# Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Features

arXiv: https://arxiv.org/abs/2305.01807 · HTML: https://mlsanity.com/paper/2305.01807/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 117 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization](https://mlsanity.com/paper/2009.05204/) (2020)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [Computing Graph Neural Networks: A Survey from Algorithms to Accelerators](https://mlsanity.com/paper/2010.00130/) (2020)
- [Convergence and Stability of Graph Convolutional Networks on Large Random Graphs](https://mlsanity.com/paper/2006.01868/) (2020)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)
- [A Graph Neural Network Framework for Causal Inference in Brain Networks](https://mlsanity.com/paper/2010.07143/) (2020)
- [Data-Efficient Brain Connectome Analysis via Multi-Task Meta-Learning](https://mlsanity.com/paper/2206.04486/) (2022)
- [Predicting Brain Age using Transferable coVariance Neural Networks](https://mlsanity.com/paper/2210.16363/) (2022)

## Built on by (most cited first, 5 of 5)

- [Spatiotemporal Covariance Neural Networks](https://mlsanity.com/paper/2409.10068/) (2024)
- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Towards a Foundation Model for Brain Age Prediction using coVariance Neural Networks](https://mlsanity.com/paper/2402.07684/) (2024)
- [CoVariance Filters and Neural Networks over Hilbert Spaces](https://mlsanity.com/paper/2509.13178/) (2025)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

Graph convolutional networks (GCN) leverage topology-driven graph convolutional operations to combine information across the graph for inference tasks. In our recent work, we have studied GCNs with covariance matrices as graphs in the form of coVariance neural networks (VNNs) that draw similarities with traditional PCA-driven data analysis approaches while offering significant advantages over them. In this paper, we first focus on theoretically characterizing the transferability of VNNs. The notion of transferability is motivated from the intuitive expectation that learning models could generalize to "compatible" datasets (possibly of different dimensionalities) with minimal effort. VNNs inherit the scale-free data processing architecture from GCNs and here, we show that VNNs exhibit transferability of performance over datasets whose covariance matrices converge to a limit object. Multi-scale neuroimaging datasets enable the study of the brain at multiple scales and hence, can validate the theoretical results on the transferability of VNNs. To gauge the advantages offered by VNNs in neuroimaging data analysis, we focus on the task of "brain age" prediction using cortical thickness features. In clinical neuroscience, there has been an increased interest in machine learning algorithms which provide estimates of "brain age" that deviate from chronological age. We leverage the architecture of VNNs to extend beyond the coarse metric of brain age gap in Alzheimer's disease (AD) and make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD, and (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific principal components of the anatomical covariance matrix. We further leverage the transferability of VNNs to cross validate the above observations across different datasets.