2026-07-23 04:00 UTCOriginal source2 min readUpdated: 2026-07-23 08:25 UTC

Native Multi-Dimensional Subquadratic Operators via Input Dependent Long Convolutions

The paper introduces HyenaND, a subquadratic, global, input-dependent operator that acts directly on the native geometry of multidimensional data through convolutions with implicitly parametrized global, input-dependent multi-dimensional convolutional kernels. Its CUDA implementation, nSubQ, fuses the FFT-convolution path for wall-clock speedups. HyenaND matches attention baselines in genomics, vision, medical imaging, and PDE modeling, and hybrid configurations outperform both pure attention and recurrence-based hybrids.

SourcearXiv Machine LearningAuthor: David R. Wessels, Farhad Ramezanghorbani, David W. Romero, Alireza Moradzadeh, Olivia Viessmann, Maksim Zhdanov, John St. John, Ken Janik, David M Knigge, Yucheng Tang, Erik J Bekkers, Saee Gopal Paliwal

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[Submitted on 1 Jul 2026]

Title:Native Multi-Dimensional Subquadratic Operators via Input Dependent Long Convolutions

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Abstract:Subquadratic alternatives to attention require compromises when applied to multi-dimensional data: standard convolutions lack global receptive fields and input dependency, while recurrent models require rasterizing data such as images, volumes, and partial differential equation (PDE) into an ad-hoc $1\rm D$ scan order that violates their spatial structure. We introduce \textit{HyenaND}, a subquadratic, global, input-dependent operator that acts directly on the native geometry of multidimensional data through convolutions with implicitly parametrized global, input-dependent multi-dimensional convolutional kernels. Our CUDA implementation, \texttt{nSubQ}, fuses the FFT-convolution path to turn HyenaND's $\mathcal{O}(L \log L)$ scaling into wall-clock speedups. Across long-context genomics, computer vision, medical imaging, and PDE modeling, pure HyenaND stacks match the accuracy of strong attention baselines, while hybrid configurations that interleave HyenaND and attention layers outperform both pure attention and strong recurrence-based hybrids.

Subjects:

Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML)

Cite as: arXiv:2607.19378 [cs.LG]

(or arXiv:2607.19378v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.19378

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: David Wessels [view email] [v1] Wed, 1 Jul 2026 02:39:18 UTC (3,922 KB)

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