# Dilated Convolutional Neural Networks for Sequential Manifold-valued Data

arXiv: https://arxiv.org/abs/1910.02206 · HTML: https://mlsanity.com/paper/1910.02206/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2019.

## Built on by (most cited first, 11 of 11)

- [Riemannian Local Mechanism for SPD Neural Networks](https://mlsanity.com/paper/2201.10145/) (2022)
- [Adaptive Log-Euclidean Metrics for SPD Matrix Learning](https://mlsanity.com/paper/2303.15477/) (2023)
- [Riemannian Multinomial Logistics Regression for SPD Neural Networks](https://mlsanity.com/paper/2305.11288/) (2023)
- [Deep Efficient Continuous Manifold Learning for Time Series Modeling](https://mlsanity.com/paper/2112.03379/) (2021)
- [Neural Networks on Symmetric Spaces of Noncompact Type](https://mlsanity.com/paper/2601.01097/) (2026)
- [Deep Geometric Learning with Monotonicity Constraints for Alzheimer's Disease Progression](https://mlsanity.com/paper/2310.03353/) (2023)
- [A survey of manifold learning and its applications for multimedia](https://mlsanity.com/paper/2310.12986/) (2023)
- [Rega-Net:Retina Gabor Attention for Deep Convolutional Neural Networks](https://mlsanity.com/paper/2211.12698/) (2022)
- [Noisy Data Visualization using Functional Data Analysis](https://mlsanity.com/paper/2406.03396/) (2024)
- [MSAD-Net: Multiscale and Spatial Attention-based Dense Network for Lung Cancer Classification](https://mlsanity.com/paper/2504.14626/) (2025)
- [Electric Vehicle Identification from Behind Smart Meter Data](https://mlsanity.com/paper/2509.19316/) (2025)

## Abstract (arXiv)

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often, sizable empirical improvements are possible when the geometry of such data spaces are incorporated into the design of the model, architecture, and the algorithms. Motivated by neuroimaging applications, we study formulations where the data are em sequential manifold-valued measurements. This case is common in brain imaging, where the samples correspond to symmetric positive definite matrices or orientation distribution functions. Instead of a recurrent model which poses computational/technical issues, and inspired by recent results showing the viability of dilated convolutional models for sequence prediction, we develop a dilated convolutional neural network architecture for this task. On the technical side, we show how the modules needed in our network can be derived while explicitly taking the Riemannian manifold structure into account. We show how the operations needed can leverage known results for calculating the weighted Fr'echet Mean (wFM). Finally, we present scientific results for group difference analysis in Alzheimer's disease (AD) where the groups are derived using AD pathology load: here the model finds several brain fiber bundles that are related to AD even when the subjects are all still cognitively healthy.