# Fourier Transform Multiple Instance Learning for Whole Slide Image Classification

arXiv: https://arxiv.org/abs/2510.15138 · HTML: https://mlsanity.com/paper/2510.15138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 59 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Data Efficient and Weakly Supervised Computational Pathology on Whole Slide Images](https://mlsanity.com/paper/2004.09666/) (2020)
- [Resolution-robust Large Mask Inpainting with Fourier Convolutions](https://mlsanity.com/paper/2109.07161/) (2021)
- [Dual-stream Multiple Instance Learning Network for Whole Slide Image Classification with Self-supervised Contrastive Learning](https://mlsanity.com/paper/2011.08939/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [BRACS: A Dataset for BReAst Carcinoma Subtyping in H&E Histology Images](https://mlsanity.com/paper/2111.04740/) (2021)
- [Artificial Intelligence for Digital and Computational Pathology](https://mlsanity.com/paper/2401.06148/) (2023)
- [Interventional Bag Multi-Instance Learning On Whole-Slide Pathological Images](https://mlsanity.com/paper/2303.06873/) (2023)
- [Virchow: A Million-Slide Digital Pathology Foundation Model](https://mlsanity.com/paper/2309.07778/) (2023)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [SwinFIR: Revisiting the SwinIR with Fast Fourier Convolution and Improved Training for Image Super-Resolution](https://mlsanity.com/paper/2208.11247/) (2022)
- [Feature Re-Embedding: Towards Foundation Model-Level Performance in Computational Pathology](https://mlsanity.com/paper/2402.17228/) (2024)
- [Attention-Challenging Multiple Instance Learning for Whole Slide Image Classification](https://mlsanity.com/paper/2311.07125/) (2023)
- [A Closer Look at AUROC and AUPRC under Class Imbalance](https://mlsanity.com/paper/2401.06091/) (2024)
- [Multiple Instance Learning for Digital Pathology: A Review on the State-of-the-Art, Limitations & Future Potential](https://mlsanity.com/paper/2206.04425/) (2022)
- [Task-specific Fine-tuning via Variational Information Bottleneck for Weakly-supervised Pathology Whole Slide Image Classification](https://mlsanity.com/paper/2303.08446/) (2023)
- [Differentiable Zooming for Multiple Instance Learning on Whole-Slide Images](https://mlsanity.com/paper/2204.12454/) (2022)
- [Computational Pathology: A Survey Review and The Way Forward](https://mlsanity.com/paper/2304.05482/) (2023)
- [DGR-MIL: Exploring Diverse Global Representation in Multiple Instance Learning for Whole Slide Image Classification](https://mlsanity.com/paper/2407.03575/) (2024)
- [Cross-scale Multi-instance Learning for Pathological Image Diagnosis](https://mlsanity.com/paper/2304.00216/) (2023)
- [An interpretable machine learning system for colorectal cancer diagnosis from pathology slides](https://mlsanity.com/paper/2301.02608/) (2023)
- [SCMIL: Sparse Context-aware Multiple Instance Learning for Predicting Cancer Survival Probability Distribution in Whole Slide Images](https://mlsanity.com/paper/2407.00664/) (2024)
- [WSI-SAM: Multi-resolution Segment Anything Model (SAM) for histopathology whole-slide images](https://mlsanity.com/paper/2403.09257/) (2024)
- [RetMIL: Retentive Multiple Instance Learning for Histopathological Whole Slide Image Classification](https://mlsanity.com/paper/2403.10858/) (2024)
- [Integrative Graph-Transformer Framework for Histopathology Whole Slide Image Representation and Classification](https://mlsanity.com/paper/2403.18134/) (2024)
- [Prompting Whole Slide Image Based Genetic Biomarker Prediction](https://mlsanity.com/paper/2407.09540/) (2024)

## Abstract (arXiv)

Whole Slide Image (WSI) classification relies on Multiple Instance Learning (MIL) with spatial patch features, yet existing methods struggle to capture global dependencies due to the immense size of WSIs and the local nature of patch embeddings. This limitation hinders the modeling of coarse structures essential for robust diagnostic prediction. We propose Fourier Transform Multiple Instance Learning (FFT-MIL), a framework that augments MIL with a frequency-domain branch to provide compact global context. Low-frequency crops are extracted from WSIs via the Fast Fourier Transform and processed through a modular FFT-Block composed of convolutional layers and Min-Max normalization to mitigate the high variance of frequency data. The learned global frequency feature is fused with spatial patch features through lightweight integration strategies, enabling compatibility with diverse MIL architectures. FFT-MIL was evaluated across six state-of-the-art MIL methods on three public datasets (BRACS, LUAD, and IMP). Integration of the FFT-Block improved macro F1 scores by an average of 3.51% and AUC by 1.51%, demonstrating consistent gains across architectures and datasets. These results establish frequency-domain learning as an effective and efficient mechanism for capturing global dependencies in WSI classification, complementing spatial features and advancing the scalability and accuracy of MIL-based computational pathology.