001412F/exportcitation)                                                        |
+| ASAM                | *Adaptive Sharpness-Aware Minimization*                                                           | [github](https://github.com/davda54/sam)                                                                       | <https://arxiv.org/abs/2102.11600>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210211600K/exportcitation)                                                        |
+| GSAM                | *Surrogate Gap Guided Sharpness-Aware Minimization*                                               | [github](https://github.com/juntang-zhuang/GSAM)                                                               | <https://openreview.net/pdf?id=edONMAnhLu->                                                 | [cite](https://github.com/juntang-zhuang/GSAM#citation)                                                                             |
+| D-Adaptation        | *Learning-Rate-Free Learning by D-Adaptation*                                                     | [github](https://github.com/facebookresearch/dadaptation)                                                      | <https://arxiv.org/abs/2301.07733>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230107733D/exportcitation)                                                        |
+| AdaFactor           | *Adaptive Learning Rates with Sublinear Memory Cost*                                              | [github](https://github.com/DeadAt0m/adafactor-pytorch)                                                        | <https://arxiv.org/abs/1804.04235>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180404235S/exportcitation)                                                        |
+| Apollo              | *An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization*   | [github](https://github.com/XuezheMax/apollo)                                                                  | <https://arxiv.org/abs/2009.13586>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv200913586M/exportcitation)                                                        |
+| NovoGrad            | *Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks*      | [github](https://github.com/lonePatient/NovoGrad-pytorch)                                                      | <https://arxiv.org/abs/1905.11286>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190511286G/exportcitation)                                                        |
+| Lion                | *Symbolic Discovery of Optimization Algorithms*                                                   | [github](https://github.com/google/automl/tree/master/lion)                                                    | <https://arxiv.org/abs/2302.06675>                                                          | [cite](https://github.com/google/automl/tree/master/lion#citation)                                                                  |
+| Ali-G               | *Adaptive Learning Rates for Interpolation with Gradients*                                        | [github](https://github.com/oval-group/ali-g)                                                                  | <https://arxiv.org/abs/1906.05661>                                                          | [cite](https://github.com/oval-group/ali-g#adaptive-learning-rates-for-interpolation-with-gradients)                                |
+| SM3                 | *Memory-Efficient Adaptive Optimization*                                                          | [github](https://github.com/google-research/google-research/tree/master/sm3)                                   | <https://arxiv.org/abs/1901.11150>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190111150A/exportcitation)                                                        |
+| AdaNorm             | *Adaptive Gradient Norm Correction based Optimizer for CNNs*                                      | [github](https://github.com/shivram1987/AdaNorm)                                                               | <https://arxiv.org/abs/2210.06364>                                                          | [cite](https://github.com/shivram1987/AdaNorm/tree/main#citation)                                                                   |
+| RotoGrad            | *Gradient Homogenization in Multitask Learning*                                                   | [github](https://github.com/adrianjav/rotograd)                                                                | <https://openreview.net/pdf?id=T8wHz4rnuGL>                                                 | [cite](https://github.com/adrianjav/rotograd#citing)                                                                                |
+| A2Grad              | *Optimal Adaptive and Accelerated Stochastic Gradient Descent*                                    | [github](https://github.com/severilov/A2Grad_optimizer)                                                        | <https://arxiv.org/abs/1810.00553>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000553D/exportcitation)                                                        |
+| AccSGD              | *Accelerating Stochastic Gradient Descent For Least Squares Regression*                           | [github](https://github.com/rahulkidambi/AccSGD)                                                               | <https://arxiv.org/abs/1704.08227>                                                          | [cite](https://github.com/rahulkidambi/AccSGD#citation)                                                                             |
+| SGDW                | *Decoupled Weight Decay Regularization*                                                           | [github](https://github.com/loshchil/AdamW-and-SGDW)                                                           | <https://arxiv.org/abs/1711.05101>                                                          | [cite](https://github.com/loshchil/AdamW-and-SGDW#contact)                                                                          |
+| ASGD                | *Adaptive Gradient Descent without Descent*                                                       | [github](https://github.com/ymalitsky/adaptive_GD)                                                             | <https://arxiv.org/abs/1910.09529>                                                          | [cite](https://github.com/ymalitsky/adaptive_GD#reference)                                                                          |
+| Yogi                | *Adaptive Methods for Nonconvex Optimization*                                                     |                                                                                                                | [NIPS 2018](https://papers.nips.cc/paper/8186-adaptive-methods-for-nonconvex-optimization)  | [cite](https://proceedings.neurips.cc/paper_files/paper/2018/hash/90365351ccc7437a1309dc64e4db32a3-Abstract.html)                   |
+| SWATS               | *Improving Generalization Performance by Switching from Adam to SGD*                              |                                                                                                                | <https://arxiv.org/abs/1712.07628>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2017arXiv171207628S/exportcitation)                                                        |
+| Fromage             | *On the distance between two neural networks and the stability of learning*                       | [github](https://github.com/jxbz/fromage)                                                                      | <https://arxiv.org/abs/2002.03432>                                                          | [cite](https://github.com/jxbz/fromage#citation)                                                                                    |
