# Modeling the Shape of the Brain Connectome via Deep Neural Networks

arXiv: https://arxiv.org/abs/2203.06122 · HTML: https://mlsanity.com/paper/2203.06122/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [Structural Connectome Atlas Construction in the Space of Riemannian Metrics](https://mlsanity.com/paper/2103.05730/) (2021)
- [Geodesic Fiber Tracking in White Matter using Activation Function](https://mlsanity.com/paper/2104.02097/) (2021)

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

- [MTS-Net: Dual-Enhanced Positional Multi-Head Self-Attention for 3D CT Diagnosis of May-Thurner Syndrome](https://mlsanity.com/paper/2406.04680/) (2024)
- [A foundation for systematic analysis of transformers and RNNs for tractography](https://mlsanity.com/paper/2610.01894/) (2026)

## Abstract (arXiv)

The goal of diffusion-weighted magnetic resonance imaging (DWI) is to infer the structural connectivity of an individual subject's brain in vivo. To statistically study the variability and differences between normal and abnormal brain connectomes, a mathematical model of the neural connections is required. In this paper, we represent the brain connectome as a Riemannian manifold, which allows us to model neural connections as geodesics. This leads to the challenging problem of estimating a Riemannian metric that is compatible with the DWI data, i.e., a metric such that the geodesic curves represent individual fiber tracts of the connectomics. We reduce this problem to that of solving a highly nonlinear set of partial differential equations (PDEs) and study the applicability of convolutional encoder-decoder neural networks (CEDNNs) for solving this geometrically motivated PDE. Our method achieves excellent performance in the alignment of geodesics with white matter pathways and tackles a long-standing issue in previous geodesic tractography methods: the inability to recover crossing fibers with high fidelity.