Multi-Layer Perceptron Including Glial Pulse andSwitching between Learning and Non-Learning†

Chihiro Ikuta† , Yoko Uwate† , Yoshifumi Nishio† , and Guoan Yang‡
Dept. of Electrical and Electronic Eng., Tokushima University, 2-1 Minami-Josanjima, Tokushima Japan
Email: {ikuta, uwate, nishio}@ee.tokushima-u.ac.jp
Dept. of Automation Science and Technology, School of Electronic and Information Eng.,
Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an City, Shaanxi Province, China
Email: gayang@mail.xjtu.deu.cn

Abstract— A glia is a nervous cell which is existing in abrain. This cell changes a Ca2+ concentration. This ion affects
a neuron membrane potential and it is propagated to theneighboring glia. Moreover, the Ca2; directly affects the humanmemory by increasing of a D-serine. From these functions, we
propose a Multi-Layer Perceptron (MLP) including glial pulse
and switching between a learning and non-learning. In thismethod, the neurons in the hidden-layer received the pulse fromconnected glias. The pulse is generated depending on the neuron
outputs and it is propagated to the neighboring glias and neurons.
Moreover, the neurons are separated to some groups. Each groupperiodically switches a learning term and a non-learning term.
Each group starts the learning term having a small lag each other.
We consider that a performance of the MLP improves by two
different methods influencing each other. By two simulations, we
confirm that the MLP obtains the high solving ability by using
our methods.

I. I NTRODUCTION
The functions of human brain are composed of nervous cells
which are a neuron and a glia. The neuron transmits signals
to other neurons by using an electrical stimulus. However,
the glia did not attract attention, because many researchersconsidered that the glial function is only a support of theneurons. Recently, some researchers discovered the novel glial
functions [1][2]. The glia uses various ions concentrations
which become a transporter of the signals [3][4]. We notice theCa2+ , because the Ca2+ transmits to a wide range in the brain
and relates closely to the neuron works. We have proposed
the several applications of the glial functions to Multi-Layer
Perceptron (MLP).
We know that Ca2+ to be generated by the glia affects
the state of the neighboring glias and the neuron membranepotential [5][6]. From this function, we proposed the MLP
with positive and negative pulse glial chain [7]. In this method,
the neurons in the hidden-layer receive the pulse from theconnected glia. This pulse affects neuron threshold and it
excites the neighboring glias. The excited glia also generates
the pulse, thus the pulse is propagated to the wide range. In the
MLP with positive and negative pulse glial chain, this network
can solve the tasks with a high nonlinearity, however the pulse
disrupts the solution convergence in easy tasks.
On the other hand, Takatas reported that a Ca2+ affects thesynaptic Long-Term Potentiation (LTP) by an experiment onliving animals [8]. In that research, they used two mice. One

978-1-4673-5762-3/13/$31.00 ©2013 IEEE

mouse has a normal glia. The other mouse has the geneticallymodified glia which cannot increase the Ca2+ concentration.
In the mouse with genetically-modified glia, the neuron could
not observe the LTP. In the normal mouse, the researchers
observed the LTP from the increase of the response. Moreover,the increase of the D-serine was observed in increasing theCa2+ concentration. The D-serine is an important ion for LTP.
Thereby, we can say that the glia relates closely to the LTPof the synapse. We considered that this experimental result
can be applied to an artificial neural network. We proposed
the MLP with the learning and non-learning terms [9]. In thismethod, the neurons in the hidden-layer are separated to somegroups and have the learning term and the non-learning term.
Two terms are periodically switched and the start times ofthe learning term are different in each group. On the other
hand, the MLP with learning and non-learning terms has abetter performance than the standard MLP in the easy anddifficult tasks. However, this method basically depends on
Back Propagation (BP) algorithm [10]. Thus, this MLP does
not have the superiority for the tasks with high nonlinearity.
In this study, we propose a Multi-Layer Perceptron (MLP)
including the glial pulse and switching between the learningand the non-learning. We combine two glial application models which have mutually different characteristics. When thepulse is input to the MLP, the amount of updates of weights are
increased. Thus the MLP can obtain the energy for escaping
out from the local minimum, however the learning becomes
unstable by this pulse. In the proposed MLP, only a part of
the weights is updated, because the weights are not updated
during the non-learning term. The learning and non-learningterms inhibit that the learning becomes unstable. We believethat the MLP obtains both characteristics by combining two
glial methods. By the simulations of two different tasks, we
confirm the performance of the proposed MLP.
II. P ROPOSED METHOD
The MLP is a famous feed forward neural network. It
is applied to an approximation of function, a classificationtask, a data mining, and so on. For the MLP learning, theBP algorithm is proposed by D.E. Rumelhart [10]. In thisalgorithm, updated weights are calculated for decreasing anerror from a partial differentiation of error of the MLP.

