Integrating Mathematical Modeling and Neurobiological Principles in GAN Architectures
Keywords:
Neural Networks, Generative Adversarial Networks, Neurobiological In- spiration, Mathematical Optimization, Artificial Intelligence, Machine Learning, Deep LearningAbstract
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
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
How to Cite
Issue
Section
License

This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
Terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.