+| MSVAG               | *Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients*                       | [github](https://github.com/lballes/msvag)                                                                     | <https://arxiv.org/abs/1705.07774>                                                          | [cite](https://github.com/lballes/msvag#citation)                                                                                   |
+| AdaMod              | *An Adaptive and Momental Bound Method for Stochastic Learning*                                   | [github](https://github.com/lancopku/AdaMod)                                                                   | <https://arxiv.org/abs/1910.12249>                                                          | [cite](https://github.com/lancopku/AdaMod#citation)                                                                                 |
+| AggMo               | *Aggregated Momentum: Stability Through Passive Damping*                                          | [github](https://github.com/AtheMathmo/AggMo)                                                                  | <https://arxiv.org/abs/1804.00325>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180400325L/exportcitation)                                                        |
+| QHAdam              | *Quasi-hyperbolic momentum and Adam for deep learning*                                            | [github](https://github.com/facebookresearch/qhoptim)                                                          | <https://arxiv.org/abs/1810.06801>                                                          | [cite](https://github.com/facebookresearch/qhoptim#reference)                                                                       |
+| PID                 | *A PID Controller Approach for Stochastic Optimization of Deep Networks*                          | [github](https://github.com/tensorboy/PIDOptimizer)                                                            | [CVPR 18](http://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdf)                     | [cite](https://github.com/tensorboy/PIDOptimizer#citation)                                                                          |
+| Gravity             | *a Kinematic Approach on Optimization in Deep Learning*                                           | [github](https://github.com/dariush-bahrami/gravity.optimizer)                                                 | <https://arxiv.org/abs/2101.09192>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210109192B/exportcitation)                                                        |
+| AdaSmooth           | *An Adaptive Learning Rate Method based on Effective Ratio*                                       |                                                                                                                | <https://arxiv.org/abs/2204.00825v1>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220400825L/exportcitation)                                                        |
+| SRMM                | *Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates* | [github](https://github.com/HanbaekLyu/SRMM)                                                                   | <https://arxiv.org/abs/2201.01652>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220101652L/exportcitation)                                                        |
+| AvaGrad             | *Domain-independent Dominance of Adaptive Methods*                                                | [github](https://github.com/lolemacs/avagrad)                                                                  | <https://arxiv.org/abs/1912.01823>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191201823S/exportcitation)                                                        |
+| PCGrad              | *Gradient Surgery for Multi-Task Learning*                                                        | [github](https://github.com/tianheyu927/PCGrad)                                                                | <https://arxiv.org/abs/2001.06782>                                                          | [cite](https://github.com/tianheyu927/PCGrad#reference)                                                                             |
+| AMSGrad             | *On the Convergence of Adam and Beyond*                                                           |                                                                                                                | <https://openreview.net/pdf?id=ryQu7f-RZ>                                                   | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190409237R/exportcitation)                                                        |
+| Lookahead           | *k steps forward, 1 step back*                                                                    | [github](https://github.com/pytorch/examples/tree/main/imagenet)                                               | <https://arxiv.org/abs/1907.08610>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190708610Z/exportcitation)                                                        |
+| PNM                 | *Manipulating Stochastic Gradient Noise to Improve Generalization*                                | [github](https://github.com/zeke-xie/Positive-Negative-Momentum)                                               | <https://arxiv.org/abs/2103.17182>                                                          | [cite](https://github.com/zeke-xie/Positive-Negative-Momentum#citing)                                                               |
+| GC                  | *Gradient Centralization*                                                                         | [github](https://github.com/Yonghongwei/Gradient-Centralization)                                               | <https://arxiv.org/abs/2004.01461>                                                          | [cite](https://github.com/Yonghongwei/Gradient-Centralization#citation)                                                             |
+| AGC                 | *Adaptive Gradient Clipping*                                                                      | [github](https://github.com/deepmind/deepmind-research/tree/master/nfnets)                                     | <https://arxiv.org/abs/2102.06171>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210206171B/exportcitation)                                                        |
+| Stable WD           | *Understanding and Scheduling Weight Decay*                                                       | [github](https://github.com/zeke-xie/stable-weight-decay-regularization)                                       | <https://arxiv.org/abs/2011.11152>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2020arXiv201111152X/exportcitation)                                                        |
+| Softplus T          | *Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM*                           |                                                                                                                | <https://arxiv.org/abs/1908.00700>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv190800700T/exportcitation)                                                        |
+| Un-tuned w/u        | *On the adequacy of untuned warmup for adaptive optimization*                                     |                                                                                                                | <https://arxiv.org/abs/1910.04209>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2019arXiv191004209M/exportcitation)                                                        |
