ABSTRACT
We describe an efficient algorithm for learning from examples a class of feedforward neural networks with real inputs and outputs in a real-value generalization of the Probably Approximately Correct (PAC) model. These networks can approximate an arbitrary function with an arbitrary precision. The learning algorithm can accommodate a fairly general worst-case noise model. The main improvement over previous work is that the running time of the algorithm grows only polynomially as the size of the target network increases (there is still an exponential dependence on the dimension of the input space, however). The main computational tool is an iterative “loading” algorithm which adds new hidden units to the hypothesis network sequentially. This avoids the difficult problem of optimizing the weights of all units simultaneously.
- 1.A. Barton. Universal approximation bounds for supperpositions of a sigmoidal function. IEEE ~ransactions on Information Theory, 39(3):930-945, May 1993.Google Scholar
- 2.C. Darken, M. Donahue, L. Ourvits, and E. Sontag. Rate of approximation results for neural network learning. Technical Report 93-07, Siemens Res. Corp., Princeton, NJ, 1993.Google Scholar
- 3.C. Darken, M. Donahue, L. Gurvits, and E. Sonta~. Rate of approximation results motivated by robust neural network learning. In Proc. Sizth Annual A CM Conference on Computational Learning Theory, 1993. Google ScholarDigital Library
- 4.H. Edelsbrunner, J. O'Rourke, and R. Seidel. Constructing arrangements of lines and hyperplanes with applications. SIAM Journal on Computing, 15(2):341- 363, May 1986. Google ScholarDigital Library
- 5.D. Haussler. Decision theoretic generalizations of the PAC model for neural nets and other lcarning applications. Information and Computation, (100):78-150, 1992. Google ScholarDigital Library
- 6.K. Hornik. Approximation capabilities of multilayer ~eedforward networks. Neural Networks, 4:251-257, 1991. Google ScholarDigital Library
- 7.M. Kearns and M. Li. Learning in the presence of malicious errors. SIAM Journal on Computing, 22(4):807- 873, August 1993. Google ScholarDigital Library
- 8.M. J. Kearns, 1%. E. Schapire, and L. M. Sellie. Toward efficient agnostic learning. In Proc. 5th A CM Workshop on Computational Learning Theory, pages 341- 352, 1992. Google ScholarDigital Library
- 9.W. Maass. Agnostic PAC-learning of functions on analog neural nets. In Proc. 7th Annual IEEE Conference on Neural Information Processing Systems, 1993.Google Scholar
- 10.W. Maass. Bounds for the computational power and learning complexity of analog neural nets. In Proc. 25th STOC, pages 335-344, 1993. Google ScholarDigital Library
- 11.D. Pollard. Convergence of Stochastic Processes. Springcr Verlag, 1984.Google ScholarCross Ref
- 12.A. Schrljver. Theory of Linear and Integer Programming. Wiley, New-York, 1986. Google ScholarDigital Library
- 13.L. G. Valiant. Learning disjunctions of conjuntlons. In Proc. 9th International Joint Conference on Artificial Intelligence, pages 560-566, 1985.Google Scholar
Index Terms
- Efficient learning of continuous neural networks
Recommendations
Efficient learning algorithms yield circuit lower bounds
We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circuit class C in Angluin's model of exact learning from membership and ...
Deep learning in neural networks
In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarizes relevant work, much of it from the previous millennium. ...
Comments