Hardness results for neural network approximation problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1572, Issue , 1999, Pages 50-62

  Bartlett, Peter ^a   Ben David, Shai ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; LINEAR NETWORKS; NETWORK LAYERS;

HARDNESS RESULT; HIDDEN UNITS; NEURAL NETWORK APPROXIMATION; QUADRATIC LOSS; THRESHOLD NETWORKS; TRAINING EXAMPLE; TRAINING SETS; TWO-LAYER NETWORK;

MULTILAYER NEURAL NETWORKS;

EID: 84947735552     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-49097-3_5     Document Type: Conference Paper

References (19)

1. Sanjeev Arora, Laszlo Babai, Jacques Stern, and Z. Sweedyk. Hardness of approximate optima in lattices, codes, and linear systems. Journal of Computer and System Sciences, 54(2): 317-331, 1997.
2. Eric B. Baum. On learning a union of half-spaces. Journal of Complexity, 6: 67-101, 1990.
3. A. L. Blum and R. L. Rivest. Training a 3-node neural network is NP-complete. Neural Networks, 5(1): 117-127, 1992.
4. Bhaskar DasGupta, Hava T. Siegelmann, and Eduardo D. Sontag. On the complexity of training neural networks with continuous activation functions. IEEE Transactions on Neural Networks, 6(6): 1490-1504, 1995.
5. András Faragó and Gabor Lugosi. Strong universal consistency of neural network classifiers. IEEE Transactions on Information Theory, 39(4): 1146-1151, 1993.
6. O. Goldreich, S. Goldwasser, and S. Micali. How to construct random functions. Journal of the ACM, 33: 792-807, 1986.
7. D. Haussler. Decision theoretic generalizations of the PAC model for neural net and other learning applications. Inform. Comput., 100(1): 78-150, September 1992.
8. Klaus-U. Hoffgen, Hans-U. Simon, and Kevin S. Van Horn. Robust trainability of single neurons. J. of Comput. Syst. Sci., 50(1): 114-125, 1995.
9. David S. Johnson and F. P. Preparata. The densest hemisphere problem. Theoretical Computer Science, 6: 93-107, 1978.
10. Lee K. Jones. The computational intractability of training sigmoidal neural networks. IEEE Transactions on Information Theory, 43(1): 167-713, 1997.
11. J. S. Judd. Neural Network Design and the Complexity of Learning. MIT Press, 1990.
12. Viggo Kann, Sanjeev Khanna, Jens Lagergren, and Alessandro Panconesi. On the hardness of approximating max-k-cut and its dual. Technical Report CJTCS-1997-2, Chicago Journal of Theoretical Computer Science, 1997.
13. Michael Kearns and Leslie G. Valiant. Cryptographic limitations on learning Boolean formulae and finite automata. In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing, pages 433-444, 1989.
14. Wee Sun Lee, Peter L. Bartlett, and Robert C. Williamson. Efficient agnostic learning of neural networks with bounded fan-in. IEEE Transactions on Information Theory, 42(6): 2118-2132, 1996.
15. Carsten Lund and Mihalis Yannakakis. On the hardness of approximating minimization problems. Journal of the ACM, 41(5): 960-981, 1994.
16. Nimrod Megiddo. On the complexity of polyhedral separability. Discrete Computational Geometry, 3: 325-337, 1988.
17. C. H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. Journal of Computer and System Science, 43: 425-440, 1991.
18. Erez Petrank. The hardness of approximation: Gap location. Computational Complexity, 4(2): 133-157, 1994.
19. Van H. Vu. On the infeasibility of training neural networks with small squared errors. In Michael I. Jordan, Michael J. Kearns, and Sara A. Solla, editors, Advances in Neural Information Processing Systems, volume 10, pages 371-377. The MIT Press, 1998.