# Native Multi-Dimensional Subquadratic Operators via Input Dependent Long Convolutions

arXiv: https://arxiv.org/abs/2607.19378 · HTML: https://mlsanity.com/paper/2607.19378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 54 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Swin UNETR: Swin Transformers for Semantic Segmentation of Brain Tumors in MRI Images](https://mlsanity.com/paper/2201.01266/) (2022)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Zoology: Measuring and Improving Recall in Efficient Language Models](https://mlsanity.com/paper/2312.04927/) (2023)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Mamba-ND: Selective State Space Modeling for Multi-Dimensional Data](https://mlsanity.com/paper/2402.05892/) (2024)
- [FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes](https://mlsanity.com/paper/2110.08059/) (2021)
- [FlashAttention-4: Algorithm and Kernel Pipelining Co-Design for Asymmetric Hardware Scaling](https://mlsanity.com/paper/2603.05451/) (2026)

## Abstract (arXiv)

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 1rm D scan order that violates their spatial structure. We introduce textitHyenaND, 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, textttnSubQ, fuses the FFT-convolution path to turn HyenaND's 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.