Learning polynomials with neural networks

31st International Conference on Machine Learning, ICML 2014

Volumn 5, Issue , 2014, Pages 3955-3963

  Andoni, Alexandr ^a   Panigrahy, Rina ^a   Valiant, Gregory ^b   Zhang, Li ^a  

^a MICROSOFT RESEARCH   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPLEX NETWORKS; LEARNING SYSTEMS; POLYNOMIALS; RANDOM PROCESSES;

GRADIENT DESCENT; GRADIENT DESCENT ALGORITHMS; GRADIENT DESCENT METHOD; LEARNING NEURAL NETWORKS; RANDOM PERTURBATIONS; SPARSE POLYNOMIALS; SUITABLE CONDITIONS; THEORETICAL GUARANTEES;

NETWORK LAYERS;

EID: 84919789307     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. Alekhnovich, Michael. More on average case vs approximation complexity. In Proceedings of the Symposium on Foundations of Computer Science (FOCS), 2003.
2. Andoni, Alexandr, Panigrahy, Rina, Valiant, Gregory, and Zhang, Li. Learning sparse polynomial functions. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 2014.
3. Applebaum, Benny, Ishai, Yuval, and Kushilevitz, Eyal. Cryptography in ncTj. SIAM Journal on Computing, 36 (4):845-888, 2006.
4. Applebaum, Benny, Barak, Boaz, and Wigderson, Avi. Public-key cryptosystem from different assumptions. In Proceedings of the Symposium on Theory of Computing (STOC), 2010.
5. Barron, Andrew R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory, 39(3):930-945, 1993.
6. Barron, Andrew R. Approximation and estimation bounds for artificial neural networks. Machine Learning, 14: 115-133, 1994.
7. Bengio, Y. Learning deep architectures for ai. Foundations and Trends in Machine Learning, 2009.
8. Bengio, Y., Lamblin, P., Popovici, D., and Larochelle, H. Greedy layer-wise training of deep networks. In NIPS, 2007.
9. Bengio, Yoshua. Deep learning of representations: Looking forward. arXiv preprint arXiv:1305.0445, 2013.
10. Goodfellow, I. J., Warde-Farley, D., Mirza, M., Courville, A., and Bengio, Y. Maxout networks. In ICML, 2013.
11. Hinton, G. E., Osinderoand, S., and Teh, Y. A fast learning algorithm for deep belief nets. Neural Computation, 18: 1527-1554, 2006.
12. Krizhevsky, A., Sutskever, I., and Hinton, G. E. Imagenet classification with deep convolutional neural networks. In NIPS, 2012.
13. Peikert, Chris. Public-key cryptosystems from the worst-case shortest vector problem. In Proceedings of the Symposium on Theory of Computing (STOC), 2009.
14. Ranzato, M., Poultney, C, Chopra, S., and LeCun, Y. Efficient learning of sparse representations with an energy-based model. NIPS, 2006.
15. Regev, Oded. On lattices, learning with errors, random linear codes, and cryptography. In STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, pp. 84-93, New York, NY, USA, 2005. ACM. ISBN 1-58113-960-8. doi: http: //doi.acm.org/10.1145/1060590.1060603.
16. Saxe, Andrew M, McClelland, James L, and Ganguli, Surya. Dynamics of learning in deep linear neural networks. NIPS Workshop on Deep Learning, 2013.
17. Wan, Li, Zeiler, Matthew, Zhang, Sixin, LeCun, Yann, and Fergus, Rob. Regularization of neural networks using dropconnect. In ICML, 2013.