+| Norm Loss           | *An efficient yet effective regularization method for deep neural networks*                       |                                                                                                                | <https://arxiv.org/abs/2103.06583>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2021arXiv210306583G/exportcitation)                                                        |
+| AdaShift            | *Decorrelation and Convergence of Adaptive Learning Rate Methods*                                 | [github](https://github.com/MichaelKonobeev/adashift)                                                          | <https://arxiv.org/abs/1810.00143v4>                                                        | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv181000143Z/exportcitation)                                                        |
+| AdaDelta            | *An Adaptive Learning Rate Method*                                                                |                                                                                                                | <https://arxiv.org/abs/1212.5701v1>                                                         | [cite](https://ui.adsabs.harvard.edu/abs/2012arXiv1212.5701Z/exportcitation)                                                        |
+| Amos                | *An Adam-style Optimizer with Adaptive Weight Decay towards Model-Oriented Scale*                 | [github](https://github.com/google-research/jestimator)                                                        | <https://arxiv.org/abs/2210.11693>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221011693T/exportcitation)                                                        |
+| SignSGD             | *Compressed Optimisation for Non-Convex Problems*                                                 | [github](https://github.com/jxbz/signSGD)                                                                      | <https://arxiv.org/abs/1802.04434>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2018arXiv180204434B/exportcitation)                                                        |
+| Sophia              | *A Scalable Stochastic Second-order Optimizer for Language Model Pre-training*                    | [github](https://github.com/Liuhong99/Sophia)                                                                  | <https://arxiv.org/abs/2305.14342>                                                          | [cite](https://github.com/Liuhong99/Sophia)                                                                                         |
+| Prodigy             | *An Expeditiously Adaptive Parameter-Free Learner*                                                | [github](https://github.com/konstmish/prodigy)                                                                 | <https://arxiv.org/abs/2306.06101>                                                          | [cite](https://github.com/konstmish/prodigy#how-to-cite)                                                                            |
+| PAdam               | *Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks*    | [github](https://github.com/uclaml/Padam)                                                                      | <https://arxiv.org/abs/1806.06763>                                                          | [cite](https://github.com/uclaml/Padam#citation)                                                                                    |
+| LOMO                | *Full Parameter Fine-tuning for Large Language Models with Limited Resources*                     | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2306.09782>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
+| AdaLOMO             | *Low-memory Optimization with Adaptive Learning Rate*                                             | [github](https://github.com/OpenLMLab/LOMO)                                                                    | <https://arxiv.org/abs/2310.10195>                                                          | [cite](https://github.com/OpenLMLab/LOMO#citation)                                                                                  |
+| Tiger               | *A Tight-fisted Optimizer, an optimizer that is extremely budget-conscious*                       | [github](https://github.com/bojone/tiger)                                                                      |                                                                                             | [cite](https://github.com/bojone/tiger/blob/main/README_en.md#citation)                                                             |
+| CAME                | *Confidence-guided Adaptive Memory Efficient Optimization*                                        | [github](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME)                            | <https://aclanthology.org/2023.acl-long.243/>                                               | [cite](https://github.com/huawei-noah/Pretrained-Language-Model/tree/master/CAME#citation)                                          |
+| WSAM                | *Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Term*             | [github](https://github.com/intelligent-machine-learning/dlrover/blob/master/atorch/atorch/optimizers/wsam.py) | <https://arxiv.org/abs/2305.15817>                                                          | [cite](https://github.com/intelligent-machine-learning/dlrover)                                                                     |
+| Aida                | *A DNN Optimizer that Improves over AdaBelief by Suppression of the Adaptive Stepsize Range*      | [github](https://github.com/guoqiang-zhang-x/Aida-Optimizer)                                                   | <https://arxiv.org/abs/2203.13273>                                                          | [cite](https://github.com/guoqiang-zhang-x/Aida-Optimizer?tab=readme-ov-file#1-brief-description-of-aida)                           |
+| GaLore              | *Memory-Efficient LLM Training by Gradient Low-Rank Projection*                                   | [github](https://github.com/jiaweizzhao/GaLore)                                                                | <https://arxiv.org/abs/2403.03507>                                                          | [cite](https://github.com/jiaweizzhao/GaLore/tree/master?tab=readme-ov-file#citation)                                               |
+| Adalite             | *Adalite optimizer*                                                                               | [github](https://github.com/VatsaDev/adalite)                                                                  | <https://github.com/VatsaDev/adalite>                                                       | [cite](https://github.com/VatsaDev/adalite)                                                                                         |
+| bSAM                | *SAM as an Optimal Relaxation of Bayes*                                                           | [github](https://github.com/team-approx-bayes/bayesian-sam)                                                    | <https://arxiv.org/abs/2210.01620>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv221001620M/exportcitation)                                                        |
