IEEE Workshop on Nonlinear Circuit Networks
December 11-12, 2015

Artificial Neuron-Glia Network Including Random
Glia Pulse Generation
Chihiro Ikuta1,2 , Yoko Uwate1 and Yoshifumi Nishio1
1

Dept. of Electrical and Electronic Eng., Tokushima University
2-1 Minami-Josanjima, Tokushima Japan
Email: {ikuta, uwate, nishio} @ee.tokushima-u.ac.jp
2
Course of Electrical Engineering, Dept. of Creative Technology Eng.,National Institute of Technology, Anan College,
265, Aoki, Minobayashi, Anan, Tokushima, Japan
Email: ikuta@anan-nct.ac.jp
Abstract—A human brain is composed of two kinds of cells
which are a neuron and a glia. These cells correlate each otherand compose a higher brain functions. In this study, we propose
an artificial neuron-glia network including including oscillatory
glia excitation threshold. This network based on a multilayer
perceptron and glias are connected with neurons in a hidden
layer. The glia is excited by the output of connected neuron. Then,the glia generates a pulse, and this pulse transmits to neighboring
glias and the connected neuron. In this model, we introduce a
randomly oscillation to a glia excitation threshold. This oscillation
gives a probabilistic glia excitation in near the glia excitationthreshold. We consider that the probabilistic glia excitation isefficiency to a network learning. By computer simulation, we
confirm that the proposed model has better performance thanthe conventional models.

I.

the glia can change between a generation and a stopping
generation of the pulse by the randomly oscillation of glia
excitation threshold. By the change of the pulse generation,
the pulse propagation is also changed. We consider that therandomly oscillation of excitation threshold gives more energy
to the network. We confirm that the glia improves the network
learning performance by using Two-Spiral Problem (TSP).
II.

P ROPOSED N ETWORKA proposed network based on a multilayer perceptron. Theneurons make layers and have connections with the neurons
in the neighboring layers. The proposed network has the glias
in the hidden layer shown as Fig. 1.

I NTRODUCTION

In this study, we propose an artificial neuron-glia network
including random glia pulse generation which is based onrelationships between the neuron and the glia. The glia isconnected with the neurons in the hidden layer and is excitedby the output of the connecting neuron. The excited glia
generates a pulse. This pulse transmits to other glia andneurons in the hidden layer. When the glia receives the pulse,
the glia is also excited. In the case of the neuron, the pulse
increases the neuron threshold. In this model, we introduce
the randomly oscillation to the glia excitation threshold. The
excitation threshold oscillates within defined value during alearning. When the learning of the network converges, theoutput of the neuron is fixity. Thereby, the pattern of theglia pulse generation is also fixed. In the proposed model,

Neuron…

A human brain has many functions. For a long time, thesefunctions are only composed of neurons. Recently, some researches reported that a glia also related to the brain functions[1][3]. These works confirmed the glia transmits signals toneurons and glias by using an ion concentration. Moreover,the glia has many receptors to ions such as glutamate acid,adenosine triphosphate, calcium [4][6]. Among them, we focus
on the calcium ion. The glia transmits a signal by using thechange of calcium ion concentration [7][8]. This change ofion concentration also influences a membrane potential of theneuron. Thus, the glia closely relates to the neurons and makes
the brain works. We consider that the glia function can apply
to an artificial neural network.

Glia

Fig. 1.

Proposed network.

