Combining the Perceptron Algorithm with Logarithmic Simulated Annealing

作者: A. Albrecht , C. K. Wong

DOI: 10.1023/A:1011369322571

关键词: Configuration spaceApplied mathematicsAdaptive simulated annealingArtificial neural networkEstimation theorySimulated annealingMaxima and minimaMathematicsLogarithmAlgorithmPerceptron

摘要: We present results of computational experiments with an extension the Perceptron algorithm by a special type simulated annealing. The annealing procedure employs logarithmic cooling schedule c(k)eΓ/ln(k+2), where Γ is parameter that depends on underlying configuration space. For sample sets S n-dimensional vectors generated randomly chosen polynomials w1·x1a1+···+wn·xnangt, we try to approximate positive and negative examples linear threshold functions. approximations are computed both classical our schedules. ne256,…, 1024 aie3,…, 7, outperforms about 15% when size sufficiently large. was according estimations maximum escape depth from local minima associated energy landscape.

参考文章(22)
Marvin L. Minsky, Seymour A. Papert, Perceptrons: expanded edition MIT Press. ,(1988)
Avrim L. Blum, Ronald L. Rivest, Original Contribution: Training a 3-node neural network is NP-complete Neural Networks. ,vol. 5, pp. 117- 127 ,(1992) , 10.1016/S0893-6080(05)80010-3
Andreas Albrecht, Chak-Kuen Wong, On Logarithmic Simulated Annealing ifip international conference on theoretical computer science. pp. 301- 314 ,(2000) , 10.1007/3-540-44929-9_23
A. Albrecht, S.K. Cheung, K.S. Leung, C.K. Wong, Stochastic Simulations of Two-Dimensional Composite Packings Journal of Computational Physics. ,vol. 136, pp. 559- 579 ,(1997) , 10.1006/JCPH.1997.5781
Fabio Romeo, Alberto Sangiovanni-Vincentelli, A theoretical framework for simulated annealing Algorithmica. ,vol. 6, pp. 302- 345 ,(1991) , 10.1007/BF01759049
Klaus-Uwe Höffgen, Hans Ulrich Simon, Robust trainability of single neurons conference on learning theory. pp. 428- 439 ,(1992) , 10.1145/130385.130431
Eric B. Baum, The Perceptron Algorithm Is Fast for Non-Malicious Distributions neural information processing systems. ,vol. 2, pp. 676- 685 ,(1989) , 10.1162/NECO.1990.2.2.248