+| Schedule-Free       | *Schedule-Free Optimizers*                                                                        | [github](https://github.com/facebookresearch/schedule_free)                                                    | <https://github.com/facebookresearch/schedule_free>                                         | [cite](https://github.com/facebookresearch/schedule_free)                                                                           |
+| FAdam               | *Adam is a natural gradient optimizer using diagonal empirical Fisher information*                | [github](https://github.com/lessw2020/fadam_pytorch)                                                           | <https://arxiv.org/abs/2405.12807>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240512807H/exportcitation)                                                        |
+| Grokfast            | *Accelerated Grokking by Amplifying Slow Gradients*                                               | [github](https://github.com/ironjr/grokfast)                                                                   | <https://arxiv.org/abs/2405.20233>                                                          | [cite](https://github.com/ironjr/grokfast?tab=readme-ov-file#citation)                                                              |
+| Kate                | *Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad*                     | [github](https://github.com/nazya/KATE)                                                                        | <https://arxiv.org/abs/2403.02648>                                                          | [cite](https://github.com/nazya/KATE?tab=readme-ov-file#remove-that-square-root-a-new-efficient-scale-invariant-version-of-adagrad) |
+| StableAdamW         | *Stable and low-precision training for large-scale vision-language models*                        |                                                                                                                | <https://arxiv.org/abs/2304.13013>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2023arXiv230413013W/exportcitation)                                                        |
+| AdamMini            | *Use Fewer Learning Rates To Gain More*                                                           | [github](https://github.com/zyushun/Adam-mini)                                                                 | <https://arxiv.org/abs/2406.16793>                                                          | [cite](https://github.com/zyushun/Adam-mini?tab=readme-ov-file#citation)                                                            |
+| TRAC                | *Adaptive Parameter-free Optimization*                                                            | [github](https://github.com/ComputationalRobotics/TRAC)                                                        | <https://arxiv.org/abs/2405.16642>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240516642M/exportcitation)                                                        |
+| AdamG               | *Towards Stability of Parameter-free Optimization*                                                |                                                                                                                | <https://arxiv.org/abs/2405.04376>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240504376P/exportcitation)                                                        |
+| AdEMAMix            | *Better, Faster, Older*                                                                           | [github](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch)                                               | <https://arxiv.org/abs/2409.03137>                                                          | [cite](https://github.com/nanowell/AdEMAMix-Optimizer-Pytorch?tab=readme-ov-file#reference)                                         |
+| SOAP                | *Improving and Stabilizing Shampoo using Adam*                                                    | [github](https://github.com/nikhilvyas/SOAP)                                                                   | <https://arxiv.org/abs/2409.11321>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240911321V/exportcitation)                                                        |
+| ADOPT               | *Modified Adam Can Converge with Any β2 with the Optimal Rate*                                    | [github](https://github.com/iShohei220/adopt)                                                                  | <https://arxiv.org/abs/2411.02853>                                                          | [cite](https://github.com/iShohei220/adopt?tab=readme-ov-file#citation)                                                             |
+| FTRL                | *Follow The Regularized Leader*                                                                   |                                                                                                                | <https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/41159.pdf> |                                                                                                                                     |
+| Cautious            | *Improving Training with One Line of Code*                                                        | [github](https://github.com/kyleliang919/C-Optim)                                                              | <https://arxiv.org/pdf/2411.16085v1>                                                        | [cite](https://github.com/kyleliang919/C-Optim?tab=readme-ov-file#citation)                                                         |
+| DeMo                | *Decoupled Momentum Optimization*                                                                 | [github](https://github.com/bloc97/DeMo)                                                                       | <https://arxiv.org/abs/2411.19870>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241119870P/exportcitation)                                                        |
+| MicroAdam           | *Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence*                 | [github](https://github.com/IST-DASLab/MicroAdam)                                                              | <https://arxiv.org/abs/2405.15593>                                                          | [cite](https://github.com/IST-DASLab/MicroAdam?tab=readme-ov-file#citing)                                                           |
+| Muon                | *MomentUm Orthogonalized by Newton-schulz*                                                        | [github](https://github.com/KellerJordan/Muon)                                                                 | <https://x.com/kellerjordan0/status/1842300916864844014>                                    | [cite](https://github.com/KellerJordan/Muon)                                                                                        |
+| LaProp              | *Separating Momentum and Adaptivity in Adam*                                                      | [github](https://github.com/Z-T-WANG/LaProp-Optimizer)                                                         | <https://arxiv.org/abs/2002.04839>                                                          | [cite](https://github.com/Z-T-WANG/LaProp-Optimizer?tab=readme-ov-file#citation)                                                    |
+| APOLLO              | *SGD-like Memory, AdamW-level Performance*                                                        | [github](https://github.com/zhuhanqing/APOLLO)                                                                 | <https://arxiv.org/abs/2412.05270>                                                          | [cite](https://github.com/zhuhanqing/APOLLO?tab=readme-ov-file#-citation)                                                           |
