Low-Rank Thinning

Annabelle Michael Carrell, Albert Gong, Abhishek Shetty, Raaz Dwivedi, Lester Mackey
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:6811-6848, 2025.

Abstract

The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially reducing the number of summary points. However, existing guarantees cover only a restricted range of distributions and kernel-based quality measures and suffer from pessimistic dimension dependence. To address these deficiencies, we introduce a new low-rank analysis of sub-Gaussian thinning that applies to any distribution and any kernel, guaranteeing high-quality compression whenever the kernel or data matrix is approximately low-rank. To demonstrate the broad applicability of the techniques, we design practical sub-Gaussian thinning approaches that improve upon the best known guarantees for approximating attention in transformers, accelerating stochastic gradient training through reordering, and distinguishing distributions in near-linear time.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-carrell25a, title = {Low-Rank Thinning}, author = {Carrell, Annabelle Michael and Gong, Albert and Shetty, Abhishek and Dwivedi, Raaz and Mackey, Lester}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {6811--6848}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/carrell25a/carrell25a.pdf}, url = {https://proceedings.mlr.press/v267/carrell25a.html}, abstract = {The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially reducing the number of summary points. However, existing guarantees cover only a restricted range of distributions and kernel-based quality measures and suffer from pessimistic dimension dependence. To address these deficiencies, we introduce a new low-rank analysis of sub-Gaussian thinning that applies to any distribution and any kernel, guaranteeing high-quality compression whenever the kernel or data matrix is approximately low-rank. To demonstrate the broad applicability of the techniques, we design practical sub-Gaussian thinning approaches that improve upon the best known guarantees for approximating attention in transformers, accelerating stochastic gradient training through reordering, and distinguishing distributions in near-linear time.} }
Endnote
%0 Conference Paper %T Low-Rank Thinning %A Annabelle Michael Carrell %A Albert Gong %A Abhishek Shetty %A Raaz Dwivedi %A Lester Mackey %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-carrell25a %I PMLR %P 6811--6848 %U https://proceedings.mlr.press/v267/carrell25a.html %V 267 %X The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially reducing the number of summary points. However, existing guarantees cover only a restricted range of distributions and kernel-based quality measures and suffer from pessimistic dimension dependence. To address these deficiencies, we introduce a new low-rank analysis of sub-Gaussian thinning that applies to any distribution and any kernel, guaranteeing high-quality compression whenever the kernel or data matrix is approximately low-rank. To demonstrate the broad applicability of the techniques, we design practical sub-Gaussian thinning approaches that improve upon the best known guarantees for approximating attention in transformers, accelerating stochastic gradient training through reordering, and distinguishing distributions in near-linear time.
APA
Carrell, A.M., Gong, A., Shetty, A., Dwivedi, R. & Mackey, L.. (2025). Low-Rank Thinning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:6811-6848 Available from https://proceedings.mlr.press/v267/carrell25a.html.

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