A. Random Glia Pulse Generation
The glias are one-by-one connected with the neurons in thehidden-layer. In this model, the glias and the neurons correlate
each other. The glia receives the connecting neuron output
and is excited by the connecting neuron output. The excitation
conditions of the glia are described by Eq, (1).
ψi (t + 1) =
1,{θn (t) < yi ∪ ψi+1 (t − D) = 1∪ ψi−1 (t − D) = 1)} ∩ (t − τi > θg ),, (1)
 −1, {1 − θn (t) > yi ∪ ψi+1 (t − D) = 1∪ ψi−1 (t − D) = 1)} ∩ (t − τi > θg )γψi (t), else,
where ψ is an output of a glia, i is a position number ofthe glia in the hidden-layer, γ is an attenuation parameter- 27 -(0 < γ < 1), y is an output of a connecting neuron, θn isa glia excitation threshold, τ is a time of a previous pulse
generation, θg is a period of inactivity, and D is a delay timeof a glial effect When the connecting neuron output is larger
than the glia excitation threshold (θn (t)), the glia is excited andgenerates the positive pulse. And also, when the connecting
neuron output is smaller than 1 − θn (t) of the glia, the glia isexcited and generates the negative pulse. The generated pulse
transmits to the neighboring glias and the connecting neuron.
The pulse excites the neighboring glias and increases the innerstate of the connecting neuron. The neighboring glias also
generate the pulse, thereby the pulse transmits to all glias.
When the glia generates the pulse, the glia starts the periodof inactivity. If this glia receives the neuron output and/or theneighboring glial pulse, the glia cannot be excited again during
period of inactivity.
In this study, we introduce the randomly oscillation of glia
excitation threshold to the pulse glial chain. The randomly
oscillation is described by Eq. (2).
θn (t) = r(t) (a < r < b),(2)where r is random function, and a and b is constant value. The
value of the excitation threshold oscillates between a and b.
We use Mersenne Twister pseudo-random number [9] for therandom function. Figure 2 shows example of the relationships
between the randomly oscillation of glia excitation threshold
and the output of the neurons. We consider three cases ofthe output of the neuron in the simulation. The output of theneuron (A) does not reach the glia excitation threshold, thereby
the connected glia is not excited by this neuron. The output ofthe neuron (B) is into the amplitude of the randomly oscillationof glia excitation threshold when the output of this neuron isconverged. In this case, the connected glia with neuron (B)is stochastically excited. The output of the neuron (C) completely overcomes the randomly oscillation of glia excitationthreshold when the output of this neuron is converged. Theconnected glia with the neuron (C) is excited independent fromthe randomly oscillation of glia excitation threshold. In theproposed method, several glias are stochastically excited by therandomly oscillation of glia excitation threshold. We consider
that the randomly oscillation of glia excitation threshold breaks
the periodic pulse generation of the glias, thereby the glias caneffectively give the energy to the network.

between the neurons. The standard updating rule of the neuron
is defined as shown in Eq. (3).
n∑yi (t + 1) = f wij (t)xj (t) − θi (t) ,(3)j=1where y is an output of the neuron, w is a weight of theconnection, x is an input of the neuron, and θ is an excitationthreshold of the neuron. In this equation, the weight of theconnection and the threshold of the neuron are learned basedon the BP algorithm. Next, we show the proposed updating
rule of the neuron. We add the generated pulse of the glia ψto the excitation threshold of the neuron. In this study, thisupdating rule is only used for the neurons in the hidden-layer.
The updating rule is described by Eq. (4).
n∑yi (t + 1) = f wij (t)xj (t) − θi (t) + αψi (t) ,(4)j=1where α is a weight of the glial effect. A peek of the generated
pulse is changed according to α. We choose an optimal valueof α for solving a task by a heuristic search. The generated
pulse is independent from the learning of the network, thus thispulse can gives an energy to the network and helps for escaping
out from the local minimum. The weight of the connection
and the excitation threshold of the neuron are learned by backpropagation algorithm (BP) [10]. On the other hand, the glial
pulse does not learn by the BP; thus the glia gives the energy
to the network when the network falls into local minimum.
ψ is updated by Eq. (1). Equations (3) and (4) are used as asigmoidal function to an activating function of neuron and isdescribed by Eq. (5).
1,
1 + e−awhere a is an inner state of the neuron.
f (a) =III.

(1)
(2)
(3)
(4)
(5)

0.8

0.6

0.2

Excitation threshold of the glia
Output of neuron (A)Output of neuron (B)Output of neuron (C)0t

Fig. 2. Relationships between randomly oscillation of glia excitation threshold
and the output of the neurons.

B. Updating rule of neuron
The neuron has multi-input and single-output, and we canchange the neuron output by tuning the weights of connections

S IMULATION

We use five kinds of the networks for comparison of theperformance.

10.4

(5)

The standard MLP
The MLP with random noise
The MLP with random timing pulses
The MLP with pulse glial chainThe neuron-glia network including random glia pulse
generation

The standard MLP (1) does not have the external unit, thus
this MLP often falls into the local minimum. The MLP
with random noise (2) has a uniformed random noise in theexcitation threshold of the neurons in the hidden-layer. TheMLP with random timing pulses (3) has a pulse oscillationin the excitation threshold of the neurons in the hidden-layer,
and this pulse is generated at random. The MLP with pulse
glial chain (4) has a glial pulse in the excitation threshold of
the neurons in the hidden-layer. In this model, the excitationthreshold of glia is constant value. The pulse generation pattern
becomes periodic when the output of the neuron is convergedby the learning. The neuron-glia network including random
glia pulse generation (5) is the proposed network. We use a- 28 -

Two-Spiral Problem (TSP) for a task of the networks. TheTSP is a famous task for the artificial neural network and has
a high nonlinearity [11][12]. In this task, the network learns
the classification of two dimensions coordinates of two spirals.
The learning spiral points is shown in Fig. 3.
10.8

neuron output. This pulse transmits to the neighboring glias
and the neurons. In the proposed model, the glia has therandomly oscillation in the excitation threshold. The pulse
generation becomes randomly toward the end of learning by
the randomly oscillation of glia excitation threshold. The random pulse generation is efficiency to the network learning. We
confirmed that the proposed MLP has the better performance
than the conventional MLPs.

y0.6
00.4

R EFERENCES10.2

000.2

0.4

0.6

0.8

1xFig. 3.

