2014 International Symposium on Nonlinear Theory and its Applications
NOLTA2014, Luzern, Switzerland, September 14-18, 2014

Neuro-Glia Network with Neurogenesis
Chihiro Ikuta, Yoko Uwate, and Yoshifumi NIshio†Department of Electrical and Electronics Engineering, Tokushima University
2-1, Minami-Josanjima, Tokushima, Japan
Email: {ikuta, uwate, nishio}@ee.tokushima-u.ac.jp
Abstract— In this study, we propose a neuro-glia network with neurogenesis based on a Multi-Layer Perceptron (MLP) with pulse glial chain based on individual inactivity period. This network has a connection between aglia and a neuron in a hidden-layer. The glia generates apulse and this pulse is propagated to the neurons and theneighboring glias. The pulse generation cycle is dynamically changed by the neuron output. By a frequency of thepulse generation, the glia chooses an important neuron andan unimportant neuron. In the neurogenesis, the unimportant neuron is removed and a newborn neuron is connectedin the same position as the removed neuron. We consider
that the pulse of the glia gives an energy for escaping out
from a local minimum, moreover the number of contributory neurons for the network performance increase by theneurogenesis. We confirm that the proposed MLP has abetter performance than the previous MLP and show characteristics of the proposed MLP.
1. Introduction
Brain is composed of two kinds of nerve cells which
are a glia and a neuron. The neuron has been investigatedabout biological characteristics and applications for manyyears. The neurons connect with other neurons and transmit electric signals each other. On the other hand, the glia
was considered to the supporting cell for the neuron. Actually, the glia exists between the neurons and a blood vessel
and provides necessary nutrients which are carried into theblood vessel to the neurons. Recently, some researchersreported that the glia controls an ion concentration [1]-[3].
The glia uses various kinds of ions such as a glutamate acid,an adenosine triphosphate, a Ca2+ , and so on [4]. Amongthem, we focus on the Ca2+ . The concentration of the Ca2+
increases by the excited glia and the increasing of the concentration of the Ca2+ excites the neighboring glias. Thechange of the concentration of the Ca2+ triggers a chain reaction. Moreover, the glia transmits signals to other glias
by the concentration of the Ca2+ .
In the previous study, we proposed the Multi-Layer Perceptron (MLP) with pulse glial chain based on individual
inactivity period which is inspired from the biological characteristics of the glia [5]. We one-by-one connect the glias
with the neurons in the hidden-layer. The glia generates
the pulse when the neuron output is larger than the threshold of the excitation of the glia. The generated pulse istransmitted to the connecting neuron and the neighboring
glias. The neighboring glias are excited by the transmitted
pulse and generate the pulse, thus the pulse is transmitted
into the glial network. In the previous MLP, a period of inactivity (interval of the pulse generation) becomes shorter
according to the connecting neuron output. Thereby, thepulse generation becomes diﬀerent pattern in each glia.
This change of the pattern in each glia gives variety forthe learning of the MLP and improves the learning performance. Moreover, we check the number of pulse generations in each glia during the iterations, thereby importantneurons for the network performance are connected withthe glias which generate many pulses.
In this study, we propose the neuro-glia network withneurogenesis which is extended from the MLP with pulse
glial chain based on individual inactivity period. The glia
can find the important neurons and the unimportant neurons by the pulse generation. In this network, the unimportant neurons in the hidden-layer are removed and thenewborn neurons are connected in the same position, then
the weight of connections defines at random (we call thisprocess ‘neurogenesis’). By the neurogenesis, we considerthat the number of contributory neurons for the network
performance increase. We confirm that the performance ofthe proposed MLP improves than the previous MLP, moreover we show the characteristics of the proposed MLP by
the computer simulations.
2. Proposed MLP
The MLP is one of feed forward neural networks. This
network can be applied to various nonlinear tasks. The output of the MLP is decided by the weight of connection between the neurons. In general, the weight of connection istuned by a Back Propagation (BP) algorithm [6]. The BPalgorithm is useful for the learning of the MLP, however
this algorithm often falls into a local minimum.
In the proposed MLP, we connect the glias with the neurons shown as Fig. 1. The glia is excited by the output of
the connecting neuron. Then, the glia generates the pulse.
This pulse is input to the connecting neuron threshold andis transmitted to the neighboring glias. The neighboringglias are excited by the transmitted pulse and also generate
the pulse. Thereby, the pulse is transmitted into the glialnetwork. Moreover, the period of inactivity of the glia becomes shorter when the glia is excited in continuity. By- 508 -Glia
Newborn
neuronNeuronGenerationpulse

Figure 1: Proposed MLP.

