WildCat: Near-Linear Attention in Theory and Practice

Tobias Schröder, Lester Mackey
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:108454-108484, 2026.

Abstract

We introduce WildCat, a high-accuracy, low-cost approach to compressing the attention mechanism in neural networks. While attention is a staple of modern network architectures, it is also notoriously expensive to deploy due to resource requirements that scale quadratically with the input sequence length $n$. WildCat avoids these quadratic costs by only attending over a small weighted coreset. Crucially, we select the coreset using a fast but spectrally-accurate subsampling algorithm – randomly pivoted Cholesky – and weight the elements optimally to minimise reconstruction error. Remarkably, given bounded inputs, WildCat approximates exact attention with super-polynomial $O(n^{-\sqrt{\log(\log(n))}})$ error decay while running in near-linear $O(n^{1+o(1)})$ time. In contrast, prior practical approximations either lack error guarantees or require quadratic runtime to guarantee such high fidelity. We couple this advance with a GPU-optimised PyTorch implementation and a suite of benchmark experiments demonstrating the benefits of WildCat for image generation, image classification, and language model KV cache compression.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-schroder26a, title = {{W}ild{C}at: Near-Linear Attention in Theory and Practice}, author = {Schr\"{o}der, Tobias and Mackey, Lester}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {108454--108484}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/schroder26a/schroder26a.pdf}, url = {https://proceedings.mlr.press/v306/schroder26a.html}, abstract = {We introduce WildCat, a high-accuracy, low-cost approach to compressing the attention mechanism in neural networks. While attention is a staple of modern network architectures, it is also notoriously expensive to deploy due to resource requirements that scale quadratically with the input sequence length $n$. WildCat avoids these quadratic costs by only attending over a small weighted coreset. Crucially, we select the coreset using a fast but spectrally-accurate subsampling algorithm – randomly pivoted Cholesky – and weight the elements optimally to minimise reconstruction error. Remarkably, given bounded inputs, WildCat approximates exact attention with super-polynomial $O(n^{-\sqrt{\log(\log(n))}})$ error decay while running in near-linear $O(n^{1+o(1)})$ time. In contrast, prior practical approximations either lack error guarantees or require quadratic runtime to guarantee such high fidelity. We couple this advance with a GPU-optimised PyTorch implementation and a suite of benchmark experiments demonstrating the benefits of WildCat for image generation, image classification, and language model KV cache compression.} }
Endnote
%0 Conference Paper %T WildCat: Near-Linear Attention in Theory and Practice %A Tobias Schröder %A Lester Mackey %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-schroder26a %I PMLR %P 108454--108484 %U https://proceedings.mlr.press/v306/schroder26a.html %V 306 %X We introduce WildCat, a high-accuracy, low-cost approach to compressing the attention mechanism in neural networks. While attention is a staple of modern network architectures, it is also notoriously expensive to deploy due to resource requirements that scale quadratically with the input sequence length $n$. WildCat avoids these quadratic costs by only attending over a small weighted coreset. Crucially, we select the coreset using a fast but spectrally-accurate subsampling algorithm – randomly pivoted Cholesky – and weight the elements optimally to minimise reconstruction error. Remarkably, given bounded inputs, WildCat approximates exact attention with super-polynomial $O(n^{-\sqrt{\log(\log(n))}})$ error decay while running in near-linear $O(n^{1+o(1)})$ time. In contrast, prior practical approximations either lack error guarantees or require quadratic runtime to guarantee such high fidelity. We couple this advance with a GPU-optimised PyTorch implementation and a suite of benchmark experiments demonstrating the benefits of WildCat for image generation, image classification, and language model KV cache compression.
APA
Schröder, T. & Mackey, L.. (2026). WildCat: Near-Linear Attention in Theory and Practice. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:108454-108484 Available from https://proceedings.mlr.press/v306/schroder26a.html.

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