By Shinya Suzumura, Ryohei Nakano (auth.), Alessandro E. Villa, Włodzisław Duch, Péter Érdi, Francesco Masulli, Günther Palm (eds.)
The two-volume set LNCS 7552 + 7553 constitutes the court cases of the twenty second overseas convention on man made Neural Networks, ICANN 2012, held in Lausanne, Switzerland, in September 2012. The 162 papers incorporated within the complaints have been conscientiously reviewed and chosen from 247 submissions. they're geared up in topical sections named: theoretical neural computation; details and optimization; from neurons to neuromorphism; spiking dynamics; from unmarried neurons to networks; complicated firing styles; move and movement; from sensation to conception; item and face popularity; reinforcement studying; bayesian and echo nation networks; recurrent neural networks and reservoir computing; coding architectures; interacting with the mind; swarm intelligence and decision-making; mulitlayer perceptrons and kernel networks; education and studying; inference and popularity; aid vector machines; self-organizing maps and clustering; clustering, mining and exploratory research; bioinformatics; and time weries and forecasting.
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Extra resources for Artificial Neural Networks and Machine Learning – ICANN 2012: 22nd International Conference on Artificial Neural Networks, Lausanne, Switzerland, September 11-14, 2012, Proceedings, Part II
Consequently, the derivative term aﬀects the learning speed and the robustness to noise is clariﬁed. A Derivation of Order Parameter Equations The order parameter equations ((5) and (6)) are derived from learning equation (3). To obtain the deterministic diﬀerential equation for Q, we square both sides of (3) and then average the terms in the equation by using the distribution of P (x, y). Since Q has a self-averaging property, we get (Q(m+1) )2 = (Q(m) )2 + η2 2 2η δx + δ , N N (9) 16 K. Hara et al.
0 and we set B = 1, J 0 = 1, and ξ = N . In the simulation, N = 1000. The curves in the ﬁgures K. Hara et al. 05 0 Generalization error Generalization error 14 20 Generalization error Fig. 2. 05 T 0 5 10 15 20 Fig. 3. 0. 7. 5. 05 0 Generalization error Generalization error From analytical results, √ the eﬀect of the noise in the diﬀerential equation of Q2 increased from σ 2 / 3 to σ 2 by replacing from the derivative term g (x) to a constant a. (10) and (8)) This change in Q2 causes a larger generalization error.
Table 2 shows the experimental conditions. Figure 6 shows the learning process of the proposed method. We see again reducibility mapping (red circles) triggered error reduction nicely guiding the 8 S. Suzumura and R. Nakano search. Figure 7 shows true values of Bessel function Jα (x), while Fig. 8 shows output of complex-valued MLP learned by the proposed method. From Fig. 8 a small J(=3) gives rather poor fitting and poor extrapolation, while a large J(=7) gives unstable fitting. Excellent fitting and extrapolation was obtained for J=5.