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However the solution of the MLP is often falls into a local
minimum. Because the BP algorithm uses the steepest decent
method. For this problem, we use a noise. We hope thatthe noise gives the energy for escaping out from the local
minimum. The noise is efficient to difficult tasks, becausea difficult task has many local minima. However, the noise
encumbers the learning when the MLP solves the easy task.
In this study, we propose the MLP including the glial pulse
and switching between the learning and non-learning which isinspired from the glial works in the brain. We give two glial
works to the MLP. The construction of the proposed MLP ispresented in Fig. 1.

⎛⎞𝑛∑𝑤𝑖𝑗 (𝑡)𝑥𝑗 (𝑡) − 𝜃𝑖 (𝑡)⎠ ,𝑦𝑖 (𝑡 + 1) = 𝑓 ⎝

(3)

𝑗=1

where 𝑦 is an output of the neuron, 𝑤 is a weight ofconnection, 𝑥 is an input of the neuron, and 𝜃 is a thresholdof neuron. Next, we show a proposed updating rule of theneuron. We add the glial effect to the threshold of neuron,
because the glial effect influences to the membrane potential
in the biological system. This updating rule is used to neurons
in the hidden layer. It is described by Eq. (4).
⎛⎞𝑛∑𝑤𝑖𝑗 (𝑡)𝑥𝑗 (𝑡) − 𝜃𝑖 (𝑡) + 𝛼𝜓𝑖 (𝑡)⎠ ,(4)𝑦𝑖 (𝑡 + 1) = 𝑓 ⎝𝑗=1

where 𝛼 is a weight of the glial effect. We can change the glial
effect by tuning 𝛼. In this equation, the weight of connection
and the threshold are changed by BP algorithm as same as thestandard updating rule of the neuron. However, the glial effectis not changed. It is updated by Eq. (1).

Pulse noise

NeuronSeparated group

Fig. 1.

Proposed MLP.

A. The method of pulse doping
We proposed the efficient method of doping pulse for the
MLP [7]. It is inspired from the biological glias. The pulse isgenerated depending on the neuron output. If the neuron has
a large output, the positive pulse is generated. If the neuron
has a small output, the negative pulse is generated. Moreover,the pulses are propagated to the neighboring neurons. We
confirmed that the pulses which have position relationships
improve the learning performance. The glia has two different
states which are the positive response and the negative response. We define the output function as the positive responseof the glia in Eq. (1).
𝜓𝑖 (𝑡 + 1) ={ 1, {(𝜃 < 𝑦 ∪ 𝜓𝑛𝑖𝛾𝜓𝑖 (𝑡), 𝑒𝑙𝑠𝑒,

𝑖+1,𝑖−1 (𝑡 − 𝑖 ∗ 𝐷) = 1)

∩ (𝜃𝑔 > ∣𝜓𝑖 (𝑡)∣)} ,(1)where 𝜓 is an output of a glia, 𝛾 is an attenuated parameter, 𝑦is an output of a connecting neuron, 𝜃𝑛 is a glia threshold of
excitation, 𝜃𝑔 is a period of inactivity, and 𝐷 is a delay timeof a glial effect. Moreover, we define the output function for
the negative response of the glia in Eq. (2).
𝜓𝑖 (𝑡 + 1) ={−1, {(1 − 𝜃𝑛 > 𝑦𝑖 ∪ 𝜓𝑖+1,𝑖−1 (𝑡 − 𝑖 ∗ 𝐷) = −1)∩ (𝜃𝑔 > ∣𝜓𝑖 (𝑡)∣)} (2)𝛾𝜓𝑖 (𝑡), 𝑒𝑙𝑠𝑒,
The neuron has multi-inputs and a single output. We canchange the neuron output by tuning of the weights of connections. The standard updating rule of the neuron is defined by
Eq. (3).