2.1. Updating rule of neuron
The neuron has multi-input and single output. The standard updating rule of the neuron is defined by Eq. (1).
 n∑(1)yi (t + 1) = f  wi j (t)x j (t) − θi (t) ,2.2. Glial pulse
The glia has a response to the output of the connecting
neuron. The glia response is described by Eq. 4.
ψi (t + 1) = 1, {(θ < y ∪ ψnii+1,i−1 (t − i ∗ D) = 1)
∩ (τi ≥ θgi )},γψi (t), else,

where ψ is an output of a glia, i is a position of the glia, θn isa glia threshold of excitation, y is an output of a connected
neuron, D is a delay time of a glial eﬀect, τ is local time of
the glia during a period of inactivity, θg is a length of theperiod of inactivity, γ is an attenuated parameter. When theoutput of the connecting neuron is larger than the excitationthreshold of the glia, the glia generates pulse. Then, theoutput of the glia ψ has 1. After that the pulse decreases inan exponential fashion. The pulse excites the neighboring
glia which has a delay of the iteration D.
In the previous study, we proposed the glia which dynamically changes the period of inactivity according to theoutput of the connecting neuron. If the glia continuouslyreceives the large output from the connecting neuron, theperiod of inactivity (θg ) of this glia becomes shorter. Eachglia has diﬀerent period of inactivity, thereby the glial network obtains the various pulse generation pattern. Thechange of the period of inactivity and the pulse generation
are shown in Fig. 2.
10.5

j=100200

400

600

800

1000200400600

800

1000t
(a) Pulse generation (varied period of inactivity).

1ψb(t)

where y is an output of the neuron, w is a weight of connection, x is an input of the neuron, and θ is a threshold ofneuron. In this equation, the weight of connection and thethreshold of the neuron are learned by BP algorithm. Thus,
the neuron output is depended on the BP learning. Next, weshow a proposed updating rule of the neuron. We add theglial pulse to the threshold of neuron. We use this updating
rule to the neurons in the hidden layer. It is described byEq. (2).
 n∑(2)yi (t + 1) = f  wi j (t)x j (t) − θi (t) + αψi (t) ,(4)ψa(t)

this process, each glia has a diﬀerent pulse generation cycle. In the proposed MLP, we introduce the neurogenesis
into the neurons in the hidden-layer. The neurogenesis happens at a regular iteration. The removed neuron is chosen
by the number of pulse generations of the connected glia. If
the number of the pulse generation of the connected glia issmaller than the decided value, the connecting neurons areremoved and newborn neurons are connected in the sameposition. The weight of connection of the newborn neuron
is decided at random.

0.500t(b) Pulse generation (periodic).

Figure 2: Varying period of inactivity. (a) The frequencyof the pulse generation. (b) Periodic pulse generation.

j=1

where α is a weight of the glial eﬀect. We can change theglial eﬀect by change of α. In this equation, the weightof connection and the threshold are changed by BP algorithm. The glial is independent from BP algorithm, thus
the weight of the glial eﬀect is not changed by BP algorithm. Equations (1) and (2) uses a sigmoidal function for
an activating function which is described by Eq. (3).
f (a) =
where a is an inner state.

1
1 + e−a(3)2.3. Neurogenesis
The neurogenesis happens into the adult human brain,
moreover some researchers reported that the connecting
position of the newborn neuron is decided by the glia [7].
In the proposed model (shown as Fig. 3), we introduce theneurogenesis to the neurons in the hidden-layer. We countthe number of excitations of the glia. If the number of excitations of the glia is smaller than the constant value, theneuron is removed and the newborn neuron is connected- 509 -

in the same position. We give the random value to every
weight of connection of the newborn neuron.

Figure 3: Neurogenesis.

3. Simulation

3.1. Learning performance
We obtain the result from 100 trials, and one trial has
100000 iterations. In every trial, we give diﬀerent initialcondition. In this simulation, the neurogenesis happens
at 50000 iterations. Then, if the number of pulse generations is small, the neuron is removed and we set a newborn
neuron. From the simulation result, we obtain four kindsof evaluation indexes which are average, minimum, maximum, and standard deviation. Firstly, we show a learning
performance when the MLP learns the 98 spiral points. Thesimulation result is shown in Table 1. From this result, thestandard MLP is the worst of all in the average. This MLP
often falls into a local minimum. Actually, the maximumof the error is the highest of all. The proposed MLP has abetter performance than the previous MLP in the average,
the minimum, and the standard deviation.
Table 1: Learning performance of spiral of 98 points.
Average Minimum Maximum Std. Dev.
(1) 0.03443
0.000070.18375
0.02422(2) 0.00340
0.00005
0.041020.00845(3) 0.00188
0.000150.03071
0.00517

In this study, we use a Two-spiral Problem (TSP) for thesimulation task shown as Fig. 4. The TSP is a famous task
for the artificial neural network and has a high nonlinearity[8] [9]. The MLP learns the classification of the spirals.

