# Semantic Segmentation using Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2209.08667 · HTML: https://mlsanity.com/paper/2209.08667/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 18 Sep 2022.

## Builds on (most cited first, 30 of 35)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation](https://mlsanity.com/paper/1909.11065/) (2019)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Look into Person: Self-supervised Structure-sensitive Learning and A New Benchmark for Human Parsing](https://mlsanity.com/paper/1703.05446/) (2017)
- [In-Place Activated BatchNorm for Memory-Optimized Training of DNNs](https://mlsanity.com/paper/1712.02616/) (2017)
- [Devil in the Details: Towards Accurate Single and Multiple Human Parsing](https://mlsanity.com/paper/1809.05996/) (2018)
- [Image-based Localization using Hourglass Networks](https://mlsanity.com/paper/1703.07971/) (2017)
- [Residual Conv-Deconv Grid Network for Semantic Segmentation](https://mlsanity.com/paper/1707.07958/) (2017)
- [PolyNet: A Pursuit of Structural Diversity in Very Deep Networks](https://mlsanity.com/paper/1611.05725/) (2016)
- [Fast, Exact and Multi-Scale Inference for Semantic Image Segmentation with Deep Gaussian CRFs](https://mlsanity.com/paper/1603.08358/) (2016)
- [Convolutional Neural Networks combined with Runge-Kutta Methods](https://mlsanity.com/paper/1802.08831/) (2018)

## Built on by (most cited first, 6 of 6)

- [Sentence Attention Blocks for Answer Grounding](https://mlsanity.com/paper/2309.11593/) (2023)
- [Empowering Visually Impaired Individuals: A Novel Use of Apple Live Photos and Android Motion Photos](https://mlsanity.com/paper/2309.08022/) (2023)
- [Improving Normalization with the James-Stein Estimator](https://mlsanity.com/paper/2312.00313/) (2023)
- [On the Effect of Image Resolution on Semantic Segmentation](https://mlsanity.com/paper/2402.05398/) (2024)
- [Multi-Scale Semantic Segmentation with Modified MBConv Blocks](https://mlsanity.com/paper/2402.04618/) (2024)
- [Early Fusion of Features for Semantic Segmentation](https://mlsanity.com/paper/2402.06091/) (2024)

## Abstract (arXiv)

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the derivative of the continuous dynamics of hidden state can be parameterized by an ODE. It has been shown that this type of neural network is able to produce the same results as an equivalent residual network for image classification. In this paper, we design a novel neural ODE for the semantic segmentation task. We start by a baseline network that consists of residual modules, then we use the modules to build our neural ODE network. We show that our neural ODE is able to achieve the state-of-the-art results using 57% less memory for training, 42% less memory for testing, and 68% less number of parameters. We evaluate our model on the Cityscapes, CamVid, LIP, and PASCAL-Context datasets.