B. The method of the switching between learning term andthe non-learning term
The neurons in the hidden-layer are separated to somegroups. Each group has the learning term and the non-learning
term. Two terms are periodically changed. The weights ofconnections are tuned according to the standard BP algorithm.
However, the weights between the input-layer and the hiddenlayer are only updated during the learning term. Thus, during
the non-learning term, the MLP charges the error, because theother weights are changed. By this method, the MLP obtains abetter performance in easy and difficult tasks than the standard
MLP. This method is useful to some tasks, however, it cannot
escape out from the deep local minimum. Because this method
basically depends on the standard BP algorithm.
C. Time flow of the proposed method
We show the flow of the learning of the proposed MLP in
Fig. 2. The pulse is generated by the connected glia dependingon the neuron output. By this pulse, we believe that the MLP
escapes out from the local minimum. The generated pulse ispropagated to the neighboring neurons with the iterations. In
this example, one group is composed of two neurons. Everygroup has same time length of the learning term and the nonlearning term. The learning term and the non-learning term areperiodically changed. During the learning term, the neurons
are learned by BP algorithm. During the non-learning term, theweights of connections between the hidden-layer neuron andthe input-layer neurons are not updated. First group goes into
the learning term. Other groups sojourn to the non-learning
term. Second group goes into the learning term, then thefirst group remains the learning term. In the middle of thelearning term of the second group, the first group goes into
the non-learning term. After that, every group repeats changing
between the learning term and the non-learning term. During
the iterations, the MLP receives the pulse from the glias.
The pulse doping is switching between the learning and nonlearning terms have different characteristics. The pulse locally2108

gives a large energy to the MLP. When the pulse is input tothe MLP, the updated weights are increased. Thus the learning
becomes unstable by this pulse. By combining of two kinds ofmethods, only a part weights are updated, moreover the MLP
can obtain the energy from the pulse. In the proposed method,
the MLP receives the pulse and this pulse affects only a part ofweights. We consider that the MLP can search good solutionsin the wide range by including these methods.
Pulse

Group 1Delay

The number of neurons

Fig. 2.

Time flow of the learning term and non-learning term.

III. S IMULATIONS𝑃𝑀 𝑆𝐸 =1 ∑(𝑇𝑛 − 𝑂𝑛 )2 ,
𝑃 𝑛=1

(5)

where 𝑃 is the number of the pairs of the input and thesupervised value, 𝑇 is a supervised value, 𝑂 is an output of
the MLP.
A. Simulation results of learning logistic map
The logistic map is described by Eq. (6).
{}𝜒(𝑡 + 1) = 𝑎𝜒(𝑡) 1 − 𝜒(𝑡) ,(6)0.001390.001380.001370.00136

MSE

In this section, we show two simulation results. We give
two kinds of tasks to the MLP. Firstly, the MLP learns
the logistic map. This task shows the performance of thefunction approximation. The logistic map is described by
one-dimensional map, thus, we presume that it is easily
solved by the MLP. Secondly, the MLP computes the TwoSpiral Problem (TSP). This task has high nonlinearity. From
two simulations, we confirm the solving performance of the
proposed MLP. We compare the performance of the proposed
MLP to the standard MLP, MLP with positive and negative
pulse glial chain (previous 1), and MLP with learning andnon-learning terms (previous 2). In the MLP with positive
and negative pulse glial chain, the neurons in the hiddenlayer receive the pulses from connected glias. The MLP withlearning and non-learning terms has the learning term and thenon-learning term. For the index of the error, we use the Mean
Square Error (MSE) for both simulation results. The MSE is
described by Eq. (5).

where 𝑎 is control parameter of chaos. We use 𝑎 = 4, then,the logistic map generates fully-developed-chaos. The MLP
receives 𝜒(𝑡) as input and learns 𝜒(𝑡 + 1). In this simulation,
the neurons are arranged in 1-12-1 and the iterations are 10000
times. The simulation results are shown in Fig. 3. We show
three curves which are the proposed MLP, the standard MLP,
and the previous 1. In the proposed MLP (the noise amplitudeis zero), this MLP is same as the previous 2, because theinfluence of pulse is removed. We change the pulse amplitude
which is input to the neurons threshold of the hidden-layer.
From this result, the learning term and the non-learning term
are efficient to the MLP performance. Because the proposed
MLP is better than the standard MLP without reference tothe pulse amplitude. The previous 1 has the pulse in thethresholds of the hidden-layer neurons. In general, the noise
doping improves the performance because it give the energy
for escaping out from the local minimum. In the easy task,
the standard MLP is not trapped into the local minimum
and rapidly finds a good solution. The average error of theprevious method increases according to the increase of thepulse amplitude. We consider that the pulse disrupts the MLP
learning. Although the proposed MLP and the previous MLP
have the same generation mechanism of the pulse in thehidden-layer, the performances of the MLPs are different.
Moreover, the performance of the proposed MLP is the best of
all when the noise amplitude is 0.02. From this result, we cansay that the two glial effects improves the MLP performanceby the mutual influence.

