# R-Mixup: Riemannian Mixup for Biological Networks

arXiv: https://arxiv.org/abs/2306.02532 · HTML: https://mlsanity.com/paper/2306.02532/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 107 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 46)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Twins: Revisiting the Design of Spatial Attention in Vision Transformers](https://mlsanity.com/paper/2104.13840/) (2021)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Puzzle Mix: Exploiting Saliency and Local Statistics for Optimal Mixup](https://mlsanity.com/paper/2009.06962/) (2020)
- [MixText: Linguistically-Informed Interpolation of Hidden Space for Semi-Supervised Text Classification](https://mlsanity.com/paper/2004.12239/) (2020)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Remix: Rebalanced Mixup](https://mlsanity.com/paper/2007.03943/) (2020)
- [PixMix: Dreamlike Pictures Comprehensively Improve Safety Measures](https://mlsanity.com/paper/2112.05135/) (2021)
- [Brain Network Transformer](https://mlsanity.com/paper/2210.06681/) (2022)
- [BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networks](https://mlsanity.com/paper/2204.07054/) (2022)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [FBNETGEN: Task-aware GNN-based fMRI Analysis via Functional Brain Network Generation](https://mlsanity.com/paper/2205.12465/) (2022)
- [Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysis](https://mlsanity.com/paper/2207.00813/) (2022)
- [SuperMix: Supervising the Mixing Data Augmentation](https://mlsanity.com/paper/2003.05034/) (2020)
- [C-Mixup: Improving Generalization in Regression](https://mlsanity.com/paper/2210.05775/) (2022)
- [SeqMix: Augmenting Active Sequence Labeling via Sequence Mixup](https://mlsanity.com/paper/2010.02322/) (2020)
- [MAtt: A Manifold Attention Network for EEG Decoding](https://mlsanity.com/paper/2210.01986/) (2022)
- [Graph Neural Network for Interpreting Task-fMRI Biomarkers](https://mlsanity.com/paper/1907.01661/) (2019)
- [MixSpeech: Data Augmentation for Low-resource Automatic Speech Recognition](https://mlsanity.com/paper/2102.12664/) (2021)
- [GraphMixup: Improving Class-Imbalanced Node Classification on Graphs by Self-supervised Context Prediction](https://mlsanity.com/paper/2106.11133/) (2021)
- [SumGNN: Multi-typed Drug Interaction Prediction via Efficient Knowledge Graph Summarization](https://mlsanity.com/paper/2010.01450/) (2020)
- [AlignMixup: Improving Representations By Interpolating Aligned Features](https://mlsanity.com/paper/2103.15375/) (2021)

## Built on by (most cited first, 9 of 9)

- [Knowledge-Infused Prompting: Assessing and Advancing Clinical Text Data Generation with Large Language Models](https://mlsanity.com/paper/2311.00287/) (2023)
- [RC-Mixup: A Data Augmentation Strategy against Noisy Data for Regression Tasks](https://mlsanity.com/paper/2405.17938/) (2024)
- [Tailoring Mixup to Data for Calibration](https://mlsanity.com/paper/2311.01434/) (2023)
- [Riemannian Geometry-Based EEG Approaches: A Literature Review](https://mlsanity.com/paper/2407.20250/) (2024)
- [ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks](https://mlsanity.com/paper/2602.23285/) (2026)
- [Curvature Enhanced Data Augmentation for Regression](https://mlsanity.com/paper/2506.06853/) (2025)
- [RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs](https://mlsanity.com/paper/2602.22981/) (2026)
- [Enhancing Protein Representation Learning via Manifold Restore Mixing](https://mlsanity.com/paper/2606.22307/) (2026)
- [Temporal Geometry of Deep Networks: Hyperbolic Representations of Training Dynamics for Intrinsic Explainability](https://mlsanity.com/paper/2610.03000/) (2026)

## Abstract (arXiv)

Biological networks are commonly used in biomedical and healthcare domains to effectively model the structure of complex biological systems with interactions linking biological entities. However, due to their characteristics of high dimensionality and low sample size, directly applying deep learning models on biological networks usually faces severe overfitting. In this work, we propose R-MIXUP, a Mixup-based data augmentation technique that suits the symmetric positive definite (SPD) property of adjacency matrices from biological networks with optimized training efficiency. The interpolation process in R-MIXUP leverages the log-Euclidean distance metrics from the Riemannian manifold, effectively addressing the swelling effect and arbitrarily incorrect label issues of vanilla Mixup. We demonstrate the effectiveness of R-MIXUP with five real-world biological network datasets on both regression and classification tasks. Besides, we derive a commonly ignored necessary condition for identifying the SPD matrices of biological networks and empirically study its influence on the model performance. The code implementation can be found in Appendix E.