Target points.

We obtain the experimental results from 100 trials about
each MLP. In each trial, we give the different initial weightsof connections. The MLP has 50000 iterations during one trial
and learns 130 data sets of spiral points. We use the threelayers MLP, and the number of neurons in each layer is 2-401. We use Mean Square Error (MSE) for the error function.
The MSE is described by Eq. (6).
1 ∑(Tn − On )2 ,N n=1NM SE =(6)where N is the number of learning datum, T is a target value,
and O is an output of MLP.
We show the accuracy of the classification to the learning
data set. The learning performance of networks is shown inTable I. The standard MLP (1) is the worst of all in theaverage error, the minimum error and the maximum error. We
can say that the standard MLP (1) falls into local minimum.
The MLP with random noise (2) and the MLP with randomtiming pulse (3) reduce the error than the standard MLP (1),however these methods do not have a large difference fromthe standard MLP (1). On the other hand, the MLP with pulse
glial chain (4) and the proposed network (5) decrease the error
more than others. The maximum error of proposed network issmaller than the MLP with pulse glial chain (4). In the caseof the MLP with pulse glial chain (4), the pulse generation
pattern becomes periodically toward the end of learning. The
randomly oscillation of glia excitation threshold changes thepulse generation pattern toward the end of learning; thus thepulse gives the more energy to the network
TABLE I.
(1)
(2)
(3)
(4)
(5)

Average
0.12269
0.108470.114390.019900.01436

IV.

[1] P.G. Haydon, “Glia: Listening and Talking to the Synapse,” Nature
Reviews Neuroscience, vol.2, pp.844-847, 2001.
[2] R.D. Fields, B. Stevens-Graham, “New Insights into Neuron-Glia Communication,” Science, vol.298, pp.556-562, 2002.
[3] G.I Hatton, V. Parpura, “Glia Neuronal Signaling,” 2004, Kluwer
Academic Publishers.
[4] S. Koizumi, M. Tsuda, Y. Shigemoto-Nogami and K. Inoue, “DynamicInhibition of Excitatory Synaptic Transmission by Astrocyte-Derived
ATP in Hippocampal Cultures,” Proc. National Academy of Science ofU.S.A, vol.100, pp.11023-11028, Mar. 2003.
[5] S. Ozawa, “Role of Glutamate Transporters in Excitatory Synapses inCerebellar Purkinje Cells,” Brain and Nerve, vol.59, pp.669-676, 2007.
[6] G. Perea and A. Araque, “Glial Calcium Signaling and Neuro-GliaCommunication,” Cell Calcium, vol.38, pp.375-382, 2005.
[7] S. Kriegler and S.Y. Chiu, “Calcium Signaling of Glial Cells along
Mammalian Axons,” The Journal of Neuroscience, vol.13, pp.42294245, 1993.
[8] M.P. Mattoson and S.L. Chan, “Neuronal and Glial Calcium Signalingin Alzheimer’s Disease,” Cell Calcium, vol.34, pp.385-397, 2003.
[9] M. Matsumoto and T. Nishimura, “Mersenne twister: a 623dimensionally equidistributed uniform pseudo-random number generator,” ACM Transactions on Modeling and Computer Simulation, vol.8(1), pp.3-30, 1998.
[10] D.E. Rumelhart, G.E. Hinton and R.J. Williams, “Learning Representations by Back-Propagating Errors,” Nature, vol.323-9, pp.533-536,
1986.
[11] J.R. Alvarez-Sanchez, “Injecting Knowledge into the Solution of theTwo-Spiral Problem,” Neural Computing & Applications, vol.8, pp.265272, 1999.
[12] H. Sasaki, T. Shiraishi and S. Morishita, “High Precision Learning
for Neural Networks by Dynamic Modification of Their Network
Structure,” Dynamics & Design Conference, pp.411-1–411-6, 2004.

L EARNING PERFORMANCE .
Minimum
0.008310.00047
0.007400.000670.00069

Maximum
0.23857
0.24278
0.26349
0.116640.08139

Std. Dev.
0.055540.057420.057420.02226
0.01688

C ONCLUSION

In this study, we have proposed the artificial neuron-glia
network including random glia pulse generation. The glias
are one-by-one connected with the neurons in the hiddenlayer. The glia generates the pulse according to the connecting- 29 -