0.001350.001340.00133
ProposedStandard
Previous 1

0.001320.001310Fig. 3.

0.04

0.08

0.12

0.16

Pulse amplitude (α)

0.2Results of the MLPs for learning the logistic map.

B. Simulation results of learning TSPThe TSP is a famous task for the artificial neural network[11]. It is a linearly-inseparable problem, thereby it has ahigh nonlinearity [12]. The MLP receives the coordinatesof the spirals for the inputs and learns the correspondingclassifications. In this simulation, we increase the numberof neurons in the hidden-layer. The MLP is composed of
the neurons (constructed 2-40-1). The iterations are 1000000
times. Figure 4 shows the two spirals for the MLP. In thisfigure, the spirals are composed of 130 points.
The simulation result is summarized in Table I. The average
error of the standard MLP is the worst of all. Because the TSP
has high nonlinearity, thus the standard MLP is trapped into

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1

1

0.8

Input 2

0.6

0.1

0.4

MSE

0.2
0
0

0.2

0.4

0.6

0.8

0.01

1

ProposedStandard
Previous 1
Previous 2

Input 1

Fig. 4.

Two-spiral Problem.
0.001
0the local minimum. The simulation result of the previous 2
is worse than the previous 1. The previous 2 has the learningterm and the non-learning term. During the non-learning term,
the weights are not updated, thus it affects the MLP learning.
However, it basically depends on the BP algorithm. This
network cannot escape out from the deep local minimum. The
previous 1 is better than the proposed MLP and the previous 2.
The pulse locally gives a large energy to the MLP. The pulse
helps the MLP for escaping out from the local minimum. In
the proposed MLP, the pulse and the learning and non-learningterms improves the learning performance. The pulse helps
MLP learning for escaping out from a deep local minimum.
Moreover, the non-learning term inhibits the learning curve
becoming oscillatory. Because the weights are not updated
during the non-learning term. The MLP has the large error
by the pulse, however only a part of weights is updated.
TABLE I

Fig. 5.

20000

40000

60000

Iterations (t)80000 100000

Learning curves of three MLPs.

the neurons in the hidden-layer have two different methods.
Firstly, these neurons receive the pulse to the thresholds.
Secondly, these neurons are separated to some groups. Eachgroup periodically switches the learning and non-learningterms. The neurons are only updated to the weights during
learning terms. By two kinds of simulations, we showed theperformance of the proposed MLP. From the results, we
confirm that two kinds of methods are efficient to the MLP
learning. Moreover, the MLP performance is improved by two
methods corresponding each other.
ACKNOWLEDGMENT
This work was partly supported by MEXT/JSPS Grant-inAid for JSPS Fellows (24⋅10018).

L EARNING PERFORMANCE .
ProposedStandard
Previous 1
Previous 2

Average0.00904
0.09604
0.01175
0.04830

Minimum
0.000270.000210.000110.00041

Maximum
0.046850.23087
0.054170.16941

R EFERENCES

Std. Dev.
0.01161
0.05751
0.013140.03763

Next, we show an example of learning curves during theiterations. The learning curve of the standard MLP is converged earlier than the others and this curve becomes smooth.
Because the solution of the MLP converges to the nearest
local optimum solution from the initial condition. The MLP
with learning and non-learning terms (previous 2) obtain abetter solution than the standard MLP. However, this orbit
is similar to the standard MLP. The oscillation of this curveis hardly observed. From this result, we can say that thelearning basically depends on the BP algorithm. The curves ofother two methods often oscillate during the iterations. We cansee that the error is rapidly decreased after oscillation of thelearning curve. From this behavior, the MLP is obtained theenergy from the doping pulse, thus the MLP can escape out
from the local minimum. In the proposed MLP, the learning
curve becomes step-like after 60000 times. We consider thatit happens by the influences both the pulse and the learningand non-learning terms. Because it has both characteristics oftwo previous method.
IV. C ONCLUSION
We have proposed the MLP including the glial pulse andswitching between learning and non-learning. In our method,[1] P.G. Haydon, “Glia: Listening and Talking to the Synapse,” Nature
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