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KH-SGD

Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.

For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.

@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}

This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.

Dependencies

This code has been tested with the following operating system, Python, and PyTorch combinations:

  • Rocky 8.9, Python 3.10, Torch 2.6.0

The following dependences are needed to run the experiment:

  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers

Below are step by step commands to create a Conda environment with the proper dependencies:

conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.

Experiments

To recreate the reordered SGD experiments of Low-Rank Thinning, please run

torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.

To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.

To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.

Contributing

This project welcomes contributions and suggestions. Most contributions require you to agree to a Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.

When you submit a pull request, a CLA bot will automatically determine whether you need to provide a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions provided by the bot. You will only need to do this once across all repos using our CLA.

This project has adopted the Microsoft Open Source Code of Conduct. For more information see the Code of Conduct FAQ or contact opencode@microsoft.com with any additional questions or comments.

Trademarks

This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft trademarks or logos is subject to and must follow Microsoft's Trademark & Brand Guidelines. Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship. Any use of third-party trademarks or logos are subject to those third-party's policies.

About

KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.

arxiv.org/pdf/2502.12063

Topics

acceleratedcompressiondiscrepancykernel-halvingsgd

Resources

Readme
License

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Code of conduct

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try {
var __m = "github.com";
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Skip to content
BranchesTags
Repository files navigation
KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
Resources
Readme
License
Code of conduct
Code of conduct
Security policy
Security policy
Activity
Custom properties
Stars
3 stars
Watchers
4 watching
Forks
3 forks
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, 'i');
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injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
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})();
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try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
Resources
Readme
License
Code of conduct
Code of conduct
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Security policy
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Stars
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Watchers
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
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})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
Resources
Readme
License
Code of conduct
Code of conduct
Security policy
Security policy
Activity
Custom properties
Stars
3 stars
Watchers
4 watching
Forks
3 forks
Report repository
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Used by
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
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})();
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var __m = "youtube.com";
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Skip to content
BranchesTags
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KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
Resources
Readme
License
Code of conduct
Code of conduct
Security policy
Security policy
Activity
Custom properties
Stars
3 stars
Watchers
4 watching
Forks
3 forks
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
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})();
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KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
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KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
Resources
Readme
License
Code of conduct
Code of conduct
Security policy
Security policy
Activity
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Stars
3 stars
Watchers
4 watching
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3 forks
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if (__m === '*' || __re.test(location.href)) {
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KH-SGD
Kernel Halving SGD (KH-SGD) iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
For a detailed description of the KH-SGD algorithm and its guarantees, see Low-Rank Thinning.
@inproceedings{carrell2025lowrank,
title={Low-Rank Thinning},
author={Annabelle Michael Carrell and Albert Gong and Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=iAkg2nVmvN}
}
This codebase reproduces the reordered SGD experiments of Low-Rank Thinning and is derived from the code of CD-GraB.
Dependencies
This code has been tested with the following operating system, Python, and PyTorch combinations:
  • Rocky 8.9, Python 3.10, Torch 2.6.0
The following dependences are needed to run the experiment:
  • Python >= 3.9
  • PyTorch >= 2.0.0
  • CUDA >= 11.7 on linux
  • torchopt
  • torchvision
  • functorch
  • transformers
Below are step by step commands to create a Conda environment with the proper dependencies:
conda create -n khsgd python=3.10
conda activate khsgd
# Follow instructions at https://pytorch.org/get-started/locally/ for your system
pip3 install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cu118
conda install torchopt
conda install functorch
conda install transformers

After, download the HMDA preprocessed files and place them under data/HMDA/.
Experiments
To recreate the reordered SGD experiments of Low-Rank Thinning, please run
torchrun --nproc_per_node=1 --nnodes=1 --master_addr="localhost" --master_port=35500 main-LR-HMDA.py --sorter <SORT> --seed <SEED> --lr 5e-3 --node_cnt 1

with <SORT> replaced by each of the sorters ("CD-GraB", "D-RR", "KH-SGD", "SBW") and <SEED> replaced by each seed in the range 1-5.
To recreate the plot, run python LR-HMDA.py in the notebooks/LR-HMDA directory.
To recreate the supplementary plot, add torch.save(gathered_grads, f"PREFIX_{batch}") to line 291 in d_hmda.py. Run the main script as described above. Then, run notebooks/LR-HMDA/sing_vals.ipynb, with PREFIX as FILENAME_PREFIX (by default it is all_grads_epoch) appended to your data location.
Contributing
This project welcomes contributions and suggestions. Most contributions require you to agree to a
Contributor License Agreement (CLA) declaring that you have the right to, and actually do, grant us
the rights to use your contribution. For details, visit https://cla.opensource.microsoft.com.
When you submit a pull request, a CLA bot will automatically determine whether you need to provide
a CLA and decorate the PR appropriately (e.g., status check, comment). Simply follow the instructions
provided by the bot. You will only need to do this once across all repos using our CLA.
This project has adopted the Microsoft Open Source Code of Conduct.
For more information see the Code of Conduct FAQ or
contact opencode@microsoft.com with any additional questions or comments.
Trademarks
This project may contain trademarks or logos for projects, products, or services. Authorized use of Microsoft
trademarks or logos is subject to and must follow
Microsoft's Trademark & Brand Guidelines.
Use of Microsoft trademarks or logos in modified versions of this project must not cause confusion or imply Microsoft sponsorship.
Any use of third-party trademarks or logos are subject to those third-party's policies.
About
KH-SGD iteratively reorders datapoints during stochastic gradient descent training to provably accelerate convergence.
arxiv.org/pdf/2502.12063
Topics
acceleratedcompressiondiscrepancykernel-halvingsgd
Resources
Readme
License
Code of conduct
Code of conduct
Security policy
Security policy
Activity
Custom properties
Stars
3 stars
Watchers
4 watching
Forks
3 forks
Report repository
Releases
Packages
Used by
Contributors
Languages