+| MARS                | *Unleashing the Power of Variance Reduction for Training Large Models*                            | [github](https://github.com/AGI-Arena/MARS)                                                                    | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AGI-Arena/MARS/tree/main?tab=readme-ov-file#citation)                                                     |
+| SGDSaI              | *No More Adam: Learning Rate Scaling at Initialization is All You Need*                           | [github](https://github.com/AnonymousAlethiometer/SGD_SaI)                                                     | <https://arxiv.org/abs/2411.10438>                                                          | [cite](https://github.com/AnonymousAlethiometer/SGD_SaI?tab=readme-ov-file#citation)                                                |
+| Grams               | *Gradient Descent with Adaptive Momentum Scaling*                                                 |                                                                                                                | <https://arxiv.org/abs/2412.17107>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241217107C/exportcitation)                                                        |
+| OrthoGrad           | *Grokking at the Edge of Numerical Stability*                                                     | [github](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability)                         | <https://arxiv.org/abs/2501.04697>                                                          | [cite](https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability?tab=readme-ov-file#citation)                    |
+| Adam-ATAN2          | *Scaling Exponents Across Parameterizations and Optimizers*                                       |                                                                                                                | <https://arxiv.org/abs/2407.05872>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv240705872E/exportcitation)                                                        |
+| SPAM                | *Spike-Aware Adam with Momentum Reset for Stable LLM Training*                                    | [github](https://github.com/TianjinYellow/SPAM-Optimizer)                                                      | <https://arxiv.org/abs/2501.06842>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250106842H/exportcitation)                                                        |
+| TAM                 | *Torque-Aware Momentum*                                                                           |                                                                                                                | <https://arxiv.org/abs/2412.18790>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2024arXiv241218790M/exportcitation)                                                        |
+| FOCUS               | *First Order Concentrated Updating Scheme*                                                        | [github](https://github.com/liuyz0/FOCUS)                                                                      | <https://arxiv.org/abs/2501.12243>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250112243M/exportcitation)                                                        |
+| PSGD                | *Preconditioned Stochastic Gradient Descent*                                                      | [github](https://github.com/lixilinx/psgd_torch)                                                               | <https://arxiv.org/abs/1512.04202>                                                          | [cite](https://github.com/lixilinx/psgd_torch?tab=readme-ov-file#resources)                                                         |
+| EXAdam              | *The Power of Adaptive Cross-Moments*                                                             | [github](https://github.com/AhmedMostafa16/EXAdam)                                                             | <https://arxiv.org/abs/2412.20302>                                                          | [cite](https://github.com/AhmedMostafa16/EXAdam?tab=readme-ov-file#citation)                                                        |
+| GCSAM               | *Gradient Centralized Sharpness Aware Minimization*                                               | [github](https://github.com/mhassann22/GCSAM)                                                                  | <https://arxiv.org/abs/2501.11584>                                                          | [cite](https://github.com/mhassann22/GCSAM?tab=readme-ov-file#citation)                                                             |
+| LookSAM             | *Towards Efficient and Scalable Sharpness-Aware Minimization*                                     | [github](https://github.com/rollovd/LookSAM)                                                                   | <https://arxiv.org/abs/2203.02714>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220302714L/exportcitation)                                                        |
+| SCION               | *Training Deep Learning Models with Norm-Constrained LMOs*                                        |                                                                                                                | <https://arxiv.org/abs/2502.07529>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250207529P/exportcitation)                                                        |
+| COSMOS              | *SOAP with Muon*                                                                                  | [github](https://github.com/lliu606/COSMOS)                                                                    |                                                                                             |                                                                                                                                     |
+| StableSPAM          | *How to Train in 4-Bit More Stably than 16-Bit Adam*                                              | [github](https://github.com/TianjinYellow/StableSPAM)                                                          | <https://arxiv.org/abs/2502.17055>                                                          |                                                                                                                                     |
+| AdaGC               | *Improving Training Stability for Large Language Model Pretraining*                               |                                                                                                                | <https://arxiv.org/abs/2502.11034>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250211034W/exportcitation)                                                        |
+| Simplified-Ademamix | *Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants*            | [github](https://github.com/DepenM/Simplified-AdEMAMix/)                                                       | <https://arxiv.org/abs/2502.02431>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250202431M/exportcitation)                                                        |
 
 ## Supported LR Scheduler
 
diff --git a/docs/optimizer.md b/docs/optimizer.md
index c31d32ea..e420b759 100644
--- a/docs/optimizer.md
+++ b/docs/optimizer.md
@@ -28,6 +28,10 @@
     :docstring:
     :members:
 
+::: pytorch_optimizer.AdaGC
+    :docstring:
+    :members:
+
 ::: pytorch_optimizer.AdaHessian
     :docstring:
     :members:
@@ -92,6 +96,10 @@
     :docstring:
     :members:
 
+::: pytorch_optimizer.SimplifiedAdEMAMix
+    :docstring:
+    :members:
+
 ::: pytorch_optimizer.ADOPT
