Integrating Mathematical Modeling and Neurobiological Principles in GAN Architectures

Authors

  • Dipans Verma
  • Sunil Dhaneshwar
  • Sandeep Kulkarni
  • Bharti V. Nathwani
  • Dibyendu Sekhar Mandal
  • Abhijeet Mukund Shinde

Keywords:

Neural Networks, Generative Adversarial Networks, Neurobiological In- spiration, Mathematical Optimization, Artificial Intelligence, Machine Learning, Deep Learning

Abstract

Neural networks (NNs) and generative adversarial networks (GANs) are pivotal in advancing artificial intelligence (AI), enabling breakthroughs in image synthesis, natural language processing, and speech generation. Grounded in mathematical optimization and inspired by neurobiological learning mechanisms, these models integrate rigorous computational frameworks with brain-inspired principles. This paper explores how mathematical optimization and neurobiological insights enhance GAN performance, focusing on efficiency, robustness, and generalization. By bridging theoretical rigor with practical applications, we underscore the potential of biologi- cally inspired architectures to develop adaptive and powerful AI systems.

Downloads

Download data is not yet available.

References

L F Abbott and S B Nelson. Synaptic plasticity: taming the beast. Nature Neuroscience, 3:1178–1183, 2000.

Martin Arjovsky, Soumith Chintala, and Le´ on Bottou. Wasserstein generative ad- versarial networks. International Conference on Machine Learning, pages 214–223, 2017.

Christopher M Bishop. Pattern Recognition and Machine Learning. Springer, 2006. Explains mathematical foundations of neural networks, probability, and optimiza- tion.

Tung-Fu Che, Tsung-Hsiang Yang, Chung-Yi Cheng, Hongyang Liu, and Kuang-Hsiung Hsieh. Mode regularized generative adversarial networks. In International Confer- ence on Machine Learning (ICML), pages 1104–1112, 2016.

Finale Doshi-Velez and Been Kim. Towards a rigorous science of interpretable machine learning. arXiv preprint arXiv:1702.08608, 2017.

Artur S Garcez, Luis C Lamb, and Dov M Gabbay. Neuro-symbolic artificial intelli- gence: The 3rd wave. arXiv preprint arXiv:1905.06088, 2019.

Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT Press, 2016. Comprehensive introduction to deep learning, including neural networks and GANs.

Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. Advances in Neural Information Processing Systems, 27:2672– 2680, 2014. Original paper introducing GANs.

Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville. Improved training of wasserstein gans. Advances in Neural Information Processing Systems, 30, 2017.

Michael E. Hasselmo. Neural models of memory and cognition: Cognitive and computational perspectives. MIT Press, 2005.

Simon Haykin. Neural Networks: A Comprehensive Foundation. Prentice Hall, New Jersey, 2003.

Donald O. Hebb. The organization of behavior: A neuropsychological theory. Psy- chology Press, 1949.

Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in Neural Information Processing Systems, 30, 2017.

Eugene M. Izhikevich. Dynamical systems in neuroscience: The geometry of ex- citability and bursting. MIT Press, 2007.

Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. In European Conference on Computer Vision (ECCV), pages 694–711, 2016.

Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. A style-based generator architecture for generative adversarial networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(5):862–874, 2019.

Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. Introduces the Adam optimizer.

Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. Technical Report TR-2009, University of Toronto, 2009

Downloads

Published

2025-05-20

How to Cite

1.
Verma D, Dhaneshwar S, Kulkarni S, V. Nathwani B, Sekhar Mandal D, Shinde AM. Integrating Mathematical Modeling and Neurobiological Principles in GAN Architectures. J Neonatal Surg [Internet]. 2025May20 [cited 2025Sep.24];14(7):710-9. Available from: https://www.jneonatalsurg.com/index.php/jns/article/view/6170

Similar Articles

You may also start an advanced similarity search for this article.