2006 年

A-2-15電子情報通信学会総合大会

Learning Ability of Evolving Aﬀordable Neural Networks with
Genetic Algorithm for Back Propagation Learning
Yoko Uwate(Tokushima University)
1.

Introduction

In our previous research, we have proposed a new network
structure with aﬀordable neurons in hidden layer of the feedforward neural network. We named this proposed network“Aﬀordable Neural Network” [1]. We consider that the operation of the aﬀordable neural network is especially eﬀective
on evolution of neural network in brain.
In this study, we investigate the performance of the affordable neural network when the hidden layer is evolved
using GA. By computer simulations, we consider that theaﬀordable neurons exert an important inﬂuence on evolution
process in the hidden layer of the network.

Yoshifumi Nishio(Tokushima University)
the optimal solution by increasing the number of generations.
However, the network without GA can not escape from local
minima. We can see that the network with the aﬀordable
neurons gains good performance by applying GA as shownin Fig. 1(a). On the other hand, the network without theaﬀordable neurons does not work well by applying GA asshown in Fig. 1(b). From these results, we conﬁrm that theaﬀordable neurons exert an important inﬂuence on evolution
process in the hidden layer of the network.
0.9
Affordable NN with GA

0.8

Affordable NN without GA

0.7
Error for learning data

2. Evolving Aﬀordable Neural Network
We have proposed the network structure with aﬀordable
neurons in the hidden layer of the feedforward neural network for more eﬃcient BP learning [1]. We introduced theaﬀordable neurons to reﬂect a function of the brain. The
extra neurons in the hidden layer are prepared in advance.
During the BP learning, all of the neurons in the hidden layer
are not used at every updating. Namely, some of the neurons
are selected for the learning and the rest of the neurons aredeactivated.
Correspondence between GA and hidden layer is shown in
Tab. 1.

0.5
0.4
0.3
0.2
0.1
0050

100
Generations

150200(a) Aﬀordable neural network.
0.9
Conventional NN with GA

0.8

Conventional NN without GA

Error for learning data

0.7

Tab. 1: Correspondence relationship GA and hidden
layer of neural network.
GAindividual
population
chromosome
ﬁtness

0.6hidden layer of neural network
network structure of hidden layer
population of networks
weights of neurons in hidden layer
error for learning data

0.6
0.5
0.4
0.3
0.2
0.1
0050

100
Generations

150200(b) Conventional neural network.

Fig. 1: Error between output of neural network and4. Simulated Results
In this study, we use the batch BP learning algorithm. We
consider the feedfoward neural network producing the samechaotic time series as the inputted chaotic time series generated by a skew tent map as one learning example. Thelearning time of one generation is set to 10 and the generation number is set to 100. Hence, the network with GA learn
the learning data 1000 times. For comparison, we investigate
the performance of the network without GA. We prepare 20
neurons in the hidden layer and the number of the aﬀordable
neurons is set to 6. Furthermore, we investigate the performance of conventional network without aﬀordable neurons
to make clear the learning ability of the aﬀordable neuralnetwork. Figure 1 shows the simulation result for the casethat mutation probability is set to 0.01. From this ﬁgure, theerror of the aﬀordable neural network with GA converges toteach data.
5. Conclusions
In this study, we investigated the performance of aﬀordable neural network when the hidden layer is evolved using
GA. We applied this aﬀordable neural network with GA tolearning chaotic time series generated by skew tent map. By
computer simulation, we conﬁrmed that the aﬀordable neurons exert an important inﬂuence on evolution process in thehidden layer of the network.

References[1] Y. Uwate and Y. Nishio, “Back Propagation Learningof Neural Networks with Chaotically-Selected Aﬀordable
Neurons,” IEEE International Symposium on Circuits andSystems (ISCAS’05), pp. 1481-1484, May 2005.

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