     :docstring:
     :members:
diff --git a/docs/visualization.md b/docs/visualization.md
index 7468f7a1..e186a3db 100644
--- a/docs/visualization.md
+++ b/docs/visualization.md
@@ -22,6 +22,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_AdaFactor.png)
 
+### AdaGC
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_AdaGC.png)
+
 ### AdaHessian
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_AdaHessian.png)
@@ -326,6 +330,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_SignSGD.png)
 
+### SimplifiedAdEMAMix
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_SimplifiedAdEMAMix.png)
+
 ### SM3
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_SM3.png)
@@ -392,6 +400,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_AdaFactor.png)
 
+### AdaGC
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_AdaGC.png)
+
 ### AdaHessian
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_AdaHessian.png)
@@ -696,6 +708,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_SignSGD.png)
 
+### SimplifiedAdEMAMix
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_SimplifiedAdEMAMix.png)
+
 ### SM3
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_SM3.png)
diff --git a/pyproject.toml b/pyproject.toml
index 2faadae8..6d038e2f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,17 +11,17 @@ repository = "https://github.com/kozistr/pytorch_optimizer"
 documentation = "https://pytorch-optimizers.readthedocs.io/en/latest"
 keywords = [
     "pytorch", "deep-learning", "optimizer", "lr scheduler", "A2Grad", "ASGD", "AccSGD", "AdaBelief", "AdaBound",
-    "AdaDelta", "AdaFactor", "AdaMax", "AdamG", "AdaMod", "AdaNorm", "AdaPNM", "AdaSmooth", "AdEMAMix", "ADOPT",
-    "AdaHessian", "Adai", "Adalite", "AdaLomo", "AdamMini", "AdamP", "AdamS", "Adan", "AggMo", "Aida", "AliG", "Amos",
-    "Apollo", "APOLLO", "AvaGrad", "bSAM", "CAME", "DAdaptAdaGrad", "DAdaptAdam", "DAdaptAdan", "DAdaptSGD",
-    "DAdaptLion", "DeMo", "DiffGrad", "EXAdam", "FAdam", "FOCUS", "Fromage", "FTRL", "GaLore", "Grams", "Gravity",
-    "GrokFast", "GSAM", "Kate", "Lamb", "LaProp", "LARS", "Lion", "LOMO", "Lookahead", "MADGRAD", "MARS", "MSVAG",
-    "Muno", "Nero", "NovoGrad", "OrthoGrad", "PAdam", "PCGrad", "PID", "PNM", "Prodigy", "PSGD", "QHAdam", "QHM",
-    "RAdam", "Ranger", "Ranger21", "RotoGrad", "SAM", "GCSAM", "LookSAM", "ScheduleFreeSGD", "ScheduleFreeAdamW",
-    "ScheduleFreeRAdam", "SCION", "SGDP", "Shampoo", "ScalableShampoo", "SGDW", "SignSGD", "SM3", "SOAP", "SopihaH",
-    "SPAM", "StableSPAM", "SRMM", "StableAdamW", "SWATS", "TAM", "Tiger", "TRAC", "WSAM", "Yogi", "BCE", "BCEFocal",
-    "Focal", "FocalCosine", "SoftF1", "Dice", "LDAM", "Jaccard", "Bi-Tempered", "Tversky", "FocalTversky",
-    "LovaszHinge", "bitsandbytes", "WSD", "QGaLore",
+    "AdaDelta", "AdaFactor", "AdaGC", "AdaMax", "AdamG", "AdaMod", "AdaNorm", "AdaPNM", "AdaSmooth", "AdEMAMix",
+    "Simplified-AdEMAMix", "ADOPT", "AdaHessian", "Adai", "Adalite", "AdaLomo", "AdamMini", "AdamP", "AdamS", "Adan",
+    "AggMo", "Aida", "AliG", "Amos", "Apollo", "APOLLO", "AvaGrad", "bSAM", "CAME", "DAdaptAdaGrad", "DAdaptAdam",
+    "DAdaptAdan", "DAdaptSGD", "DAdaptLion", "DeMo", "DiffGrad", "EXAdam", "FAdam", "FOCUS", "Fromage", "FTRL",
+    "GaLore", "Grams", "Gravity", "GrokFast", "GSAM", "Kate", "Lamb", "LaProp", "LARS", "Lion", "LOMO", "Lookahead",
+    "MADGRAD", "MARS", "MSVAG", "Muno", "Nero", "NovoGrad", "OrthoGrad", "PAdam", "PCGrad", "PID", "PNM", "Prodigy",
+    "PSGD", "QHAdam", "QHM", "RAdam", "Ranger", "Ranger21", "RotoGrad", "SAM", "GCSAM", "LookSAM", "ScheduleFreeSGD",
+    "ScheduleFreeAdamW", "ScheduleFreeRAdam", "SCION", "SGDP", "Shampoo", "ScalableShampoo", "SGDW", "SignSGD", "SM3",
+    "SOAP", "SopihaH", "SPAM", "StableSPAM", "SRMM", "StableAdamW", "SWATS", "TAM", "Tiger", "TRAC", "WSAM", "Yogi",
+    "BCE", "BCEFocal", "Focal", "FocalCosine", "SoftF1", "Dice", "LDAM", "Jaccard", "Bi-Tempered", "Tversky",
+    "FocalTversky", "LovaszHinge", "bitsandbytes", "WSD", "QGaLore",
 ]
 classifiers = [
     "License :: OSI Approved :: Apache Software License",
diff --git a/pytorch_optimizer/__init__.py b/pytorch_optimizer/__init__.py
index 922ad838..7f9efce7 100644
--- a/pytorch_optimizer/__init__.py
+++ b/pytorch_optimizer/__init__.py
@@ -75,6 +75,7 @@ from pytorch_optimizer.optimizer import (
     AdaBound,
     AdaDelta,
     AdaFactor,
+    AdaGC,
     AdaHessian,
     Adai,
     Adalite,
@@ -143,6 +144,7 @@ from pytorch_optimizer.optimizer import (
     SGDSaI,
     Shampoo,
     SignSGD,
+    SimplifiedAdEMAMix,
     SophiaH,
     StableAdamW,
     StableSPAM,
diff --git a/pytorch_optimizer/optimizer/__init__.py b/pytorch_optimizer/optimizer/__init__.py
index 1218f348..e094dcc4 100644
--- a/pytorch_optimizer/optimizer/__init__.py
+++ b/pytorch_optimizer/optimizer/__init__.py
@@ -13,6 +13,7 @@ from pytorch_optimizer.optimizer.adabelief import AdaBelief
 from pytorch_optimizer.optimizer.adabound import AdaBound
 from pytorch_optimizer.optimizer.adadelta import AdaDelta
 from pytorch_optimizer.optimizer.adafactor import AdaFactor
+from pytorch_optimizer.optimizer.adagc import AdaGC
 from pytorch_optimizer.optimizer.adahessian import AdaHessian
 from pytorch_optimizer.optimizer.adai import Adai
 from pytorch_optimizer.optimizer.adalite import Adalite
@@ -28,7 +29,7 @@ from pytorch_optimizer.optimizer.adanorm import AdaNorm
 from pytorch_optimizer.optimizer.adapnm import AdaPNM
 from pytorch_optimizer.optimizer.adashift import AdaShift
 from pytorch_optimizer.optimizer.adasmooth import AdaSmooth
-from pytorch_optimizer.optimizer.ademamix import AdEMAMix
+from pytorch_optimizer.optimizer.ademamix import AdEMAMix, SimplifiedAdEMAMix
 from pytorch_optimizer.optimizer.adopt import ADOPT
 from pytorch_optimizer.optimizer.agc import agc
 from pytorch_optimizer.optimizer.aggmo import AggMo
@@ -292,6 +293,7 @@ OPTIMIZER_LIST: List[OPTIMIZER] = [
     AdaLOMO,
     AdamG,
     AdEMAMix,
+    SimplifiedAdEMAMix,
     SOAP,
     ADOPT,
     FTRL,
@@ -308,6 +310,7 @@ OPTIMIZER_LIST: List[OPTIMIZER] = [
     EXAdam,
     SCION,
     StableSPAM,
+    AdaGC,
     Ranger25,
 ]
 OPTIMIZERS: Dict[str, OPTIMIZER] = {str(optimizer.__name__).lower(): optimizer for optimizer in OPTIMIZER_LIST}
diff --git a/pytorch_optimizer/optimizer/adagc.py b/pytorch_optimizer/optimizer/adagc.py
new file mode 100644
index 00000000..40ee48ec
--- /dev/null
+++ b/pytorch_optimizer/optimizer/adagc.py
@@ -0,0 +1,139 @@
+import math
+
+import torch
+
+from pytorch_optimizer.base.exception import NoSparseGradientError
+from pytorch_optimizer.base.optimizer import BaseOptimizer
+from pytorch_optimizer.base.type import BETAS, CLOSURE, DEFAULTS, LOSS, PARAMETERS
+from pytorch_optimizer.optimizer.utils import get_global_gradient_norm
+
+
+class AdaGC(BaseOptimizer):
+    r"""Improving Training Stability for Large Language Model Pretraining.
+
+    :param params: PARAMETERS. iterable of parameters to optimize or dicts defining parameter groups.
+    :param lr: float. learning rate.
+    :param betas: BETAS. coefficients used for computing running averages of gradient and the squared hessian trace.
+    :param beta: float. smoothing coefficient for EMA.
+    :param lambda_abs: float. absolute clipping threshold to prevent unstable updates from gradient explosions.
+    :param lambda_rel: float. relative clipping threshold to prevent unstable updates from gradient explosions.
+    :param warmup_steps: int. warmup steps.
+    :param weight_decay: float. weight decay (L2 penalty).
+    :param weight_decouple: bool. the optimizer uses decoupled weight decay as in AdamW.
+    :param fixed_decay: bool. fix weight decay.
+    :param eps: float. term added to the denominator to improve numerical stability.
