Aussie AI

Morphological Networks

  • Book Excerpt from "Generative AI in C++"
  • by David Spuler, Ph.D.

Morphological Networks

Another type of neural network that uses max operations is called the “morphological network”. This uses maximum, addition, and subtraction operations.

Research papers on morphological networks:

  1. Zamora, E., Sossa, H., 2017, Dendrite morphological neurons trained by stochastic gradient descent. Neurocomputing 260, 420–431 (2017), https://ieeexplore.ieee.org/document/7849933
  2. G. Ritter and P. Sussner, 1996, An introduction to morphological neural networks, Proceedings of 13th International Conference on Pattern Recognition (ICPR), vol. 4, pp. 709–717 vol.4, 1996, https://ieeexplore.ieee.org/abstract/document/547657 (Earliest multiplication-free neural network? Uses add and max.)
  3. Limonova E, Matveev D, Nikolaev D, Arlazarov VV., 2019, Bipolar morphological neural networks: convolution without multiplication, In: Twelfth International Conference on Machine Vision (ICMV 2019), 2020, vol. 11433, p. 11433, International Society for Optics and Photonics, https://arxiv.org/abs/1911.01971
  4. Elena Limonova, Daniil Alfonso, Dmitry Nikolaev, Vladimir V. Arlazarov, 2021, ResNet-like Architecture with Low Hardware Requirements, https://arxiv.org/pdf/2009.07190 (Algorithm based on max and addition.)
  5. G. X. Ritter, L. Iancu, and G. Urcid, 2003, Morphological perceptrons with dendritic structure, in The 12th IEEE International Conference on Fuzzy Systems (FUZZ), 2003. FUZZ ’03., vol. 2, May 2003, pp. 1296–1301 vol.2, https://ieeexplore.ieee.org/document/1206618 (Dendritic structure algorithm based on “lattice algebra”.)
  6. Mondal R, Santra S, Mukherjee S, Chanda B., 2019, Morphological Network: How Far Can We Go with Morphological Neurons?, arXiv:1901.00109 http://arxiv.org/abs/1901.00109 (Examines the theory of maximum of a sum, called “dilation”, and minimum of differences, called “erosion”, in neural networks.)
  7. Pessoa, L.F., Maragos, P., 2000, Neural networks with hybrid morphological/rank/linear nodes: a unifying framework with applications to handwritten character recognition, Pattern Recognition 33(6), 945–960 (2000), https://www.sciencedirect.com/science/article/abs/pii/S0031320399001570 (Various neurons including min-max methods.)
  8. Goodfellow, I.J., Warde-Farley, D., Mirza, M., Courville, A., Bengio, Y., 2013, Maxout networks, arXiv preprint arXiv:1302.4389 (2013), https://arxiv.org/abs/1302.4389 (Paper on “dropout” using maximum function.)
  9. Charisopoulos, V., Maragos, P., 2017, Morphological perceptrons: geometry and training algorithms, In: International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing. pp. 3–15 (2017), https://link.springer.com/chapter/10.1007/978-3-319-57240-6_1
  10. Wilson, S.S., 1989, Morphological networks, In: Visual Communications and Image Processing IV. vol. 1199, pp. 483–496 (1989) https://www.spie.org/Publications/Proceedings/Paper/10.1117/12.970058?SSO=1
  11. Davidson, J.L., Ritter, G.X., 1990, Theory of morphological neural networks, In: Digital Optical Computing II. vol. 1215, pp. 378–389 (1990), https://www.semanticscholar.org/paper/Theory-of-morphological-neural-networks-Davidson-Ritter/3d459fb68b8f1dc66e239d2404afb6702950a246
  12. Ranjan Mondal, Sanchayan Santra, Soumendu Sundar Mukherjee, Bhabatosh Chanda, Dec 2022, Morphological Network: How Far Can We Go with Morphological Neurons?, https://arxiv.org/abs/1901.00109
  13. Mondal, R., Santra, S., Chanda, B., 2019, Dense morphological network: An universal function approximator, arXiv preprint arXiv:1901.00109 (2019), https://arxiv.org/abs/1901.00109v1, PDF: https://arxiv.org/pdf/1901.00109v2.pdf
  14. Peter Sussner; Estevao Laureano Esmi, 2009, An introduction to morphological perceptrons with competitive learning, 2009 International Joint Conference on Neural Networks https://ieeexplore.ieee.org/document/5178860

For more research papers on morphological neural networks, see https://www.aussieai.com/research/zero-multiplication#morph.

 

• Next:

• Up: Table of Contents

• Buy: Generative AI in C++: Coding Transformers and LLMs

Generative AI in C++ The new AI programming book by Aussie AI co-founders:
  • AI coding in C++
  • Transformer engine speedups
  • LLM models
  • Phone and desktop AI
  • Code examples
  • Research citations

Get your copy from Amazon: Generative AI in C++