Next, we show the result when the MLP learns 130 spiralpoints in Table 2. The result trend is similar to the previoussimulation. The proposed MLP has a better performance
than the others.
Table 2: Learning performance of spiral of 130 points.
Average Minimum Maximum Std. Dev.
(1) 0.09604
0.000270.23087
0.05751(2) 0.00904
0.00037
0.046850.01161(3) 0.00827
0.00087
0.04633
0.00975

Figure 4: Two-Spiral Problem.
In this simulation, we compare the three kinds of theMLPs which are;3.2. Learning curve(1) The standard MLP.
(2) The MLP with pulse glial chain based on individual
period of inactivity.
(3) The neuro-glial network with neurogenesis.
The standard MLP does not have an external unit, thus this
MLP often falls into a local minimum. The MLP with pulse
glial chain based on the individual period of inactivity is
the previous model which was proposed in WCCI’14. We
use a Mean Square Error (MSE) for the evaluation of theperformance. The MSE is described by Eq. (5).

We show an example of the learning curve of the proposed MLP and the previous MLP in Fig. 5. In the proposed MLP, the neurogenesis happens at 50000 iterations.
Both learning curves have the same orbit until 50000 iterations. The learning curve of the previous MLP converges.
The learning curve of the proposed MLP is also converges
at 50000 iterations. However, the error decreases from50000 iterations. We consider that the unimportant neurons are removed by the neurogenesis, thereby the important neurons increase and the MLP learning performance
improves.
3.3. Importance of neurons

N1 ∑(T n − On )2 ,MS E =N n=1(5)

where T is a supervised signal and O is a output value ofthe neuron in the output-layer.

In this simulation, we confirm the importance of the neurons in the hidden-layer for the network performance. We
remove one neuron in the hidden-layer of the learned MLP
and obtain the error between the true value and the output. By this simulation, we can obtain contribution ratio of- 510 -1rons in the hidden-layer. The glia generates the pulse according to the output of the connecting neurons. The pulse
is transmitted to the neighboring glias and the thresholdof the connecting neuron. The period of inactivity of theglia becomes shorter when the glia continually receives thelarge output of the connecting neuron. We check the frequency of the pulse generation. When the frequency of thepulse generation is lower than the decided value, this neuron is deleted and the newborn neuron is connected in thesame position. By the computer simulation, we confirmedthat the proposed MLP obtains the better performance thanthe previous MLP, moreover, the number of the importantneurons increase by the neurogenesis.

Proposed MLP

MSE

0.1

Previous MLP

0.01

0.001

0.0001050000100000Iteration

Figure 5: Learning curves.

Frequency ofpulse generationeach neuron for the MLP performance. The result is shownin Fig. 6. (a) shows the frequency of the pulse generationin each neuron to the total iterations. (b) and (c) show theerror value for each removed neuron position when we remove one neuron in the hidden-layer. When the error of
the output is high, this neuron has high contribution for theMLP performance. Thus, this neuron is the important neuron. We can see that the number of pulse generations correlate to the importance of the neuron. In the previous MLP,
half of neurons become the unimportant neuron. On theother hand, some neurons become important neuron in theproposed MLP. We can say that unimportant neurons arechosen and are renewed to newborn neuron, thereby someneurons becomes to the important neuron.

Acknowledgments
This work was partly supported by MEXT/JSPS Grantin-Aid for JSPS Fellows (24·10018).
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MSE

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40MSE

0.60.4(c)0.200102030

40

Position of neurons

Figure 6: Contribution ratio of each neuron in the hiddenlayer. (a) Frequency of the pulse generation. (b) Contribution ration of each neuron in the previous MLP. (c) Frequency of the pulse generation. (b) Contribution ration ofeach neuron in the proposed MLP.

4. Conclusions
In this study, we have proposed the neuro-glia networkwith the neurogenesis which is inspired from the characteristics of the biological glia. We connect the glias to the neu-

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