+    """
+
+    def __init__(
+        self,
+        params: PARAMETERS,
+        lr: float = 1e-3,
+        betas: BETAS = (0.9, 0.999),
+        beta: float = 0.98,
+        lambda_abs: float = 1.0,
+        lambda_rel: float = 1.05,
+        warmup_steps: int = 100,
+        weight_decay: float = 1e-1,
+        weight_decouple: bool = True,
+        fixed_decay: bool = False,
+        eps: float = 1e-8,
+        **kwargs,
+    ):
+        self.validate_learning_rate(lr)
+        self.validate_betas(betas)
+        self.validate_range(beta, 'beta', 0.0, 1.0, '[)')
+        self.validate_positive(lambda_abs, 'lambda_abs')
+        self.validate_positive(lambda_rel, 'lambda_rel')
+        self.validate_non_negative(warmup_steps, 'warmup_steps')
+        self.validate_non_negative(weight_decay, 'weight_decay')
+        self.validate_non_negative(eps, 'eps')
+
+        defaults: DEFAULTS = {
+            'lr': lr,
+            'betas': betas,
+            'beta': beta,
+            'lambda_abs': lambda_abs,
+            'lambda_rel': lambda_rel,
+            'warmup_steps': warmup_steps,
+            'weight_decay': weight_decay,
+            'weight_decouple': weight_decouple,
+            'fixed_decay': fixed_decay,
+            'eps': eps,
+        }
+        super().__init__(params, defaults)
+
+    def __str__(self) -> str:
+        return 'AdaGC'
+
+    @torch.no_grad()
+    def reset(self):
+        pass
+
+    @torch.no_grad()
+    def step(self, closure: CLOSURE = None) -> LOSS:
+        loss: LOSS = None
+        if closure is not None:
+            with torch.enable_grad():
+                loss = closure()
+
+        for group in self.param_groups:
+            if 'step' in group:
+                group['step'] += 1
+            else:
+                group['step'] = 1
+
+            beta1, beta2 = group['betas']
+
+            bias_correction1: float = self.debias(beta1, group['step'])
+            bias_correction2_sq: float = math.sqrt(self.debias(beta2, group['step']))
+
+            for p in group['params']:
+                if p.grad is None:
+                    continue
+
+                grad = p.grad
+                if grad.is_sparse:
+                    raise NoSparseGradientError(str(self))
+
+                state = self.state[p]
+
+                if 'exp_avg' not in state:
+                    state['exp_avg'] = torch.zeros_like(grad)
+                    state['exp_avg_sq'] = torch.zeros_like(grad)
+                    state['gamma'] = torch.empty((1,), device=grad.device, dtype=grad.dtype)
+
+                self.apply_weight_decay(
+                    p=p,
+                    grad=grad,
+                    lr=group['lr'],
+                    weight_decay=group['weight_decay'],
+                    weight_decouple=group['weight_decouple'],
+                    fixed_decay=group['fixed_decay'],
+                )
+
+                gamma = state['gamma']
+
+                if group['step'] < group['warmup_steps']:
+                    grad_norm = get_global_gradient_norm(self.param_groups).add_(group['eps'])
+
+                    h_t = min(group['lambda_abs'] / grad_norm, 1.0)
+                    g_hat = grad.mul(h_t)
+
+                    g_hat_norm = g_hat.norm()
+
+                    gamma.copy_(g_hat_norm if group['step'] == 1 else min(gamma, g_hat_norm))
+                else:
+                    h_t = min(group['lambda_rel'] * gamma / grad.norm(), 1.0)
+                    g_hat = grad.mul(h_t)
+
+                    gamma.mul_(group['beta']).add_(g_hat.norm(), alpha=1.0 - group['beta'])
+
+                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
+                exp_avg.mul_(beta1).add_(g_hat, alpha=1.0 - beta1)
+                exp_avg_sq.mul_(beta2).addcmul_(g_hat, g_hat, value=1.0 - beta2)
+
+                update = (exp_avg / bias_correction1) / exp_avg_sq.sqrt().div_(bias_correction2_sq).add_(group['eps'])
+
+                p.add_(update, alpha=-group['lr'])
+
+        return loss
diff --git a/pytorch_optimizer/optimizer/ademamix.py b/pytorch_optimizer/optimizer/ademamix.py
index 1fb843dd..5873d983 100644
--- a/pytorch_optimizer/optimizer/ademamix.py
+++ b/pytorch_optimizer/optimizer/ademamix.py
@@ -161,3 +161,137 @@ class AdEMAMix(BaseOptimizer):
                 p.add_(update, alpha=-step_size)
 
         return loss
+
+
+class SimplifiedAdEMAMix(BaseOptimizer):
+    r"""Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants.
+
+    :param params: PARAMETERS. iterable of parameters to optimize or dicts defining parameter groups.
+    :param lr: float. learning rate.
+    :param betas: BETAS. coefficients used for computing running averages of gradient and the squared hessian trace.
+    :param alpha: float. coefficient for mixing the current gradient and EMA.
+    :param beta1_warmup: Optional[int]. number of warmup steps used to increase beta1.
+    :param min_beta1: float. minimum value of beta1 to start from.
+    :param weight_decay: float. weight decay (L2 penalty).
+    :param weight_decouple: bool. the optimizer uses decoupled weight decay as in AdamW.
+    :param fixed_decay: bool. fix weight decay.
+    :param eps: float. term added to the denominator to improve numerical stability.
