# HartleyMHA: Self-Attention in Frequency Domain for Resolution-Robust and Parameter-Efficient 3D Image Segmentation

arXiv: https://arxiv.org/abs/2310.04466 · HTML: https://mlsanity.com/paper/2310.04466/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [CoTr: Efficiently Bridging CNN and Transformer for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.03024/) (2021)
- [SOFT: Softmax-free Transformer with Linear Complexity](https://mlsanity.com/paper/2110.11945/) (2021)
- [UTNet: A Hybrid Transformer Architecture for Medical Image Segmentation](https://mlsanity.com/paper/2107.00781/) (2021)
- [3D Segmentation with Exponential Logarithmic Loss for Highly Unbalanced Object Sizes](https://mlsanity.com/paper/1809.00076/) (2018)
- [3D Segmentation with Fully Trainable Gabor Kernels and Pearson's Correlation Coefficient](https://mlsanity.com/paper/2201.03644/) (2022)

## Built on by (most cited first, 2 of 2)

- [M3DA: Benchmark for Unsupervised Domain Adaptation in 3D Medical Image Segmentation](https://mlsanity.com/paper/2502.17029/) (2025)
- [Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment](https://mlsanity.com/paper/2606.24851/) (2026)

## Abstract (arXiv)

With the introduction of Transformers, different attention-based models have been proposed for image segmentation with promising results. Although self-attention allows capturing of long-range dependencies, it suffers from a quadratic complexity in the image size especially in 3D. To avoid the out-of-memory error during training, input size reduction is usually required for 3D segmentation, but the accuracy can be suboptimal when the trained models are applied on the original image size. To address this limitation, inspired by the Fourier neural operator (FNO), we introduce the HartleyMHA model which is robust to training image resolution with efficient self-attention. FNO is a deep learning framework for learning mappings between functions in partial differential equations, which has the appealing properties of zero-shot super-resolution and global receptive field. We modify the FNO by using the Hartley transform with shared parameters to reduce the model size by orders of magnitude, and this allows us to further apply self-attention in the frequency domain for more expressive high-order feature combination with improved efficiency. When tested on the BraTS'19 dataset, it achieved superior robustness to training image resolution than other tested models with less than 1% of their model parameters.