# Longitudinal Self-supervised Learning Using Neural Ordinary Differential Equation

arXiv: https://arxiv.org/abs/2310.10431 · HTML: https://mlsanity.com/paper/2310.10431/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 18 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Longitudinal Self-Supervised Learning](https://mlsanity.com/paper/2006.06930/) (2020)
- [Modeling Disease Progression In Retinal OCTs With Longitudinal Self-Supervised Learning](https://mlsanity.com/paper/1910.09420/) (2019)
- [Local Spatiotemporal Representation Learning for Longitudinally-consistent Neuroimage Analysis](https://mlsanity.com/paper/2206.04281/) (2022)
- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [Self-Supervised Longitudinal Neighbourhood Embedding](https://mlsanity.com/paper/2103.03840/) (2021)
- [TINC: Temporally Informed Non-Contrastive Learning for Disease Progression Modeling in Retinal OCT Volumes](https://mlsanity.com/paper/2206.15282/) (2022)
- [Learning to Compare Longitudinal Images](https://mlsanity.com/paper/2304.02531/) (2023)

## Built on by (most cited first, 3 of 3)

- [LaTiM: Longitudinal representation learning in continuous-time models to predict disease progression](https://mlsanity.com/paper/2404.07091/) (2024)
- [Automated Detection of Myopic Maculopathy in MMAC 2023: Achievements in Classification, Segmentation, and Spherical Equivalent Prediction](https://mlsanity.com/paper/2401.03615/) (2024)
- [Alzheimers Disease Progression Prediction Based on Manifold Mapping of Irregularly Sampled Longitudinal Data](https://mlsanity.com/paper/2511.20154/) (2025)

## Abstract (arXiv)

Longitudinal analysis in medical imaging is crucial to investigate the progressive changes in anatomical structures or disease progression over time. In recent years, a novel class of algorithms has emerged with the goal of learning disease progression in a self-supervised manner, using either pairs of consecutive images or time series of images. By capturing temporal patterns without external labels or supervision, longitudinal self-supervised learning (LSSL) has become a promising avenue. To better understand this core method, we explore in this paper the LSSL algorithm under different scenarios. The original LSSL is embedded in an auto-encoder (AE) structure. However, conventional self-supervised strategies are usually implemented in a Siamese-like manner. Therefore, (as a first novelty) in this study, we explore the use of Siamese-like LSSL. Another new core framework named neural ordinary differential equation (NODE). NODE is a neural network architecture that learns the dynamics of ordinary differential equations (ODE) through the use of neural networks. Many temporal systems can be described by ODE, including modeling disease progression. We believe that there is an interesting connection to make between LSSL and NODE. This paper aims at providing a better understanding of those core algorithms for learning the disease progression with the mentioned change. In our different experiments, we employ a longitudinal dataset, named OPHDIAT, targeting diabetic retinopathy (DR) follow-up. Our results demonstrate the application of LSSL without including a reconstruction term, as well as the potential of incorporating NODE in conjunction with LSSL.