# Learning Deep Morphological Networks with Neural Architecture Search

arXiv: https://arxiv.org/abs/2106.07714 · HTML: https://mlsanity.com/paper/2106.07714/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 89 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 30 of 44)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [PC-DARTS: Partial Channel Connections for Memory-Efficient Architecture Search](https://mlsanity.com/paper/1907.05737/) (2019)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Richer Convolutional Features for Edge Detection](https://mlsanity.com/paper/1612.02103/) (2016)
- [A Survey on Evolutionary Neural Architecture Search](https://mlsanity.com/paper/2008.10937/) (2020)
- [A Survey on Neural Architecture Search](https://mlsanity.com/paper/1905.01392/) (2019)
- [DeepEdge: A Multi-Scale Bifurcated Deep Network for Top-Down Contour Detection](https://mlsanity.com/paper/1412.1123/) (2014)
- [Few-shot Neural Architecture Search](https://mlsanity.com/paper/2006.06863/) (2020)
- [CMA-ES for Hyperparameter Optimization of Deep Neural Networks](https://mlsanity.com/paper/1604.07269/) (2016)

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

- [An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks](https://mlsanity.com/paper/2310.04584/) (2023)
- [Training Deep Morphological Neural Networks as Universal Approximators](https://mlsanity.com/paper/2505.09710/) (2025)
- [The Lattice Overparametrization Paradigm for the Machine Learning of Lattice Operators](https://mlsanity.com/paper/2310.06639/) (2023)
- [Single Domain Generalization for Alzheimer's Detection from 3D MRIs with Pseudo-Morphological Augmentations and Contrastive Learning](https://mlsanity.com/paper/2505.22465/) (2025)
- [NAS-BNN: Neural Architecture Search for Binary Neural Networks](https://mlsanity.com/paper/2408.15484/) (2024)
- [Morphological Perceptron with Competitive Layer: Training Using Convex-Concave Procedure](https://mlsanity.com/paper/2509.05697/) (2025)

## Abstract (arXiv)

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of non-linear operators are derivations of activation functions or pooling functions. Mathematical morphology is a branch of mathematics that provides non-linear operators for a variety of image processing problems. We investigate the utility of integrating these operations in an end-to-end deep learning framework in this paper. DNNs are designed to acquire a realistic representation for a particular job. Morphological operators give topological descriptors that convey salient information about the shapes of objects depicted in images. We propose a method based on meta-learning to incorporate morphological operators into DNNs. The learned architecture demonstrates how our novel morphological operations significantly increase DNN performance on various tasks, including picture classification and edge detection.