A Two-Step Rule for Backpropagation

Year 2023, Volume: 6 Issue: 1, 57 - 69, 16.06.2023

Ahmed Boughammoura

https://doi.org/10.53508/ijiam.1265832

Cited By: 2

Abstract

We present a simplified computational rule for the back-propagation formulas for artificial neural networks. In this work, we provide a generic two-step rule for the back-propagation algorithm in matrix notation. Moreover, this rule incorporates both the forward and backward phases of the computations involved in the learning process. Specifically, this recursive computing rule permits the propagation of the changes to all synaptic weights in the network, layer by layer, efficiently. In particular, we use this rule to compute both the up and down partial derivatives of the cost function of all the connections feeding into the output layer.

Keywords

Artificial Neural Networks, Deep learning, Back-propagation, Feed-Forward

References

• Alber, M., Bello, I., Zoph, B., Kindermans, P. J., Ramachandran, P., & Le, Q. (2018). Backprop evolution. Preprint at https://arxiv.org/abs/1808.02822.
• Baldi, P. (2021). Deep learning in science. Cambridge University Press.
• Boughammoura, A. (2023). Backpropagation and F-adjoint. Preprint at https://arxiv.org/abs/2304.13820.
• Hojabr, R., Givaki, K., Pourahmadi, K., Nooralinejad, P., Khonsari, A., Rahmati, D., & Najafi, M. H. (2020, October). TaxoNN: A Light-Weight Accelerator for Deep Neural Network Training. In 2020 IEEE International Symposium on Circuits and Systems (ISCAS) (pp. 1-5). IEEE.
• McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5, 115-133.
• Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. nature, 323 (6088), 533-536.
• Schmidhuber, J. (2015). Deep learning in neural networks: An overview. Neural networks, 61, 85-117.
• Ye, J. C. (2022). Geometry of Deep Learning. Springer Singapore.