A Proposal on Machine Learning via Dynamical Systems
Weinan E
Communications in Mathematics and Statistics ›› 2017, Vol. 5 ›› Issue (1) : 1 -11.
A Proposal on Machine Learning via Dynamical Systems
We discuss the idea of using continuous dynamical systems to model general high-dimensional nonlinear functions used in machine learning. We also discuss the connection with deep learning.
Deep learning / Machine learning / Dynamical systems
| [1] |
|
| [2] |
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction a, Springer Series in Statistics, second edition, (2013) |
| [3] |
|
| [4] |
Han, J., E, W.: in preparation |
| [5] |
Li, Q., Tai, C., E, W.: in preparation |
| [6] |
Almeida, L.B.: A learning rule for asynchronous perceptrons with feedback in a combinatorial environment. In: Proceedings ICNN 87. San Diego, IEEE (1987) |
| [7] |
LeCun, Y.: A theoretical framework for back propagation. In: Touretzky, D., Hinton, G., Sejnouski, T. (eds.) Proceedings of the 1988 connectionist models summer school, Carnegie-Mellon University, Morgan Kaufmann, (1989) |
| [8] |
Pineda, F.J.: Generalization of back propagation to recurrent and higher order neural networks. In: Proceedings of IEEE conference on neural information processing systems, Denver, November, IEEE (1987) |
| [9] |
Recht, B.: http://www.argmin.net/2016/05/18/mates-of-costate/ |
| [10] |
E, W., Ming, P.: Calculus of Variations and Differential Equations, lecture notes, to appear |
| [11] |
He, K., Zhang, X., Ren, S., Sun, J.: Identity mapping in deep residual networks. (July, 2016) arXiv:1603.05027v3 |
| [12] |
|
| [13] |
|
| [14] |
Wang, C., Li, Q., E, W., Chazelle, B.: Noisy Hegselmann–Krause systems: phase transition and the 2R-conjecture. In: Proceedings of 55th IEEE Conference on Decision and Control, Las Vegas, (2016) (Full paper at arXiv:1511.02975v3, 2015) |
| [15] |
|
/
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|
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