+    """
+
+    def __init__(
+        self,
+        params: PARAMETERS,
+        lr: float = 1e-4,
+        betas: BETAS = (0.99, 0.95),
+        weight_decay: float = 0.0,
+        weight_decouple: bool = True,
+        fixed_decay: bool = False,
+        alpha: float = 0.0,
+        beta1_warmup: Optional[int] = None,
+        min_beta1: float = 0.9,
+        eps: float = 1e-8,
+        **kwargs,
+    ):
+        self.validate_learning_rate(lr)
+        self.validate_betas(betas)
+        self.validate_non_negative(alpha, 'alpha')
+        self.validate_non_negative(min_beta1, 'min_beta1')
+        self.validate_non_negative(weight_decay, 'weight_decay')
+        self.validate_non_negative(eps, 'eps')
+
+        defaults: DEFAULTS = {
+            'lr': lr,
+            'betas': betas,
+            'alpha': alpha,
+            'beta1_warmup': beta1_warmup,
+            'min_beta1': min_beta1,
+            'weight_decay': weight_decay,
+            'weight_decouple': weight_decouple,
+            'fixed_decay': fixed_decay,
+            'eps': eps,
+        }
+
+        super().__init__(params, defaults)
+
+    def __str__(self) -> str:
+        return 'SimplifiedAdEMAMix'
+
+    @torch.no_grad()
+    def reset(self):
+        pass
+
+    @staticmethod
+    def linear_hl_warmup_scheduler(step: int, beta_end: float, beta_start: float = 0.0, warmup: int = 1) -> float:
+
+        def f(beta: float, eps: float = 1e-8) -> float:
+            return math.log(0.5) / math.log(beta + eps) - 1.0
+
+        def f_inv(t: float) -> float:
+            return math.pow(0.5, 1.0 / (t + 1))
+
+        if step < warmup:
+            a: float = step / float(warmup)
+            return f_inv((1.0 - a) * f(beta_start) + a * f(beta_end))
+
+        return beta_end
+
+    @torch.no_grad()
+    def step(self, closure: CLOSURE = None) -> LOSS:
+        loss: LOSS = None
+        if closure is not None:
+            with torch.enable_grad():
+                loss = closure()
+
+        for group in self.param_groups:
+            if 'step' in group:
+                group['step'] += 1
+            else:
+                group['step'] = 1
+
+            beta1, beta2 = group['betas']
+
+            if group['beta1_warmup']:
+                beta1 = self.linear_hl_warmup_scheduler(
+                    group['step'], beta_end=beta1, beta_start=group['min_beta1'], warmup=group['beta1_warmup']
+                )
+
+            for p in group['params']:
+                if p.grad is None:
+                    continue
+
+                grad = p.grad
+                if grad.is_sparse:
+                    raise NoSparseGradientError(str(self))
+
+                state = self.state[p]
+
+                if len(state) == 0:
+                    state['exp_avg'] = torch.zeros_like(p)
+                    state['exp_avg_sq'] = torch.zeros_like(p)
+                    state['num_sum'] = 0.0
+                    state['den_sum'] = 0.0
+
+                self.apply_weight_decay(
+                    p=p,
+                    grad=grad,
+                    lr=group['lr'],
+                    weight_decay=group['weight_decay'],
+                    weight_decouple=group['weight_decouple'],
+                    fixed_decay=group['fixed_decay'],
+                )
+
+                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
+
+                exp_avg.mul_(beta1).add_(grad, alpha=1.0 - beta1)
+                exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1.0 - beta2)
+
+                state['num_sum'] = beta1 * state['num_sum'] + 1.0
+                state['den_sum'] = beta2 * state['den_sum'] + (1.0 - beta2)
+
+                de_nom = exp_avg_sq.sqrt().add_(math.sqrt(state['den_sum']) * group['eps'])
+
+                update = (group['alpha'] * grad + exp_avg).div_(de_nom).div_(math.sqrt(state['den_sum']))
+
+                p.add_(update, alpha=-group['lr'])
+
+        return loss


Test patch:
diff --git a/tests/constants.py b/tests/constants.py
index 2336bad9..c5f27b58 100644
--- a/tests/constants.py
+++ b/tests/constants.py
@@ -30,6 +30,7 @@ from pytorch_optimizer.optimizer import (
     AdaBound,
     AdaDelta,
     AdaFactor,
+    AdaGC,
     AdaHessian,
     Adai,
     Adalite,
@@ -86,6 +87,7 @@ from pytorch_optimizer.optimizer import (
     SGDSaI,
     Shampoo,
     SignSGD,
+    SimplifiedAdEMAMix,
     SophiaH,
     StableAdamW,
     StableSPAM,
@@ -513,6 +515,7 @@ OPTIMIZERS: List[Tuple[Any, Dict[str, Union[float, bool, int]], int]] = [
     (AdamG, {'lr': 1e0, 'p': 0.5}, 60),
     (AdEMAMix, {'lr': 1e0}, 3),
     (AdEMAMix, {'lr': 1e0, 't_alpha_beta3': 5}, 3),
+    (SimplifiedAdEMAMix, {'lr': 1e0, 'beta1_warmup': 2, 'weight_decay': 1e-3}, 3),
     (
         SOAP,
         {'lr': 1e0, 'shampoo_beta': 0.95, 'precondition_frequency': 1, 'merge_dims': False, 'precondition_1d': True},
@@ -567,6 +570,7 @@ OPTIMIZERS: List[Tuple[Any, Dict[str, Union[float, bool, int]], int]] = [
     (EXAdam, {'lr': 1e-1, 'weight_decay': 1e-3}, 5),
     (SCION, {'lr': 5e-1, 'constraint': False, 'weight_decay': 1e-3}, 5),
     (SCION, {'lr': 1e-1, 'constraint': True, 'lmo_type': 'col_norm'}, 10),
+    (AdaGC, {'lr': 1e-1, 'warmup_steps': 2, 'weight_decay': 1e-3}, 5),
     (Ranger25, {'lr': 1e-1}, 3),
     (Ranger25, {'lr': 1e-1, 't_alpha_beta3': 5}, 3),
     (Ranger25, {'lr': 5e-2, 'stable_adamw': False, 'orthograd': False, 'eps': None, 'lookahead_merge_time': 2}, 3),
diff --git a/tests/test_load_modules.py b/tests/test_load_modules.py
index 3e0206be..3d21d11f 100644
--- a/tests/test_load_modules.py
+++ b/tests/test_load_modules.py
@@ -34,7 +34,7 @@ def test_load_lr_scheduler_invalid(invalid_lr_scheduler_names):
 
 
 def test_get_supported_optimizers():
-    assert len(get_supported_optimizers()) == 97
+    assert len(get_supported_optimizers()) == 99
     assert len(get_supported_optimizers('adam*')) == 8
     assert len(get_supported_optimizers(['adam*', 'ranger*'])) == 11